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+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 1: Background to Numerical Methods"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.10: Conversion_to_Binary_System_and_to_Base_N.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.10\n",
+"//Conversion to Binary System and to Base N\n",
+"//Page no. 9\n",
+"clc;close;clear;\n",
+"\n",
+"b=dec2bin(oct2dec('1753'))\n",
+"disp(b,'Binary form of 1753 is =');    //inbuilt function\n",
+"b=dec2hex(oct2dec('1753'))\n",
+"disp(b,'Hexadecimal form of 1753 is =');    //inbuilt function\n",
+"//conversion from octal to binary\n",
+"b=dec2bin(hex2dec('A478'))\n",
+"disp(b,'Binary form of A478 is =');    //inbuilt function\n",
+"b=dec2oct(hex2dec('A478'))\n",
+"disp(b,'Octal form of A478 is =');    //inbuilt function\n",
+"//conversion from octal to binary\n",
+"s=dec2bin(oct2dec('3'));\n",
+"s1=dec2bin(oct2dec('154'));    //inbuilt function\n",
+"printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)\n",
+"s=dec2hex(oct2dec('3'));\n",
+"s1=dec2hex(oct2dec('154'));    //inbuilt function\n",
+"printf('\n\n Hexadecimal form of 3.154 is = \n\n %s.%s',s,s1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.13: 1s_compliment_and_2s_compliment.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.13\n",
+"//1s compliment and 2s compliment\n",
+"//Page no. 11\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=com1(x)      //function for 1s compliment\n",
+"    for i=8:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        if(floor((xd*10)+0.1)==1)\n",
+"            x1(1,i)=0;\n",
+"        else\n",
+"            x1(1,i)=1;\n",
+"        end\n",
+"        x=x-xd;\n",
+"    end\n",
+"endfunction\n",
+"function [x1]=com2(x)         //function for 2s compliment()\n",
+"    for i=8:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        if(int((xd*10)+0.1)==1)\n",
+"            x1(1,i)=0;\n",
+"        else\n",
+"            x1(1,i)=1;\n",
+"        end\n",
+"    end\n",
+"    for i=8:-1:1\n",
+"        if (x1(1,i)==0) then\n",
+"           x1(1,i)=1;\n",
+"           break;\n",
+"        else\n",
+"           x1(1,i)=0;\n",
+"        end\n",
+"        \n",
+"    end\n",
+"endfunction\n",
+"a=[00010011,01110110,11101101,10000001,10000000,00000000];\n",
+"for i=1:6\n",
+"    printf('1s Compliment of %.8i=',a(i));\n",
+"    disp(com1(a(i)))\n",
+"    printf('2s Compliment of %.8i=',a(i));\n",
+"    disp(com2(a(i)))\n",
+"    printf('\n\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.14: 1s_compliment.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.14\n",
+"//1s compliment\n",
+"//Page no. 12\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=com1(x)      //function for 1s compliment\n",
+"    for i=8:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        if(floor((xd*10)+0.1)==1)\n",
+"            x1(1,i)=0;\n",
+"        else\n",
+"            x1(1,i)=1;\n",
+"        end\n",
+"        x=x-xd;\n",
+"    end\n",
+"endfunction\n",
+"a=[00010011,01110110,11101101,10000001,10000000,00000000];\n",
+"for i=1:6\n",
+"    printf('1s Compliment of %.8i=',a(i));\n",
+"    disp(com1(a(i)))\n",
+"    printf('\n\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.15: Addition_and_Subtraction.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.15\n",
+"//Addition and Subtraction\n",
+"//Page no. 13\n",
+"clc;clear;close;\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    for i=1:10\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=10:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=0;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    disp(x1,'Addition of 173 and 141= ')\n",
+"endfunction\n",
+"function [x1]=sub(x,y)           //function for subtraction of binaries\n",
+"        c=0;\n",
+"        for i=1:10\n",
+"            x1(1,i)=0\n",
+"        end\n",
+"        for i=10:-1:1\n",
+"            x=x/10;\n",
+"            xd=x-fix(x)\n",
+"            x=x-xd;\n",
+"            y=y/10;\n",
+"            yd=y-fix(y)\n",
+"            y=y-yd;\n",
+"            if c==1 then\n",
+"                if floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==1 then\n",
+"                    x1(1,i)=0;c=1;\n",
+"                elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                    x1(1,i)=1;c=0;\n",
+"                elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1\n",
+"                    x1(1,i)=1;c=1;\n",
+"                elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==0\n",
+"                    x1(1,i)=0;c=0;\n",
+"                end\n",
+"            else\n",
+"                if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                    x1(1,i)=1;c=1;\n",
+"                elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                    x1(1,i)=0;c=0;\n",
+"                elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==0\n",
+"                    x1(1,i)=1;c=0;\n",
+"                elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==1\n",
+"                    x1(1,i)=1;c=1;\n",
+"                end\n",
+"            end\n",
+"        end\n",
+"    disp(x1,'Subtraction of 45 from 228= ')\n",
+"endfunction\n",
+"add(10101101,10001101)\n",
+"sub(11100100,00101101)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.16: Additio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.16\n",
+"//Addition\n",
+"//Page no. 14\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    printf('Addition of %.4i and %.4i= ',x,y)\n",
+"    for i=1:4\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=4:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=1;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    \n",
+"    disp(x1)\n",
+"endfunction\n",
+"add(0010,0101);\n",
+"add(1110,1011);\n",
+"add(1110,0101);\n",
+"add(0010,1011);\n",
+"add(1110,0010);\n",
+"add(0000,0000);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.17: Additio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.17\n",
+"//Addition\n",
+"//Page no. 14\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    printf('Addition of %.4i and %.4i= ',x,y)\n",
+"    for i=1:5\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=5:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=1;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    \n",
+"    disp(x1)\n",
+"endfunction\n",
+"\n",
+"add(0010,0101);\n",
+"add(1101,1010);\n",
+"add(1101,0101);\n",
+"add(0010,1010);\n",
+"add(1101,0010);\n",
+"add(1111,0000);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.18: Additio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.18\n",
+"//Addition\n",
+"//Page no. 15\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    printf('Addition of %.4i and %.4i= ',x,y)\n",
+"    for i=1:5\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=5:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=1;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    \n",
+"    disp(x1)\n",
+"endfunction\n",
+"\n",
+"add(0100,0101);\n",
+"add(1100,1011);\n",
+"add(1000,1000);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.19: Additio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.19\n",
+"//Addition\n",
+"//Page no. 15\n",
+"clc;close;clear;\n",
+"\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    printf('Addition of %.4i and %.4i= ',x,y)\n",
+"    for i=1:5\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=5:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=1;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    \n",
+"    disp(x1)\n",
+"endfunction\n",
+"\n",
+"add(0010,0101);\n",
+"add(11110,11011);\n",
+"add(1000,0101);\n",
+"add(00010,11011);\n",
+"add(11110,00010);\n",
+"add(11111,0000);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.1: Conversion_to_Decimal_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.1\n",
+"//Conversion to Decimal System\n",
+"//Page no. 4\n",
+"clc;close;clear;\n",
+"function [s]=bas2dec(x,b)\n",
+"    xi=int(x)\n",
+"    xd=x-int(x)\n",
+"    s=0\n",
+"    for i=1:10\n",
+"        xi=xi/10\n",
+"        s=s+(10*(xi-fix(xi))*b^(i-1))\n",
+"        xi=int(xi)\n",
+"        if(xi==0)\n",
+"            break\n",
+"        end\n",
+"    end\n",
+"    for i=1:1\n",
+"        xd=xd*10;\n",
+"        s=s+(ceil(xd)/b^(i))\n",
+"        xd=xd-fix(xd)\n",
+"        if(xd==0)\n",
+"            break\n",
+"        end\n",
+"    end\n",
+"endfunction\n",
+"\n",
+"//conversion from hexadecimal to decimal system\n",
+"disp(hex2dec('1A2C'),'1A2C=');     //inbuit function\n",
+"\n",
+"//conversion from hexadecimal to decimal system\n",
+"disp(bas2dec(428.5,8),'428.5=')   //inline function\n",
+"\n",
+"//conversion from hexadecimal to decimal system\n",
+"disp(bas2dec(120.1,3),'120.1=')     //inline function"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.20: Subtractio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.20\n",
+"//Subtraction\n",
+"//Page no. 16\n",
+"clc;close;clear;\n",
+"function [x1]=add(x,y)                  //function for addition of binaries\n",
+"    c=0;\n",
+"    for i=1:5\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    for i=5:-1:1\n",
+"        x=x/10;\n",
+"        xd=x-fix(x)\n",
+"        x=x-xd;\n",
+"        y=y/10;\n",
+"        yd=y-fix(y)\n",
+"        y=y-yd;\n",
+"        if c==1 then\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=1;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=1;c=0;\n",
+"            else\n",
+"                x1(1,i)=0;c=0;\n",
+"            end\n",
+"        else\n",
+"            if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then\n",
+"                x1(1,i)=0;c=1;\n",
+"            elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0\n",
+"                x1(1,i)=0;c=0;\n",
+"            else\n",
+"                x1(1,i)=1;c=0;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    disp(x1,'Addition of 173 and 141= ')\n",
+"endfunction\n",
+"\n",
+"add(0100,1011);\n",
+"add(1100,0101);\n",
+"add(1000,1000);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.23: Multiplicatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.23\n",
+"//Multiplication\n",
+"//Page no. 18\n",
+"clc;clear;close;\n",
+"\n",
+"function [x1]=mul(x,y)\n",
+"    for i=1:8\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    printf('Multiplication of %.4i and %.4i = ',x,y)\n",
+"    x=x*y;\n",
+"    c=0;\n",
+"    for i=8:-1:1\n",
+"        x=x/10;\n",
+"        xd=floor((x-fix(x))*10+0.1)\n",
+"        if c==1 then\n",
+"            if xd==0 then\n",
+"                x1(1,i)=1;c=0\n",
+"            elseif xd==1\n",
+"                x1(1,i)=0;\n",
+"                c=1;\n",
+"            elseif xd==2\n",
+"                x1(1,i)=1;c=1;\n",
+"            end\n",
+"        else\n",
+"            if xd==0 | xd==1 then\n",
+"                x1(1,i)=xd;c=0\n",
+"            elseif xd==2\n",
+"                x1(1,i)=0;\n",
+"                i=i-1;c=1;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    disp(x1)\n",
+"endfunction\n",
+"mul(1110,1011);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.24: Multiplicatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.24\n",
+"//Multiplication\n",
+"//Page no. 18\n",
+"clc;clear;close;\n",
+"\n",
+"function [x1]=mul(x,y)\n",
+"    for i=1:8\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    printf('Multiplication of %.4i and %.4i = ',x,y)\n",
+"    x=x*y;\n",
+"    c=0;\n",
+"    for i=8:-1:1\n",
+"        x=x/10;\n",
+"        xd=floor((x-fix(x))*10+0.1)\n",
+"        if c==1 then\n",
+"            if xd==0 then\n",
+"                x1(1,i)=1;c=0\n",
+"            elseif xd==1\n",
+"                x1(1,i)=0;\n",
+"                c=1;\n",
+"            elseif xd==2\n",
+"                x1(1,i)=1;c=1;\n",
+"            end\n",
+"        else\n",
+"            if xd==0 | xd==1 then\n",
+"                x1(1,i)=xd;c=0\n",
+"            elseif xd==2\n",
+"                x1(1,i)=0;\n",
+"                i=i-1;c=1;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    disp(x1)\n",
+"endfunction\n",
+"mul(1110,1011);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.25: Divisio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.25\n",
+"//Division\n",
+"//Page no. 19\n",
+"clc;close;clear;\n",
+"function [co]=com(x,y)\n",
+"    co=1;\n",
+"    for i=1:length(x)\n",
+"        if x(i)>y(i) then\n",
+"            break\n",
+"        elseif x(i)==y(i)\n",
+"            continue\n",
+"        else\n",
+"            co=0;break\n",
+"        end\n",
+"    end\n",
+"endfunction\n",
+"function [x1]=sub(x,y)           //function for subtraction of binaries\n",
+"        c=0;m=0;\n",
+"        for i=1:5\n",
+"            x1(1,i)=0\n",
+"        end\n",
+"        for i=5:-1:1\n",
+"            if c==1 then\n",
+"                if x(i)==0 & y(i)==1 then\n",
+"                    x1(1,i)=0;c=1;\n",
+"                elseif x(i)==0 & y(i)==0\n",
+"                    x1(1,i)=1;c=0;\n",
+"                elseif x(i)==1 & y(i)==1\n",
+"                    x1(1,i)=1;c=1;\n",
+"                elseif x(i)==1 & y(i)==0\n",
+"                    x1(1,i)=0;c=0;\n",
+"                end\n",
+"            else\n",
+"                if x(i)==1 & y(i)==1 then\n",
+"                    x1(1,i)=0;c=0;\n",
+"                elseif x(i)==0 & y(i)==0\n",
+"                    x1(1,i)=0;c=0;\n",
+"                elseif x(i)==1 & y(i)==0\n",
+"                    x1(1,i)=1;c=0;\n",
+"                elseif x(i)==0 & y(i)==1\n",
+"                    x1(1,i)=1;c=1;\n",
+"                end\n",
+"            end\n",
+"        end\n",
+"    disp(x1,'Remainder = ')\n",
+"endfunction\n",
+"d1=11011001;d2=01011;d22=[0,0,0,0,0]\n",
+"for i=8:-1:1\n",
+"    d3=d1/10;\n",
+"    div(1,i)=int(10*(d3-int(d3)))\n",
+"    d1=d1/10\n",
+"end\n",
+"for i=5:-1:1\n",
+"    d3=d2/10;\n",
+"    d21(1,i)=int(10*(d3-int(d3))+0.5)\n",
+"    d2=d2/10\n",
+"end\n",
+"div1(1,1)=0\n",
+"for j=1:4\n",
+"    div1(1,j+1)=div(1,j)\n",
+"end\n",
+"for i1=1:5\n",
+"    printf('After Step %i : \n',i1)\n",
+"    if com(div1,d21)==1 then\n",
+"        dis(1,i1)=1\n",
+"        n=sub(div1,d21)\n",
+"    else\n",
+"        dis(1,i1)=0\n",
+"        n=sub(div1,d22)\n",
+"end\n",
+"disp(dis,'Divisor = ')\n",
+"if i1==5 then\n",
+"    break\n",
+"end\n",
+"       for j=1:5\n",
+"                if j<5 then\n",
+"                    div1(1,j)=n(j+1)\n",
+"                else\n",
+"                    div1(1,j)=div(1,i1+4)\n",
+"                end\n",
+"        end\n",
+"\n",
+"printf('\n\n\n\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.26: Multiplicatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.26\n",
+"//Multiplication\n",
+"//Page no. 19\n",
+"clc;clear;close;\n",
+"\n",
+"\n",
+"function [x1]=mul(x,y)\n",
+"    for i=1:8\n",
+"        x1(1,i)=0\n",
+"    end\n",
+"    printf('Multiplication of %.4i and %.4i = ',x,y)\n",
+"    x=x*y;\n",
+"    c=0;\n",
+"    for i=10:-1:1\n",
+"        x=x/10;\n",
+"        xd=floor((x-fix(x))*10+0.1)\n",
+"        if c==1 then\n",
+"            if xd==0 then\n",
+"                x1(1,i)=1;c=0\n",
+"            elseif xd==1\n",
+"                x1(1,i)=0;\n",
+"                c=1;\n",
+"            elseif xd==2\n",
+"                x1(1,i)=1;c=1;\n",
+"            end\n",
+"        else\n",
+"            if xd==0 | xd==1 then\n",
+"                x1(1,i)=xd;c=0\n",
+"            elseif xd==2\n",
+"                x1(1,i)=0;\n",
+"                i=i-1;c=1;\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    for i=1:10\n",
+"        if x1(1,i)==1 then\n",
+"            x1(1,i-1)=1;\n",
+"            break\n",
+"        end\n",
+"    end\n",
+"    disp(x1)\n",
+"endfunction\n",
+"mul(1110,1011);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.29: Normalized_Floating_Point_Representation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.29\n",
+"//Normalized Floating Point Representation\n",
+"//Page no. 23\n",
+"clc;clear;close;\n",
+"\n",
+"function []=fp(x)\n",
+"    x1=x;\n",
+"    if x>0 then\n",
+"        for i=1:10\n",
+"            x=x/10\n",
+"             if int(x)==0 then\n",
+"                break\n",
+"             end\n",
+"        end\n",
+"         printf('\n                                                               %i\nNormalized Floating Point Representation of %g = %.4f x 10',i,x1,x)\n",
+"     else\n",
+"         for i=1:10\n",
+"            x=x*10\n",
+"             if ceil(x)~=0 then\n",
+"                break\n",
+"             end\n",
+"         end\n",
+"         x=x/10;i=i-1;\n",
+"         printf('\n                                                                  -%i\nNormalized Floating Point Representation of %g = %.4f x 10',i,x1,x)\n",
+"    end\n",
+"    \n",
+"endfunction\n",
+"\n",
+"x=[25.12,-0.00287,87000];\n",
+"for i=1:3\n",
+"    fp(x(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.2: Conversion_Using_Shortcut_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.2\n",
+"//Conversion Using Shortcut Method\n",
+"//Page no. 4\n",
+"clc;close;clear;\n",
+"A=10;C=12;\n",
+"d=(((1)*16+A)*16+2)*16+C;\n",
+"disp(d,'Decimal form of 1A2C is =');"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.30: Add.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.30\n",
+"//Add\n",
+"//Page no. 26\n",
+"clc;clear;close;\n",
+"a=0.4532e7;b=0.5427e7;\n",
+"c=a+b\n",
+"printf('Addition of %.6g and %.6g = %.6g',a,b,c)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.31: Add.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.31\n",
+"//Add\n",
+"//Page no. 26\n",
+"clc;clear;close;\n",
+"a=0.4532e5;b=0.5427e7;\n",
+"c=a+b\n",
+"printf('Addition of %.4g and %.6g = %.6g',a,b,c)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.32: Add.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.32\n",
+"//Add\n",
+"//Page no. 26\n",
+"clc;clear;close;\n",
+"a=0.4532e3;b=0.5427e7;\n",
+"c=a+b\n",
+"printf('Addition of %.2g and %.6g = %.4g',a,b,c)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.33: Add.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.33\n",
+"//Add\n",
+"//Page no. 27\n",
+"clc;clear;close;\n",
+"a=[0.4632e3,0.4632e99];b=[0.5427e3,0.5427e99];\n",
+"\n",
+"for i=1:2\n",
+"    c(i)=a(i)+b(i)\n",
+"    printf('\nAddition of %.2g and %.2g = %.5g\n',a(i),b(i),c(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.34: Subtractio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.34\n",
+"//Subtraction\n",
+"//Page no. 27\n",
+"clc;clear;close;\n",
+"a=[0.5427e-3,0.9627e4,0.9627e-99];b=[0.9632e-4,0.9622e4,0.9622e-99];\n",
+"for i=1:3\n",
+"    c(i)=a(i)-b(i)\n",
+"    printf('\nSubtraction of %.2g from %.3g = %.6g\n',a(i),b(i),c(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.35: Multiplicatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.35\n",
+"//Multiplication\n",
+"//Page no. 28\n",
+"clc;clear;close;\n",
+"a=[0.9632e12,0.1132e12,0.1132e52,0.1132e-52];b=[0.5427e-15,0.1027e15,0.1027e50,0.1027e-50];\n",
+"for i=1:4\n",
+"    c(i)=a(i)*b(i)\n",
+"    printf('\nMultiplication of %.3g and %.2g = %.6g\n',a(i),b(i),c(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.36: Divisio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.36\n",
+"//Division\n",
+"//Page no. 28\n",
+"clc;clear;close;\n",
+"a=[0.1132e1,0.1132e-6,0.1132e6];b=[0.1000e-99,0.1000e99,0.1000e3];\n",
+"for i=1:3\n",
+"    c(i)=a(i)/b(i)\n",
+"    printf('\nDivision of %.2g by %.3g= %.3g\n',a(i),b(i),c(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.3: Conversion_to_Base_B_from_Decimal_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.3\n",
+"//Conversion to Base B from Decimal System\n",
+"//Page no. 5\n",
+"clc;close;clear;\n",
+"//conversion from binary to octal\n",
+"disp(dec2oct(bin2dec('10101101110')),'Octal form of 10101101110 is =');    //inbuilt function\n",
+"\n",
+"//conversion from binary to hexadecimal\n",
+"disp(dec2hex(bin2dec('10101101110')),'Hexadecimal form of 10101101110 is =');    //inbuilt function\n",
+"\n",
+"//conversion from binary to octal\n",
+"s=dec2oct(bin2dec('1011'));\n",
+"s1=dec2oct(bin2dec('110011010100'));    //inbuilt function\n",
+"printf('\n Octal form of 1011.1100110101 is = \n\n %s.%s',s,s1)\n",
+"\n",
+"//conversion from binary to hexadecimal\n",
+"s=dec2hex(bin2dec('1011'));\n",
+"s1=dec2hex(bin2dec('110011010100'));    //inbuilt function\n",
+"printf('\n\n Hexadecimal form of 1011.1100110101 is = \n\n %s.%s',s,s1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.4: Conversion_to_Binary_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.4\n",
+"//Conversion to Binary System\n",
+"//Page no. 6\n",
+"clc;close;clear;\n",
+"//conversion from octal to binary\n",
+"disp(dec2bin(oct2dec('1753')),'Binary form of 1753 is =');    //inbuilt function\n",
+"\n",
+"//conversion from octal to binary\n",
+"disp(dec2bin(hex2dec('A478')),'Binary form of A478 is =');    //inbuilt function\n",
+"\n",
+"//conversion from octal to binary\n",
+"s=dec2bin(oct2dec('3'));\n",
+"s1=dec2bin(oct2dec('154'));    //inbuilt function\n",
+"printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.5: Conversion_to_Binary_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.5\n",
+"//Conversion to Binary System\n",
+"//Page no. 6\n",
+"clc;close;clear;\n",
+"//conversion from octal to binary\n",
+"b=dec2bin(oct2dec('1753'))\n",
+"disp(b,'Binary form of 1753 is =');    //inbuilt function\n",
+"b=dec2hex(oct2dec('1753'))\n",
+"disp(b,'Hexadecimal form of 1753 is =');    //inbuilt function\n",
+"//conversion from octal to binary\n",
+"b=dec2bin(hex2dec('A478'))\n",
+"disp(b,'Binary form of A478 is =');    //inbuilt function\n",
+"b=dec2oct(hex2dec('A478'))\n",
+"disp(b,'Octal form of A478 is =');    //inbuilt function\n",
+"//conversion from octal to binary\n",
+"s=dec2bin(oct2dec('3'));\n",
+"s1=dec2bin(oct2dec('154'));    //inbuilt function\n",
+"printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)\n",
+"s=dec2hex(oct2dec('3'));\n",
+"s1=dec2hex(oct2dec('154'));    //inbuilt function\n",
+"printf('\n\n Hexadecimal form of 3.154 is = \n\n %s.%s',s,s1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.6: Conversion_to_Decimal_Number.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.6\n",
+"//Conversion to Decimal Number\n",
+"//Page no. 7\n",
+"clc;close;clear;\n",
+"\n",
+"disp(dec2bin(182),'Binary of 182=')   //inbuilt function"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.7: Conversion_to_Decimal_Number.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.7\n",
+"//Conversion to Decimal Number\n",
+"//Page no. 7\n",
+"clc;close;clear;\n",
+"\n",
+"disp(dec2oct(467),'Octal of 467=')           //inbuilt function"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.8: Conversion_to_Base_B_from_Binary_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.8\n",
+"//Conversion to Base B from Binary System\n",
+"//Page no. 8\n",
+"clc;close;clear;\n",
+"//conversion from binary to octal\n",
+"disp(dec2oct(bin2dec('10101101110')),'Octal form of 10101101110 is =');    //inbuilt function\n",
+"\n",
+"//conversion from binary to hexadecimal\n",
+"disp(dec2hex(bin2dec('10101101110')),'Hexadecimal form of 10101101110 is =');    //inbuilt function\n",
+"\n",
+"//conversion from binary to octal\n",
+"s=dec2oct(bin2dec('1011'));\n",
+"s1=dec2oct(bin2dec('110011010100'));    //inbuilt function\n",
+"printf('\n Octal form of 1011.1100110101 is = \n\n %s.%s',s,s1)\n",
+"\n",
+"//conversion from binary to hexadecimal\n",
+"s=dec2hex(bin2dec('1011'));\n",
+"s1=dec2hex(bin2dec('110011010100'));    //inbuilt function\n",
+"printf('\n\n Hexadecimal form of 1011.1100110101 is = \n\n %s.%s',s,s1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 1.9: Conversion_to_Binary_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 1.9\n",
+"//Conversion to Binary System\n",
+"//Page no. 8\n",
+"clc;close;clear;\n",
+"//conversion from octal to binary\n",
+"disp(dec2bin(oct2dec('1753')),'Binary form of 1753 is =');    //inbuilt function\n",
+"\n",
+"//conversion from octal to binary\n",
+"disp(dec2bin(hex2dec('A478')),'Binary form of A478 is =');    //inbuilt function\n",
+"\n",
+"//conversion from octal to binary\n",
+"s=dec2bin(oct2dec('3'));\n",
+"s1=dec2bin(oct2dec('154'));    //inbuilt function\n",
+"printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/10-Numerical_Solutions_of_System_of_Non_Linear_Equations.ipynb b/Numerical_Methods_Principles_by_Analysis/10-Numerical_Solutions_of_System_of_Non_Linear_Equations.ipynb
new file mode 100644
index 0000000..72555ea
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/10-Numerical_Solutions_of_System_of_Non_Linear_Equations.ipynb
@@ -0,0 +1,347 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 10: Numerical Solutions of System of Non Linear Equations"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.1: System_of_Non_Linear_Equations.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.1\n",
+"//System of Non Linear Equations\n",
+"//Page no. 311\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^2-exp(2*x)-4')\n",
+"deff('y=f1(x)','y=2*x-2*exp(2*x)')\n",
+"x0=0;e=0.00001\n",
+"for i=1:10\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations by newton raphshon method is %.10f',i,x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.2: Contraction_Method_and_Seidel_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.2\n",
+"//Contraction Method and Seidel Method\n",
+"//Page no. 315\n",
+"clc;clear;close;\n",
+"x(1)=0;y(1)=0\n",
+"printf('(a) Contraction Mapping\n\nn\txn\t\tyn\n--------------------------------\n 0\t%f\t%f\n',x(1),y(1))\n",
+"for i=2:9\n",
+"    x(i)=sin(x(i-1)+y(i-1))\n",
+"    y(i)=cos(x(i-1)-y(i-1))\n",
+"    printf(' %i\t%f\t%f\n',i-1,x(i),y(i))\n",
+"end\n",
+"printf('\n\n\n(b) Seidel Method\n\nn\txn\t\tyn\n--------------------------------\n 0\t%f\t%f\n',x(1),y(1))\n",
+"for i=2:9\n",
+"    x(i)=sin(x(i-1)+y(i-1))\n",
+"    y(i)=cos(x(i)-y(i-1))\n",
+"    printf(' %i\t%f\t%f\n',i-1,x(i),y(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.3: Non_Linear_System_of_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.3\n",
+"//Non Linear System of Equation\n",
+"//Page no. 315\n",
+"clc;clear;close;\n",
+"x(1,1)=1;x(1,2)=0;x(1,3)=0;\n",
+"y(1,1)=0;y(1,2)=2;y(1,3)=2;\n",
+"printf('Case -->\t\tI\t\t\t\t\II\t\t\t\tIII\n----------------------------------------------------------------------------------------------------------\nIteration\tx\t\ty\t\tx\t\ty\t\tx\t\ty\n\n    0\t\t%f\t%f\t%f\t%f\t%f\t%f\n',x(1,1),y(1,1),x(1,2),y(1,2),x(1,3),y(1,3))\n",
+"for i=2:9\n",
+"    printf('    %i\t',i-1)\n",
+"    for j=1:3\n",
+"        if j==1 | j==2 then\n",
+"            x(i,j)=(-y(i-1,j)^2-4*x(i-1,j)^2+8*x(i-1,j)+4)/8\n",
+"        y(i,j)=(2*y(i-1,j)^2-2*x(i-1,j)+1)/4\n",
+"        printf('\t%f\t%f',x(i,j),y(i,j))\n",
+"        end\n",
+"        if j==3 then\n",
+"            x(i,j)=(-y(i-1,j)^2-4*x(i-1,j)^2+11*x(i-1,j)+4)/11\n",
+"        y(i,j)=(-2*y(i-1,j)^2+8*y(i-1,j)-2*x(i-1,j)-1)/4\n",
+"        printf('\t%f\t%f',x(i,j),y(i,j))\n",
+"        end\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n\n\nNote : There are computational errors in this example given by the book')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.4: Newton_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.4\n",
+"//Newton Method\n",
+"//Page no. 317\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x1,x2)','y=x1+3*log10(x1)-x2^2')\n",
+"deff('y=f2(x1,x2)','y=2*x1^2-x1*x2-5*x1+1')\n",
+"deff('y=f11(x1,x2)','y=1+3/(log(10)*x1)')\n",
+"deff('y=f12(x1,x2)','y=-2*x2')\n",
+"deff('y=f21(x1,x2)','y=4*x1-x2-5')\n",
+"deff('y=f22(x1,x2)','y=-x1')\n",
+"x=[3.4;2.2];\n",
+"disp(x,'x(0) = ')\n",
+"for i=1:3\n",
+"    fx=[f1(x(1),x(2));f2(x(1),x(2))]\n",
+"    printf('\n fx(%i) = \n',i)\n",
+"    disp(fx)\n",
+"    A=[f11(x(1),x(2)),f12(x(1),x(2));f21(x(1),x(2)),f22(x(1),x(2)),]\n",
+"    disp(A,'A = ')\n",
+"    A_1=inv(A)\n",
+"    disp(A_1,'Inverse of A = ')\n",
+"    x=x-A_1*fx\n",
+"    printf('\n x(%i) = \n',i)\n",
+"    disp(x)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.5: Newton_Raphshon_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.5\n",
+"//Newton Raphshon Method\n",
+"//Page no. 320\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x,y)','y=x^3-3*x*y^2+1')\n",
+"deff('y=f2(x,y)','y=3*x^2*y-y^3')\n",
+"deff('y=f11(x,y)','y=3*x^2-6*y^2')\n",
+"deff('y=f12(x,y)','y=-6*x*y')\n",
+"deff('y=f21(x,y)','y=6*x*y')\n",
+"deff('y=f22(x,y)','y=3*x^2-3*y^2')\n",
+"x=[0;1];\n",
+"printf('\nx(0) = %g\ny(0) = %g\n',x(1),x(2))\n",
+"for i=1:3\n",
+"    fx=[f1(x(1),x(2));f2(x(1),x(2))]\n",
+"    printf('\n fx(%i) = \n',i)\n",
+"    disp(fx)\n",
+"    J=[f11(x(1),x(2)),f12(x(1),x(2));f21(x(1),x(2)),f22(x(1),x(2)),]\n",
+"    disp(J,'J = ')\n",
+"    d=det(J);\n",
+"    if d==0 then\n",
+"        dx1=0;dx2=0;\n",
+"    else\n",
+"        dx1=(fx(1)*J(2,2)-fx(2)*J(1,2))/d;\n",
+"        dx2=(fx(2)*J(1,1)-fx(1)*J(2,1))/d;\n",
+"    end\n",
+"    x(1)=x(1)+dx1;\n",
+"    x(2)=x(2)+dx2;\n",
+"    printf('\nx(%i) = %g\ny(%i) = %g\n',i,x(1),i,x(2))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.6: Newton_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.6\n",
+"//Newton Method\n",
+"//Page no. 322\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x,y,z)','y=x-0.1*y^2+0.05*z^2-0.7')\n",
+"deff('y=f2(x,y,z)','y=y+0.3*x^2-0.1*x*z-0.5')\n",
+"deff('y=f3(x,y,z)','y=z+0.4*y^2+0.1*x*y-1.2')\n",
+"deff('y=f11(x,y,z)','y=1')\n",
+"deff('y=f12(x,y,z)','y=-0.2*y')\n",
+"deff('y=f13(x,y,z)','y=0.1*z')\n",
+"deff('y=f21(x,y,z)','y=0.6*x-0.1*z')\n",
+"deff('y=f22(x,y,z)','y=1')\n",
+"deff('y=f23(x,y,z)','y=-0.1*x')\n",
+"deff('y=f31(x,y,z)','y=0.1*y')\n",
+"deff('y=f32(x,y,z)','y=0.8*y+0.1*x')\n",
+"deff('y=f33(x,y,z)','y=1')\n",
+"x=[0;0;0];\n",
+"printf('n\txn\t\tyn\t\tzn\n---------------------------------------------------------\n')\n",
+"for i=1:6\n",
+"    fx=[f1(x(1),x(2),x(3));f2(x(1),x(2),x(3));f3(x(1),x(2),x(3))]\n",
+"    J=[f11(x(1),x(2),x(3)),f12(x(1),x(2),x(3)),f13(x(1),x(2),x(3));f21(x(1),x(2),x(3)),f22(x(1),x(2),x(3)),f23(x(1),x(2),x(3));f31(x(1),x(2),x(3)),f32(x(1),x(2),x(3)),f33(x(1),x(2),x(3))]\n",
+"    J_1=inv(J)\n",
+"    printf(' %i\t%f\t%f\t%f\n',i-1,x(1),x(2),x(3))\n",
+"    x=x-J_1*fx\n",
+"end\n",
+"printf('\n\nThe solution is x = %f, y = %f and z = %f',x(1),x(2),x(3))\n",
+"\n",
+"printf('\n\n\nNote : There are computation errors in calculation given by the book')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.7: Iterative_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.7\n",
+"//Iterative Method\n",
+"//Page no. 326\n",
+"clc;clear;close;\n",
+"\n",
+"x=[0;0;0];\n",
+"printf('n\txn\t\tyn\t\tzn\n---------------------------------------------------------\n')\n",
+"for i=1:7\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\n',i-1,x(1),x(2),x(3))\n",
+"    x(1)=0.7+0.1*x(2)^2-0.05*x(3)^2\n",
+"    x(2)=0.5-0.3*x(1)^2+0.1*x(1)*x(3)\n",
+"    x(3)=1.2-0.4*x(2)^2-0.1*x(1)*x(2)\n",
+"end\n",
+"printf('\n\nThe solution is x = %.10f, y = %.10f and z = %.10f',x(1),x(2),x(3))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 10.8: Steepest_Descent.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 10.8\n",
+"//Steepest Descent\n",
+"//Page no. 328\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x1,x2)','y=(x1-2)^4+3*(x2+3)^2')\n",
+"x=[1;-2];\n",
+"printf('n\t     x1\t\t     x2\t\t   F(x1,x2)\n-----------------------------------------------------\n')\n",
+"for i=1:11\n",
+"    Fx=[f(x(1),x(2))];\n",
+"    J=[4*(x(1)-2)^3,6*(x(2)+3)];\n",
+"    u=(Fx*J*J'*Fx)/(J*J'*Fx*J*J'*Fx)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\n',i-1,x(1),x(2),Fx)\n",
+"    x=x-u*J'*Fx \n",
+"end\n",
+"printf('\n\nThis shows that the solution tends to x1 = %i   and   x2 = %i',ceil(x(1)),floor(x(2)))"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/11-Eigenvalues_and_Eigenvectors.ipynb b/Numerical_Methods_Principles_by_Analysis/11-Eigenvalues_and_Eigenvectors.ipynb
new file mode 100644
index 0000000..d2208de
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/11-Eigenvalues_and_Eigenvectors.ipynb
@@ -0,0 +1,786 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 11: Eigenvalues and Eigenvectors"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.10: LU_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.10\n",
+"//LU Method\n",
+"//Page no. 363\n",
+"clc;close;clear;\n",
+"\n",
+"A=[120,80,40,-16;80,120,16,-40;40,16,120,-80;-16,-40,-80,120];\n",
+"disp(A,'A =')\n",
+"L=eye(4,4);\n",
+"for l=1:20\n",
+"for j=1:4\n",
+"    for i=1:j\n",
+"        k=0\n",
+"        for p=1:i-1\n",
+"            k=k-A(i,p)*A(p,j)\n",
+"        end\n",
+"        A(i,j)=A(i,j)+k\n",
+"    end\n",
+"    for i=j+1:4\n",
+"        k=0;\n",
+"        for p=1:j-1\n",
+"            k=k-A(i,p)*A(p,j)\n",
+"        end\n",
+"        A(i,j)=(A(i,j)+k)/A(j,j) \n",
+"    end\n",
+"end\n",
+"disp(A,'Modified A = ')\n",
+"    for i=1:4\n",
+"    for j=1:4\n",
+"        if i>j then\n",
+"            L(i,j)=A(i,j)\n",
+"        else\n",
+"            U(i,j)=A(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"disp(U,'U =',L,'L =')\n",
+"A=U*L;\n",
+"printf('\n\nAfter %i iterations, matrix A =\n\n',l)\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        printf('    %.2f\t',A(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"end\n",
+"printf('\n\nTherefore the eigenvalues are the diagonal elements f the transformed triangular matrix are:\n\n')\n",
+"for i=1:4\n",
+"    printf(' %.2f,',A(i,i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.11: Generalized_Eigenvalue_Problem.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.11\n",
+"//Generalized Eigenvalue Problem\n",
+"//Page no. 365\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,1,0.5;1,1,0.25;0.5,0.25,2]\n",
+"B=[2,2,2;2,5,5;2,5,11]\n",
+"disp(B,'B =',A,'A =')\n",
+"for i=1:3\n",
+"    G(i,i)=sqrt(B(i,i))\n",
+"end\n",
+"G=[B;eye(3,3)];\n",
+"\n",
+"//transformation to frobenius matrix\n",
+"for k=3:-1:2\n",
+"    g(k)=0;\n",
+"    for j=1:k-1\n",
+"        if(g(k)<G(k,j))\n",
+"            g(k)=G(k,j)\n",
+"            p=j;\n",
+"        end\n",
+"    end\n",
+"    if(g(k)~=0)\n",
+"        for j=1:3\n",
+"            r(1,j)=G(k,j)\n",
+"        end\n",
+"        for i=1:6\n",
+"            G(i,k-1)=G(i,k-1)/g(k)\n",
+"        end\n",
+"        for j=1:3\n",
+"            if(j~=k-1)\n",
+"                l=G(k,j)\n",
+"                for i=1:6\n",
+"                    G(i,j)=G(i,j)-l*G(i,k-1)\n",
+"                end\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    for j=1:3\n",
+"        for i=1:3\n",
+"            c(i,1)=G(i,j)\n",
+"        end\n",
+"        G(k-1,j)=0\n",
+"        for i=1:3\n",
+"            G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"\n",
+"//partition g\n",
+"for i=4:6\n",
+"    for j=1:3\n",
+"        T(i-3,j)=G(i,j)\n",
+"    end\n",
+"end\n",
+"\n",
+"//eigenvalues computation\n",
+"p=poly(B,'x')\n",
+"a=roots(p)\n",
+"printf('\n\nDiagonalized Matrix B = \n\n')\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if i~=j then\n",
+"            B(i,j)=0\n",
+"        else\n",
+"            B(i,j)=a(i)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"disp(B)\n",
+"//eigenvectors computation\n",
+"for k=1:3\n",
+"    m=2\n",
+"    for l=1:3\n",
+"        y(l,k)=a(k)^(m)\n",
+"        m=m-1;\n",
+"    end\n",
+"end\n",
+"printf('\n\n')\n",
+"\n",
+"\n",
+"for k=1:3\n",
+"    for l=1:3\n",
+"        y1(l,1)=y(l,1)\n",
+"        y2(l,1)=y(l,2)\n",
+"        y3(l,1)=y(l,3)\n",
+"    end\n",
+"    x1=T*y3;\n",
+"    x2=T*y2;\n",
+"    x3=T*y1;\n",
+"end\n",
+"printf('\n\nEigenvectors of B are :\n\n')\n",
+"for i=1:3\n",
+"    printf('|%.5f|\t\t|%.5f|\t\t|%.5f|',x3(i,1),x2(i,1),x1(i,1))\n",
+"    printf('\n')\n",
+"end\n",
+"x=[x3,x2,x1]\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"B=[2,2,2;2,5,5;2,5,11]\n",
+"G=0\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if i==j then\n",
+"            G(i,j)=sqrt(B(i,j))\n",
+"        else\n",
+"            G(i,j)=0;\n",
+"        end\n",
+"    end\n",
+"end\n",
+"\n",
+"B=inv(G)*x'*A*x*inv(G)\n",
+"disp(B,'Eigenvectors of A =')\n",
+"\n",
+"printf('\n\n\nNote : Computation Error in book in caculation of eigenvector of B thus for A')\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.1: Eigenvalues_and_Eigenvectors.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.1\n",
+"//Eigenvalues and Eigenvectors\n",
+"//Page no. 333\n",
+"clc;clear;close;\n",
+"\n",
+"A1=[0.6;0.2];A2=[-0.2;0.6];A3=[-0.6;-0.2];A4=[0.2;-0.6];\n",
+"T=[1.1,-0.3;-0.3,1.9];\n",
+"B1=T*A1;B2=T*A2;B3=T*A3;B4=T*A4;\n",
+"disp(B4,B3,B2,B1,'The transformed vectors are :')\n",
+"disp('These points lie on the ellipse:')\n",
+"printf('     2      2\n(x-3y)+(3x+y)\n------ ------\n  16     4\n\n')\n",
+"A5=[0;2/sqrt(10)];\n",
+"disp('The vector (0,2/10^(1/2)) lies on the circle:')\n",
+"printf(' 2   2\nx + y = 4\n        -\n        10\n\n')\n",
+"B5=T*A5;\n",
+"disp('Also lies on the same ellipse',B5)\n",
+"printf('\n\nWe can see that there is a linear relationship between the first 4 vectors and their respective transformend vectors through the scalars known as eigenvectors and eigenvalues respectively')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.2: Leverriers_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.2\n",
+"//Leverrier's Method\n",
+"//Page no. 337\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,2,2;2,5,5;2,5,1];\n",
+"A1=A;\n",
+"C(1)=0;\n",
+"    for j=1:3\n",
+"        for k=1:3\n",
+"            if(j==k)\n",
+"                C(1)=C(1)+A1(j,k)\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    disp(A,'A=')\n",
+"        disp(A1,'A1=')\n",
+"    printf('\nC1=')\n",
+"    disp(C(1));\n",
+"for i=2:3\n",
+"    A2=A*(A1-C(i-1)*eye(3,3));\n",
+"    printf('\n\n\nA%i=',i)\n",
+"    disp(A2);\n",
+"    C(i)=0;\n",
+"    for j=1:3\n",
+"        for k=1:3\n",
+"            if(j==k)\n",
+"                C(i)=C(i)+A2(j,k)/i\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"    printf('\nC%i=',i)\n",
+"    disp(C(i))\n",
+"    A1=A2;\n",
+"end\n",
+"printf('\n\n\nTherefore the characteristic polynomial is:\n 3    2\nx - %ix - %ix %i = 0',C(1),C(2),C(3))\n",
+"\n",
+"//verification\n",
+"printf('\n\nVerification:')\n",
+"s=poly(0,'s');\n",
+"p=poly(A,'x');\n",
+"A=A-eye(3,3)*%s;\n",
+"disp(p,'=',A)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.3: Danilevsky_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.3\n",
+"//Danilevsky Method\n",
+"//Page no. 341\n",
+"clc;close;clear;\n",
+"\n",
+"A=[-1,0,0;1,-2,3;0,2,-3];\n",
+"G=[A;eye(3,3)];\n",
+"disp(G);\n",
+"//transformation to frobenius matrix\n",
+"for k=3:-1:2\n",
+"    g(k)=0;\n",
+"    for j=1:k-1\n",
+"        if(g(k)<G(k,j))\n",
+"            g(k)=G(k,j)\n",
+"            p=j;\n",
+"        end\n",
+"    end\n",
+"    if(g(k)~=0)\n",
+"        for j=1:3\n",
+"            r(1,j)=G(k,j)\n",
+"        end\n",
+"        for i=1:6\n",
+"            G(i,k-1)=G(i,k-1)/g(k)\n",
+"        end\n",
+"        disp(G)\n",
+"        for j=1:3\n",
+"            if(j~=k-1)\n",
+"                l=G(k,j)\n",
+"                for i=1:6\n",
+"                    G(i,j)=G(i,j)-l*G(i,k-1)\n",
+"                end\n",
+"            end\n",
+"        end\n",
+"        disp(G)\n",
+"    end\n",
+"    for j=1:3\n",
+"        for i=1:3\n",
+"            c(i,1)=G(i,j)\n",
+"        end\n",
+"        G(k-1,j)=0\n",
+"        for i=1:3\n",
+"            G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)\n",
+"        end\n",
+"    end\n",
+"    disp(G)\n",
+"end\n",
+"\n",
+"//partition g\n",
+"for i=4:6\n",
+"    for j=1:3\n",
+"        T(i-3,j)=G(i,j)\n",
+"    end\n",
+"end\n",
+"disp(T,'T=')\n",
+"\n",
+"//eigenvalues computation\n",
+"printf('\n\n\nCharateristic polynomial:')\n",
+"p=poly(A,'x')\n",
+"disp(p)\n",
+"printf('\n\n\nEigenvalues:')\n",
+"a=roots(p)\n",
+"disp(a')\n",
+"//eigenvectors computation\n",
+"for k=1:3\n",
+"    m=2\n",
+"    for l=1:3\n",
+"        y(l,k)=a(k,1)^(m)\n",
+"        m=m-1;\n",
+"    end\n",
+"end\n",
+"printf('\n\n')\n",
+"disp(y,'y=')\n",
+"\n",
+"//eigenvector computation\n",
+"\n",
+"for k=1:3\n",
+"    for l=1:3\n",
+"        y1(l,1)=y(l,1)\n",
+"        y2(l,1)=y(l,2)\n",
+"        y3(l,1)=y(l,3)\n",
+"    end\n",
+"    x1=T*y3;\n",
+"    x2=T*y2;\n",
+"    x3=T*y1;\n",
+"end\n",
+"printf('\n\nEigenvectors :\n')\n",
+"for i=1:3\n",
+"    printf('|%.1f|\t\t|%.1f|\t\t|%.1f|',x1(i,1),x2(i,1),x3(i,1))\n",
+"    printf('\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.4: Power_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.4\n",
+"//Power Method\n",
+"//Page no. 345\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,2;3,4];\n",
+"e=0.001;\n",
+"q0=[1;1];\n",
+"for i=1:5\n",
+"    q1=A*q0;\n",
+"    a=max(q1)\n",
+"    for j=1:2\n",
+"        q2(j)=q1(j)/a;\n",
+"    end\n",
+"    printf('\nq(%i) = %.4f     a = %.4f      Scaled q(%i) = %.4f\n       %.4f                                      %i\n\n',i,q1(1),a,i,q2(1),q1(2),q2(2))\n",
+"    q1=q2;\n",
+"    q0=q1;\n",
+"end\n",
+"printf('Hence the largest eigenvalue is %.4f with the corresponding eigenvector as %.4f\n                                                                                %i',a,q0(1),q0(2))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.5: Inverse_Power_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.5\n",
+"//Inverse Power Method\n",
+"//Page no. 347\n",
+"clc;close;clear;\n",
+"\n",
+"A=[7,6,-3;-12,-20,24;-6,-12,16];\n",
+"e=10^-6;\n",
+"X=[1;1;1];\n",
+"B=0;\n",
+"Y=[0;0;0]\n",
+"a=0;l=0;\n",
+"for i=1:2\n",
+"    printf('When a=%i\n',a);\n",
+"    C=A-a*eye();\n",
+"    disp(C,'C=')\n",
+"    C_1=inv(C);\n",
+"    disp(C_1,'Inverse of C=');\n",
+"    printf('\n\nItr       lambda                             X')\n",
+"    printf('\n------------------------------------------------------------------\n')\n",
+"    for j=1:10\n",
+"        printf('\n%i        %f           %f     %f      %f',j-1,l,X(1),X(2),X(3));\n",
+"        Y=C_1*X;\n",
+"        B=max(Y);\n",
+"        e1=abs(l-B);\n",
+"        X=Y/B;\n",
+"        m=0;\n",
+"        for k=1:3\n",
+"            m=m+(Y(k)-X(k))^2;\n",
+"        end\n",
+"        e2=sqrt(m);\n",
+"        er=max(e1,e2);\n",
+"        if(er<e)\n",
+"            break\n",
+"        end\n",
+"        l=B;\n",
+"        \n",
+"    end\n",
+"    a=-3;\n",
+"    printf('\n\n\n\n')\n",
+"end\n",
+"printf('\n\n\nNote : Computation of Y is wrong given in the book')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.6: Rayleigh_Quotient.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.6\n",
+"//Rayleigh Quotient\n",
+"//Page no. 348\n",
+"clc;close;clear;\n",
+"\n",
+"A=[10,7,8,7;7,5,6,5;8,6,10,9;7,5,9,10];\n",
+"q0=[1;1;1;1];\n",
+"for i=0:4\n",
+"    X=(A^i)*q0;\n",
+"    l=(X'*A*X)/(X'*X)\n",
+"    printf('\nLambda(%i) = %f\n',i+1,l)\n",
+"end\n",
+"printf('\n\nDominant Eigenvalue = %f\n\n\n',l)\n",
+"\n",
+"e=0.001;\n",
+"for i=1:5\n",
+"    q1=A*q0;\n",
+"    a=max(q1)\n",
+"    for j=1:4\n",
+"        q2(j)=q1(j)/a;\n",
+"    end\n",
+"\n",
+"    q1=q2;\n",
+"    q0=q1;\n",
+"end\n",
+"disp(q2,'Corresponding Eigenvector = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.7: Jacobi_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.7\n",
+"//Jacobi's Method\n",
+"//Page no. 355\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,1,1/2;1,1,1/4;1/2,1/4,2];\n",
+"C=A;\n",
+"V=[sqrt(2),0,1/2;sqrt(2),0,1/4;3/(4*sqrt(2)),-1/(4*sqrt(2)),2]\n",
+"S=eye(3,3)\n",
+"disp(A,'A =')\n",
+"VI=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if(i~=j)\n",
+"            VI=VI+A(i,j)^2                          //initial off diag norm\n",
+"        end\n",
+"    end\n",
+"end\n",
+"VI=sqrt(VI);\n",
+"VF=VI*10^-7;       //final threshold\n",
+"V1=VI/3;\n",
+"o=poly(0,'o');\n",
+"for i=1:3\n",
+"for q=2:3\n",
+"    for p=q-1:-1:1\n",
+"        if(A(p,q)>V1)\n",
+"            a=-A(p,q);\n",
+"            b=(A(p,p)-A(q,q))/2\n",
+"            if(b~=0)\n",
+"                w=b*abs(1/b)*(a/sqrt(a^2+b^2));\n",
+"            else\n",
+"                w=(a/sqrt(a^2+b^2));\n",
+"            end\n",
+"            sin0=w/sqrt(2*(1+sqrt(1-w^2)));\n",
+"            cos0=sqrt(1-sin0^2)\n",
+"        end\n",
+"        B(p,p)=A(p,p)*cos0^2+A(q,q)*sin0^2-2*A(p,q)*sin0*cos0\n",
+"            B(q,q)=A(p,p)*sin0^2+A(q,q)*cos0^2+2*A(p,q)*sin0*cos0\n",
+"            B(p,q)=(A(p,p)-A(q,q))*sin0*cos0+A(p,q)*(cos0^2-sin0^2)\n",
+"            S(i,i)=S(i,i)\n",
+"            S(i,p)=S(i,p)*cos0-S(i,q)*sin0\n",
+"            S(i,q)=S(i,p)*sin0+S(i,q)*cos0\n",
+"            \n",
+"    end\n",
+"end\n",
+"end\n",
+"disp(B,'B =')\n",
+"disp(S,'S =')\n",
+"printf('\n\n\nComputation error in the solution provided by book')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.8: Recursive_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.8\n",
+"//Recursive Formula\n",
+"//Page no. 357\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,-1,0,0;-1,2,-1,0;0,-1,2,-1;0,0,-1,2];\n",
+"l=poly(0,'l');\n",
+"p0=1;\n",
+"p1=A(1,1)-l;\n",
+"for i=2:4\n",
+"    p2=(A(i,i)-l)*p1-A(i,i-1)^2*p0;\n",
+"    p0=p1;\n",
+"    p1=p2;\n",
+"    printf('\n\np%i(l) = ',i);\n",
+"    disp(p2)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 11.9: QR_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 11.9\n",
+"//QR Method\n",
+"//Page no. 360\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,-1,0;-1,2,-1;0,-1,2];\n",
+"deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"deff('y=s2(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"disp(A,'A=')\n",
+"l0=0;f=1;m=0;s=0;w=0;\n",
+"for n=1:5\n",
+"    for j=1:2\n",
+"        for k=1:2\n",
+"            V(j,k)=A(j,k)\n",
+"        end\n",
+"    end\n",
+"    disp(V,'V=')\n",
+"    p=poly(V,'x');\n",
+"    disp('=0',p);\n",
+"    a=roots(p);\n",
+"    for j=1:2\n",
+"        printf('\na(%i) = %f',j,a(j))\n",
+"    end\n",
+"        if(abs(a(1)-V(1,1))<=abs(a(2)-V(1,1)))\n",
+"            a=a(1)\n",
+"        else\n",
+"            a=a(2)\n",
+"        end\n",
+"    printf('\na = %f\n',a)\n",
+"    s=s+a;\n",
+"    A=A-a*eye()\n",
+"    R=A;Q=eye(3,3);\n",
+"    \n",
+"   for j=1:2\n",
+"       for i=j+1:3\n",
+"           for k=1:3             //C matrix evaluation\n",
+"               for l=1:3\n",
+"                   if(k==l)\n",
+"                       if(k==i | k==j)\n",
+"                           C(k,l)=c(i,j)\n",
+"                       else\n",
+"                           C(k,l)=1\n",
+"                       end\n",
+"                   end\n",
+"                   if(k>l)\n",
+"                       if(k==i & l==j)\n",
+"                           C(k,l)=-1*s2(i,j)\n",
+"                      else\n",
+"                           C(k,l)=0\n",
+"                       end\n",
+"                   end\n",
+"                   if(k<l)\n",
+"                       if(k==j & l==i)\n",
+"                           C(k,l)=s2(i,j)\n",
+"                       else\n",
+"                           C(k,l)=0\n",
+"                       end\n",
+"                   end\n",
+"               end\n",
+"          end\n",
+"           \n",
+"           R=C*R;\n",
+"           Q=Q*C';\n",
+"           \n",
+"       end\n",
+"    end\n",
+"disp(Q,'Q=',R,'R=')\n",
+"disp(Q*R,'Q*R=')\n",
+"A=R*Q;\n",
+"disp(A,'A=')\n",
+"end\n",
+"l1=l0+s;\n",
+"for i=2:3\n",
+"    for j=2:3\n",
+"        V(i-1,j-1)=A(i,j)\n",
+"    end\n",
+"end\n",
+"disp(V,'V=')\n",
+"    p=poly(V,'x');\n",
+"    disp('=0',p);\n",
+"    a=roots(p);\n",
+"    for j=1:2\n",
+"        printf('\na(%i) = %f',j,a(j))\n",
+"    end\n",
+"    l2=l1+a(1)\n",
+"    l3=l1+a(2)\n",
+"    disp(l3,'l3=',l2,'l2=',l1,'l1=')\n",
+"printf('\n\n\nNote : Values of V varies in each step resulting in different results due to error in book calculation')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/12-Interpolation_and_Extrapolation.ipynb b/Numerical_Methods_Principles_by_Analysis/12-Interpolation_and_Extrapolation.ipynb
new file mode 100644
index 0000000..04b0fab
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/12-Interpolation_and_Extrapolation.ipynb
@@ -0,0 +1,501 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 12: Interpolation and Extrapolation"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.1: Linear_Interpolation_Technique.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.1\n",
+"//Linear Interpolation Technique\n",
+"//Page no. 372\n",
+"clc;close;clear;\n",
+"\n",
+"printf('x:    ')\n",
+"f=[1,4,9,16,25];\n",
+"for i=1:5\n",
+"    printf('%i\t',i)\n",
+"end\n",
+"printf('\nf(x):  ')\n",
+"for i=1:5\n",
+"    printf('%i\t',f(i))\n",
+"end\n",
+"x=2.5;\n",
+"x1=2;x2=3;printf('\n\nfor (2,4) and (3,9)')\n",
+"f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)\n",
+"printf('\nf(2.5) = %.1f',f(2.5))\n",
+"\n",
+"x=2.5;\n",
+"x1=2;x2=4;printf('\n\nfor (2,4) and (4,16)')\n",
+"f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)\n",
+"printf('\nf(2.5) = %.1f',f(2.5))\n",
+"\n",
+"x=2.5;\n",
+"x1=1;x2=3;printf('\n\nfor (1,1) and (3,9)')\n",
+"f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)\n",
+"printf('\nf(2.5) = %.1f',f(2.5))\n",
+"\n",
+"printf('\n\nExact value = %.2f',2.5^2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.2: Lagarangian_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.2\n",
+"//Lagarangian Method\n",
+"//Page no. 373\n",
+"clc;close;clear;\n",
+"\n",
+"xk=[-1,0,2,5];\n",
+"yk=[10,7,7,22];\n",
+"\n",
+"P=0;\n",
+"x=poly(0,'x');\n",
+"for k=0:3\n",
+"    p=yk(k+1)\n",
+"    for j=0:3\n",
+"        if(j~=k)\n",
+"            p=p*((x-xk(j+1))/(xk(k+1)-xk(j+1)))\n",
+"        end\n",
+"    end\n",
+"    P=P+p;\n",
+"end\n",
+"disp(P,'P=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.3: Aitken_Nevilles_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.3\n",
+"//Aitken-Neville's Method\n",
+"//Page no. 378\n",
+"clc;close;clear;\n",
+"\n",
+"function [x,y,z]=tran(a,b)        // function for exchanging values\n",
+"    z=a;y=b;x=z;\n",
+"endfunction\n",
+"deff('y=P(a,b,c,d,e)','y=(c(d)*b(d+1)-c(d+e)*b(d))/(a(d+e)-a(d))')  //function for finding polynomials\n",
+"xi=[0.8,1,1.2,1.4,1.6];\n",
+"yi=[2.2255,2.7183,3.3201,4.0552,4.9530];\n",
+"x=1.23\n",
+"[xi(5),xi(1),a]=tran(xi(1),xi(5))\n",
+"[xi(4),xi(1),a]=tran(xi(1),xi(4))\n",
+"[xi(3),xi(2),a]=tran(xi(2),xi(3))\n",
+"[xi(2),xi(1),a]=tran(xi(1),xi(2))\n",
+"[yi(5),yi(1),a]=tran(yi(1),yi(5))\n",
+"[yi(4),yi(1),a]=tran(yi(1),yi(4))\n",
+"[yi(3),yi(2),a]=tran(yi(2),yi(3))\n",
+"[yi(2),yi(1),a]=tran(yi(1),yi(2))\n",
+"for i=1:5\n",
+"    x_xi(i)=x-xi(i);\n",
+"end\n",
+"printf('xi     x-xi       yi\n')\n",
+"printf('------------------------\n')\n",
+"for i=1:5\n",
+"    printf('%.1f     %.2f\t%f\n',xi(i),x_xi(i),yi(i))\n",
+"end\n",
+"printf('\n\nPolynomials\n')\n",
+"printf('-----------\n')\n",
+"for i=1:4\n",
+"    for j=1:5-i\n",
+"         printf('%f\n',P(xi,yi,x_xi,j,i))\n",
+"         yi(j)=P(xi,yi,x_xi,j,i)\n",
+"    end\n",
+"    printf('\n\n\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.4: Newtons_Divided_Difference_Interpolation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.4\n",
+"//Newton's Divided Difference Interpolation\n",
+"//Page no. 381\n",
+"clc;close;clear;\n",
+"\n",
+"x=[0,1,2,3,4,5]\n",
+"y=[1,2,5,10,17,26];\n",
+"y1=y;\n",
+"deff('yi=P(a,b,d,e)','yi=(b(d+1)-b(d))/(a(d+e)-a(d))')  //function for finding polynomials\n",
+"for i=1:3\n",
+"    for j=1:6-i\n",
+"        z(j,i)=P(x,y,j,i)\n",
+"         y(j)=z(j,i)\n",
+"    end\n",
+"end\n",
+"z(6,1)=0;\n",
+"printf('x    y      f(x0,x1)        f(x0,x1,x3)    f(x0,x1,x2,x3)\n')\n",
+"printf('---------------------------------------------------------\n')\n",
+"    for j=1:6\n",
+"        printf(' %i    %i \t%i\t\t%i\t\t%i\n',x(1,j),y1(1,j),z(j,1),z(j,2),z(j,3))\n",
+"    end\n",
+"x1=2.6;\n",
+"f=y1(4)+(x1-x(4))*(z(4,1))+(x1-x(4))*(x1-x(5))*z(4,2)\n",
+"printf('\n\nf(2.6)=%.2f',f)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.5: Interpolation_Methods.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.5\n",
+"//Interpolation Methods\n",
+"//Page no. 403\n",
+"clc;close;clear;\n",
+"\n",
+"x=[0,1,2,3,4];\n",
+"y=[0,1,8,27,64];\n",
+"\n",
+"//Inverse lagrange Method\n",
+"P=0;\n",
+"y1=20;\n",
+"for k=0:4\n",
+"    p=x(k+1)\n",
+"    for j=0:4\n",
+"        if(j~=k)\n",
+"            p=p*((y1-y(j+1))/(y(k+1)-y(j+1)))\n",
+"        end\n",
+"    end\n",
+"    P=P+p;\n",
+"end\n",
+"disp(P,'Inverse Lagrange interpolation x=')\n",
+"\n",
+"\n",
+"//Newton's divide difference interpolation\n",
+"x1=x;\n",
+"deff('xi=P(a,b,d,y)','xi=(b(d+1)-b(d))/(a(d+y)-a(d))')  //function for finding polynomials\n",
+"for i=1:2\n",
+"    for j=1:5-i\n",
+"        z(j,i)=P(y,x,j,i)\n",
+"         x(j)=z(j,i)\n",
+"    end\n",
+"end\n",
+"z(5,1)=0;\n",
+"printf('\n\n y\tx      f(y0,y1)        f(y0,y1,y3)\n')\n",
+"printf('------------------------------------------\n')\n",
+"    for j=1:5\n",
+"        printf(' %i\t%i \t%i\t\t%i\t\n',y(1,j),x1(1,j),z(j,1),z(j,2))\n",
+"    end\n",
+"y1=20;\n",
+"f=x1(4)+(y1-y(4))*(z(4,1))+(y1-y(4))*(y1-y(5))*z(4,2)\n",
+"printf('\n\nNewton Divide Difference x(20)=%.2f',f)\n",
+"\n",
+"x=x1;\n",
+"//Iterated Linear Interpolation\n",
+"function [x,y,z]=tran(a,b)        // function for exchanging values\n",
+"    z=a;y=b;x=z;\n",
+"endfunction\n",
+"deff('y=P(a,b,c,d,e)','y=(c(d)*b(d+1)-c(d+e)*b(d))/(a(d+e)-a(d))')  //function for finding polynomials\n",
+"y1=20\n",
+"\n",
+"[y(4),y(1),a]=tran(y(1),y(4))\n",
+"[y(3),y(2),a]=tran(y(2),y(3))\n",
+"[x(4),x(1),a]=tran(x(1),x(4))\n",
+"[x(3),x(2),a]=tran(x(2),x(3))\n",
+"for i=1:5\n",
+"    y1_y(i)=y1-y(i);\n",
+"end\n",
+"printf('y\ty1-y\tx\n')\n",
+"printf('------------------\n')\n",
+"for i=1:5\n",
+"    printf('%.1f\t%i\t%i\n',y(i),y1_y(i),x(i))\n",
+"end\n",
+"printf('\n\nPolynomials\n')\n",
+"printf('-----------\n')\n",
+"for i=1:4\n",
+"    for j=1:5-i\n",
+"         printf('%f\n',P(y,x,y1_y,j,i))\n",
+"         x(j)=P(y,x,y1_y,j,i)\n",
+"    end\n",
+"    printf('\n\n')\n",
+"end\n",
+"printf('Iterated Linear Interpolation x(20) = %f',x(j))\n",
+"\n",
+"x=[0,1,2,3,4];\n",
+"y=[0,1,8,27,64];\n",
+"y1=y;\n",
+"//Suggested Interpolation\n",
+"\n",
+"for i=1:4\n",
+"    for j=1:5-i\n",
+"        z(j,i)=y(j+1)-y(j);\n",
+"        y(j)=z(j,i)\n",
+"    end\n",
+"end\n",
+"printf('\n\n\n x\ty\tdy\td2y\td3y\td4y\n')\n",
+"printf('--------------------------------------------\n')\n",
+"for i=1:5\n",
+"    printf(' %i\t%i\t%i\t%i\t%i\t%i\n',x(i),y1(i),z(i,1),z(i,2),z(i,3),z(i,4))\n",
+"end\n",
+"s=poly(0,'s')\n",
+"p=y1(4);k=3;\n",
+"for i=1:3\n",
+"    r=1;\n",
+"    for j=1:i\n",
+"        r=r*(s+(j-1))\n",
+"    end\n",
+"    r=r*z(k,i)/factorial(j);\n",
+"    k=k-1;\n",
+"    p=p+r;\n",
+"    printf('\n\nStage %i :',i)\n",
+"    disp(p)\n",
+"end\n",
+"s0=-7/19;\n",
+"disp(s0,'s0=');\n",
+"s1=(-7-s0*(s0+1)*6)/19\n",
+"disp(s1,'s1=')\n",
+"disp(3+s1,'x1=')\n",
+"s2=(-7-s1*(s1+1)*6-s1*(s1+1)*(s1+2))/19\n",
+"disp(s2,'s2=')\n",
+"x2=3+s2;\n",
+"disp(x2,'Suggested Interpolation x(20)=');"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.6: Chebyshev_Interpolating_Polynomial.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.6\n",
+"//Chebyshev Interpolating Polynomial\n",
+"//Page no. 407\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=1/(1+exp(-x))');\n",
+"a=-2;b=2;n=3;\n",
+"D=%pi/(2*n+2)\n",
+"for k=0:n\n",
+"    t(k+1)=-cos(D*(2*k+1))\n",
+"    x(k+1)=((a+b)/2)+(b-a)*t(k+1)/2\n",
+"    y(k+1)=f(x(k+1))\n",
+"    C(k+1)=0\n",
+"end\n",
+"for j=0:n\n",
+"    for k=0:n\n",
+"        L=(2*k+1)*D\n",
+"        C(j+1)=C(j+1)+y(k+1)*cos(j*L)\n",
+"    end\n",
+"end\n",
+"C(1)=C(1)/(n+1);\n",
+"for j=1:n\n",
+"    C(j+1)=2*C(j+1)/(n+1)\n",
+"end\n",
+"\n",
+"x=poly(0,'x')\n",
+"T(1)=1;T(2)=x;\n",
+"for j=1:n-1\n",
+"    T(j+2)=2*x*T(j+1)-T(j)\n",
+"end\n",
+"P=C(1)*T(1)\n",
+"for j=1:n\n",
+"    P=P+C(j+1)*T(j+1)\n",
+"end\n",
+"disp(P,'P3(x)=')\n",
+"printf('\n\n\nNote : Book has Calculation errors in calculation of coefficients')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.7: Double_Interpolation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.7\n",
+"//Double Interpolation\n",
+"//Page no. 409\n",
+"clc;close;clear;\n",
+"\n",
+"x=[0,1,2,3,4];\n",
+"y=[0,1,2,3,4];\n",
+"z=[0,1,8,27,64;1,3,11,31,69;4,7,16,37,76;9,13,23,45,85;16,21,32,55,96];\n",
+"printf('y / x')\n",
+"for i=1:5\n",
+"    printf('\t%i',x(i))\n",
+"end\n",
+"for i=1:5\n",
+"    printf('\n %i',y(i))\n",
+"    for j=1:5\n",
+"        printf('\t%i',z(j,i))\n",
+"    end\n",
+"end\n",
+"printf('\n\n\n')\n",
+"for i=1:5\n",
+"    x=2.5;\n",
+"    x1=2;x2=3;\n",
+"    z1(1,i)=z(i,x1+1)+(z(i,x2+1)-z(i,x1+1))*(x-x1)/(x2-x1)\n",
+"end\n",
+"printf('Values of z at x=2.5:\n\n  y')\n",
+"for i=1:5\n",
+"    printf('\t%i',y(i))\n",
+"end\n",
+"printf('\n  z')\n",
+"for i=1:5\n",
+"    printf('\t%g',z1(i))\n",
+"end\n",
+"y=1.5;\n",
+"y1=1;y2=2;\n",
+"z2=z1(y1+1)+(z1(y2+1)-z1(y1+1))*(y-y1)/(y2-y1)\n",
+"printf('\n\nValue of z at x=2.5 and y=1.5 :  %g',z2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.8: Spline_Interpolation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 12.8\n",
+"//Spline Interpolation\n",
+"//Page no. 414\n",
+"clc;close;clear;\n",
+"\n",
+"xi=[0.10,0.11,0.12,0.13,0.14,0.15,0.16,0.17];\n",
+"yi=[0.1110,0.1234,0.1361,0.1491,0.1623,0.1759,0.1897,0.2038];\n",
+"h=0.01;\n",
+"\n",
+"pi(1)=0;qi(1)=0;pi(8)=0;qi(8)=0;\n",
+"for i=2:7\n",
+"    pi(i)=-1/(4+pi(i-1))\n",
+"    qi(i)=((6/h^2)*(yi(i+1)-2*yi(i)+yi(i-1))-qi(i-1))/(4+pi(i-1))\n",
+"end\n",
+"si2(8)=0;\n",
+"si2(1)=0;si1(8)=0;\n",
+"si1(1)=0;\n",
+"for i=7:-1:2\n",
+"    si2(i)=pi(i)*si2(i+1)+qi(i)\n",
+"end\n",
+"for i=2:8\n",
+"    si1(i)=si1(i-1)+h*(si2(i)+si2(i-1))/2\n",
+"end\n",
+"printf('\n i\t xi\t fi\t   pi\t\t   qi\t\t  si2\t\t  si1')\n",
+"printf('\n---------------------------------------------------------------------------------')\n",
+"for i=1:8\n",
+"    printf('\n %i\t%g\t%g\t%f\t%f\t%f\t%f',i,xi(i),yi(i),pi(i),qi(i),si2(i),si1(i))\n",
+"end\n",
+"x=0.1325;\n",
+"i=4;\n",
+"s=yi(i)+(x-xi(i))*si1(i)+(si2(i)*(x-xi(i))^2)/2+((si2(i+1)-si2(i))/(xi(i+1)-xi(i)))*((x-xi(i))^3)/6\n",
+"printf('\n\nSpline Interpolated Value of s(0.1325) is : %f',s)"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/13-Numerical_Differentiation.ipynb b/Numerical_Methods_Principles_by_Analysis/13-Numerical_Differentiation.ipynb
new file mode 100644
index 0000000..7c54b30
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/13-Numerical_Differentiation.ipynb
@@ -0,0 +1,398 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 13: Numerical Differentiation"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.1: Differentiation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.1\n",
+"//Differentiation\n",
+"//Page no. 420\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=x^2+5')\n",
+"deff('y=f1(x,h)','y=(f(x+h)-f(x))/h')\n",
+"h=0.01;x=2.4\n",
+"d=f1(x,h)\n",
+"d1=(f1(x+h,h)-f1(x))/h\n",
+"printf('dy\n -- = %g\n dx',d)\n",
+"printf('\n\n\n d2y\n --- = %g\n dx2',d1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.2: Calculation_of_x_coordinate_of_Minimum_Point.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.2\n",
+"//Calculation of x-coordinate of Minimum Point \n",
+"//Page no. 422\n",
+"clc;close;clear;\n",
+"\n",
+"for i=1:7\n",
+"    for j=1:6\n",
+"        z(i,j)=0\n",
+"    end\n",
+"end\n",
+"h=0.2\n",
+"printf('    x       y           d          d2        d3         d4\n')\n",
+"printf('--------------------------------------------------------------')\n",
+"for i=1:7\n",
+"    z(i,1)=i/5;\n",
+"end\n",
+"z(1,2)=2.10022\n",
+"z(2,2)=1.98730\n",
+"z(3,2)=1.90940\n",
+"z(4,2)=1.86672\n",
+"z(5,2)=1.85937\n",
+"z(6,2)=1.88755\n",
+"z(7,2)=1.95147\n",
+"for i=3:6\n",
+"    for j=1:9-i\n",
+"        z(j,i)=z(j+1,i-1)-z(j,i-1)\n",
+"    end\n",
+"end\n",
+"disp(z)\n",
+"\n",
+"s=poly(0,'s')\n",
+"p=z(5,2);k=4;\n",
+"for i=3:5\n",
+"    r=1;\n",
+"    for j=1:i-2\n",
+"        r=r*(s+(j-1))\n",
+"    end\n",
+"    r=r*z(k,i)/factorial(j);\n",
+"    k=k-1;\n",
+"    p=p+r;\n",
+"    \n",
+"end\n",
+"disp(p)\n",
+"s=(-z(4,3)+z(3,4)/2)/z(3,4)\n",
+"disp(s,'s=')\n",
+"x=z(5,1)+s*h\n",
+"disp(x,'x=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.3: Newton_Forward_Difference_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.3\n",
+"//Newton's Forward Difference Formula\n",
+"//Page no. 423\n",
+"clc;close;clear;\n",
+"printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\n')\n",
+"printf('------------------------------------------------------------------------------------------')\n",
+"h=0.05;\n",
+"z=[1.00,1.00000;1.05,1.02470;1.10,1.04881;1.15,1.07238;1.20,1.09544;1.25,1.11803;1.30,1.14018]\n",
+"deff('y=f1(x,s)','y=(z(x,3)+(s-1/2)*z(x,4)+z(x,5)*(3*s^2-6*s+2)/6)/h')\n",
+"deff('y=f2(x,s)','y=(z(x,4)+z(x,5)*(s-1))/h^2')\n",
+"deff('y=f3(x,s)','y=z(x,5)/h^3')\n",
+"for i=3:6\n",
+"    for j=1:9-i\n",
+"        z(j,i)=z(j+1,i-1)-z(j,i-1)\n",
+"    end\n",
+"end\n",
+"printf('\n')\n",
+"for i=1:7\n",
+"    for j=1:6\n",
+"        if z(i,j)==0 then\n",
+"            printf(' \t')\n",
+"        else\n",
+"            printf('%.7f\t',z(i,j))\n",
+"        end\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"s=poly(0,'s')\n",
+"p=z(5,2);k=4;\n",
+"for i=3:5\n",
+"    r=1;\n",
+"    for j=1:i-2\n",
+"        r=r*(s+(j-1))\n",
+"    end\n",
+"    r=r*z(k,i)/factorial(j);\n",
+"    k=k-1;\n",
+"    p=p+r;\n",
+"    \n",
+"end\n",
+"disp(p,'y(s) = ')\n",
+"printf('\n\ny1(1) = %g',f1(1,0))\n",
+"printf('\n\ny2(1) = %g',f2(1,0))\n",
+"printf('\n\ny3(1) = %g',f3(1,0))\n",
+"printf('\n\ny1(1.025) = %g',f1(1,0.5))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.4: Newton_Backward_Difference_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.4\n",
+"//Newton's Backward Difference Formula\n",
+"//Page no. 425\n",
+"clc;close;clear;\n",
+"printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\n')\n",
+"printf('------------------------------------------------------------------------------------------')\n",
+"h=0.02;\n",
+"z=[0.96,1.8025;0.98,1.7939;1.00,1.7851;1.02,1.7763;1.04,1.7673];\n",
+"deff('y=f1(x,s)','y=(z(x,3)+(s+1/2)*z(x,4))/h')\n",
+"for i=3:6\n",
+"    for j=1:7-i\n",
+"        z(j,i)=z(j+1,i-1)-z(j,i-1)\n",
+"    end\n",
+"end\n",
+"printf('\n')\n",
+"for i=1:5\n",
+"    for j=1:6\n",
+"        if z(i,j)==0 then\n",
+"            printf(' \t')\n",
+"        else\n",
+"            printf('%.7f\t',z(i,j))\n",
+"        end\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\ny1(1) = %g',f1(2,0))\n",
+"printf('\n\ny1(1.03) = %g',f1(4,0.5))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.5: Stirlings_Central_Difference_Derivatives.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.5\n",
+"//Stirlings Central Difference Derivatives\n",
+"//Page no. 426\n",
+"clc;close;clear;\n",
+"printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\n')\n",
+"printf('---------------------------------------------------------------------------')\n",
+"h=0.01;s=0.5;\n",
+"deff('y=f1(x,s)','y=((z(x,3)+z(x-1,3))/2+s*z(x-1,4)+(z(x-1,5)+z(x-2,5))*(3*s^2-1)/12)/h')\n",
+"deff('y=f2(x,s)','y=(z(x-1,4))/h^2')\n",
+"deff('y=f3(x,s)','y=(z(x-1,5)+z(x-2,5))/(2*h^3)')\n",
+"z=[1.00,1.00000;1.01,1.00499;1.02,1.00995;1.03,1.01489;1.04,1.01980;1.05,1.02470;1.06,1.02956;1.07,1.03441;1.08,1.03923;1.09,1.04403;1.10,1.04881;1.11,1.05357;1.12,1.05830;1.13,1.06301;1.14,1.06771;1.15,1.07238;1.16,1.07703];\n",
+"for i=3:5\n",
+"    for j=1:19-i\n",
+"        z(j,i)=z(j+1,i-1)-z(j,i-1)\n",
+"    end\n",
+"end\n",
+"printf('\n')\n",
+"for i=1:17\n",
+"    for j=1:5\n",
+"        if z(i,j)==0 then\n",
+"            printf(' \t')\n",
+"        else\n",
+"            printf('%.7f\t',z(i,j))\n",
+"        end\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\ny1(1.125) = %g   (exact value = 0.4771404)',f1(13,0.5))\n",
+"printf('\n\ny2(1.125) = %g   (exact value = -0.20951)',f2(13,0.5))\n",
+"printf('\n\ny3(1.125) = %g   (exact value = 0.27935)',f3(13,0.5))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.6: Extrapolatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.6\n",
+"//Extrapolation\n",
+"//Page no. 430\n",
+"clc;close;clear;\n",
+"x=[-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8];\n",
+"y=[0.2019,0.30119,0.44933,0.67032,1,1.49182,2.22554,3.32012,4.95303]\n",
+"for i=1:4\n",
+"    printf('\nh = %g\n',x(10-i))\n",
+"    y1=(y(10-i)-y(i))/(2*x(10-i))\n",
+"    printf('f1(0) = %g\n\n',y1)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.7: Richardson_Extrapolation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.7\n",
+"//Richardson Extrapolation\n",
+"//Page no. 431\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=exp(2*x)')\n",
+"e=10^-4;h=0.8;\n",
+"D1=0;\n",
+"for i=1:4\n",
+"    printf('\n')\n",
+"    for j=1:i\n",
+"        if j==1 then\n",
+"            D(i,j)=(f(h)-f(-h))/(2*h)\n",
+"        else\n",
+"            D(i,j)=D(i,j-1)+(D(i,j-1)-D(i-1,j-1))/(2^(2*(j-1))-1)\n",
+"        end\n",
+"        printf('%g\t\t',D(i,j))\n",
+"    end\n",
+"    h=h/2\n",
+"end\n",
+"printf('\n\n\t\t\t\t\t\t  2x\nHence, the derivative of the function y = f(x) = e   at x=0 is D(3,3) = %g',D(i,j))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 13.8: Applicatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 13.8\n",
+"//Application\n",
+"//Page no. 433\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=2/x^2')\n",
+"a=1;b=2;a1=1;b1=0;\n",
+"N=4;\n",
+"h=(b-a)/(N+1);\n",
+"for j=1:N\n",
+"    s(j)=f(a+j*h)\n",
+"end\n",
+"for i=1:N\n",
+"    for j=1:N\n",
+"        if abs(i-j)==1 then\n",
+"            A(i,j)=-1\n",
+"        end\n",
+"        if i==j then\n",
+"            A(i,j)=2+s(i)*h^2\n",
+"        end\n",
+"    end\n",
+"    if i==1 then\n",
+"        k(i,1)=s(i)+a1/h^2\n",
+"    elseif i==N\n",
+"        k(i,1)=s(i)+b1/h^2\n",
+"    else\n",
+"        k(i,1)=s(i)\n",
+"    end\n",
+"end\n",
+"disp(A,'A = ')\n",
+"disp(k,'k = ')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/14-Numerical_Integration.ipynb b/Numerical_Methods_Principles_by_Analysis/14-Numerical_Integration.ipynb
new file mode 100644
index 0000000..a8bb9cc
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/14-Numerical_Integration.ipynb
@@ -0,0 +1,587 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 14: Numerical Integration"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.10: Spline_Integration_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.10\n",
+"//Spline Integration Method\n",
+"//Page no. 478\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=sind(%pi*x)')\n",
+"deff('y=f1(x,h)','y=(f(x+h)-f(x))/h')\n",
+"h=0.01;\n",
+"n=2;h=0.5;a=0;b=1;\n",
+"disp(integrate('f(x)','x',0,1),'I = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.11: Trapezoidal_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.1\n",
+"//Trapezoidal Rule\n",
+"//Page no 440\n",
+"clc;clear;close;\n",
+"x1=1.46\n",
+"for i=1:6\n",
+"    x(1,i)=x1+i/100\n",
+"end\n",
+"y=[3.86,3.90,3.96,4.02,4.06,4.12]\n",
+"\n",
+"//trapezoidal rule\n",
+"S=0;\n",
+"h=(x(6)-x1)/6\n",
+"for i=1:6\n",
+"    if(i==1 | i==6)\n",
+"        S=S+y(i)\n",
+"    else\n",
+"        S=S+2*y(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/2\n",
+"printf('\n I = %g',S)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.14: Trapezoidal_and_Simpsons_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.14\n",
+"//Trapezoidal and Simpsons Rule\n",
+"//Page no. 486\n",
+"clc;close;clear;\n",
+"\n",
+"x(1)=0.5;y(1)=0.5;h=0.25\n",
+"for i=2:3\n",
+"    x(i)=x(i-1)+h\n",
+"    y(i)=y(i-1)+h\n",
+"end\n",
+"printf(' y/x\t|\t%g\t%g\t%g',x(1),x(2),x(3))\n",
+"printf('\n--------|---------------------------')\n",
+"for i=1:3\n",
+"     printf('\n%g\t|\t',y(i))\n",
+"    for j=1:3\n",
+"        z(i,j)=x(j)*y(i)\n",
+"        printf('%g\t',z(i,j))\n",
+"    end\n",
+"end\n",
+"\n",
+"//trapezoidal rule\n",
+"s=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if i==1 & j==1 then\n",
+"            s=s+z(i,j)\n",
+"        elseif i==3 & j==3\n",
+"            s=s+z(i,j)\n",
+"        else\n",
+"            s=s+2*z(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"s=(s*(h^2))/4\n",
+"printf('\n\n')\n",
+"disp(s,'Trapezoidal Rule Sum = ')\n",
+"printf('\n\n')\n",
+"//simpsons rule\n",
+"s=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if i/2-int(i/2)==0 & j/2-int(j/2)==0 then\n",
+"            s=s+16*z(i,j)\n",
+"        elseif i/2-int(i/2)~=0 & j/2-int(j/2)~=0\n",
+"            s=s+z(i,j)\n",
+"        else\n",
+"            s=s+4*z(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"s=(s*(h^2))/9\n",
+"disp(s,'Simpsons Rule Sum = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.15: Trapezoidal_and_Simpsons_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.15\n",
+"//Trapezoidal and Simpsons Rule\n",
+"//Page no. 487\n",
+"clc;close;clear;\n",
+"\n",
+"x(1)=0;y(1)=0;h=0.25\n",
+"for i=2:5\n",
+"    x(i)=x(i-1)+h\n",
+"    y(i)=y(i-1)+h\n",
+"end\n",
+"printf(' y/x\t|\t%g\t%g\t%g\t%g\t%g',x(1),x(2),x(3),x(4),x(5))\n",
+"printf('\n--------|-------------------------------------------')\n",
+"for i=1:5\n",
+"     printf('\n%g\t|\t',y(i))\n",
+"    for j=1:5\n",
+"        z(i,j)=x(j)*y(i)\n",
+"        printf('%g\t',z(i,j))\n",
+"    end\n",
+"end\n",
+"\n",
+"//trapezoidal rule\n",
+"s=0;\n",
+"for i=1:5\n",
+"    for j=1:5\n",
+"        if i==1 & j==1 then\n",
+"            s=s+z(i,j)\n",
+"        elseif i==5 & j==5\n",
+"            s=s+z(i,j)\n",
+"        else\n",
+"            s=s+2*z(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"s=(s*(h^2))/4\n",
+"printf('\n\n')\n",
+"disp(s,'Trapezoidal Rule Sum = ')\n",
+"printf('\n\n')\n",
+"\n",
+"//simpsons rule\n",
+"s=0;\n",
+"for i=1:5\n",
+"    for j=1:5\n",
+"        if i/2-int(i/2)==0 & j/2-int(j/2)==0 then\n",
+"            if i==j then\n",
+"                s=s+16*z(i,j)\n",
+"            else\n",
+"                s=s+4*z(i,j)\n",
+"            end\n",
+"            \n",
+"        elseif i/2-int(i/2)~=0 & j/2-int(j/2)~=0\n",
+"            s=s+z(i,j)\n",
+"        else\n",
+"            s=s+4*z(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"s=(s*(h^2))/9\n",
+"disp(s,'Simpsons Rule Sum = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.16: Multiple_Integration_with_Variable_Limits.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.16\n",
+"//Multiple Integration with Variable Limits\n",
+"//Page no. 491\n",
+"clc;close;clear;\n",
+"\n",
+"deff('z=f(x)','z=x+1')\n",
+"deff('z=f1(y)','z=(y+1)^3*(y+3)^2')\n",
+"s=5/9*f(-sqrt(3/5))+8/9*f(0)+5/9*f(sqrt(3/5))\n",
+"s=s*5/9*f1(-sqrt(3/5))+8/9*f1(0)+5/9*f1(sqrt(3/5))\n",
+"s=s/256;\n",
+"disp(s,'I = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.18: Integration.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.18\n",
+"//Integration\n",
+"//Page no. 494\n",
+"clc;close;clear;\n",
+"\n",
+"s=integrate('x^2*sin(x^2)','x',0,1)\n",
+"disp(s,'I = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.19: Integration.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.19\n",
+"//Integration\n",
+"//Page no. 494\n",
+"clc;close;clear;\n",
+"\n",
+"s=integrate('sin(t)/t','t',1,999)\n",
+"disp(s,'I = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.2: Simpsons_1_3rd_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.2\n",
+"//Simpsons 1/3rd Rule\n",
+"//Page no 442\n",
+"clc;clear;close;\n",
+"x(1,1)=0\n",
+"for i=2:9\n",
+"\n",
+"    x(1,i)=x(1,1)+(i-1)*10\n",
+"end\n",
+"y=[30,31.63,33.44,35.47,37.75,40.33,43.29,46.69,50.67]\n",
+"\n",
+"//trapezoidal rule\n",
+"S=0;\n",
+"h=(x(9)-x(1))/8\n",
+"for j=1:9\n",
+"    S=0;\n",
+"    for i=1:j\n",
+"        if(i==1 | i==j)\n",
+"            S=S+y(i)\n",
+"        else\n",
+"            S=S+2*y(i)\n",
+"        end\n",
+"    end\n",
+"    S=S*h/2\n",
+"    printf('\n Velocity at t (%i) = %.2f',x(j),S)\n",
+"    y1(j)=S\n",
+"end\n",
+"\n",
+"y1(1)=0;\n",
+"//Simpsons 1/3rd Rule\n",
+"S=0;\n",
+"h=(x(9)-x(1))/8\n",
+"for i=1:9\n",
+"    if(i==1 | i==9)\n",
+"        S=S+y1(i)\n",
+"    elseif(((i)/2)-fix((i)/2)==0)\n",
+"        S=S+4*y1(i)\n",
+"    else\n",
+"        S=S+2*y1(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/3;\n",
+"S=S/1000\n",
+"printf('\n\nSimpsons 1/3rd Rule Sum = %g km',S)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.3: Trapezoidal_Rule_and_Simpsons_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.3\n",
+"//Trapezoidal Rule and Simpsons Rule\n",
+"//Page no. 442\n",
+"clc;close;clear;\n",
+"n=2;a=0;b=1;\n",
+"h=(b-a)/n\n",
+"deff('y=f(x)','y=1/(1+x)')\n",
+"for i=0:2\n",
+"    x(i+1)=i/2;\n",
+"    y(i+1)=f(x(i+1))\n",
+"end\n",
+"printf('xi\t ')\n",
+"for i=1:3\n",
+"    printf('%g\t ',x(i))\n",
+"end\n",
+"printf('\n yi\t')\n",
+"for i=1:3\n",
+"    printf('1/%g\t',1+(i-1)/2)\n",
+"end\n",
+"\n",
+"//trapezoidal rule\n",
+"S=0;\n",
+"for i=1:3\n",
+"    if(i==1 | i==3)\n",
+"        S=S+y(i)\n",
+"    else\n",
+"        S=S+2*y(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/2\n",
+"printf('\n\nTrapezoidal Rule Sum = %g',S)\n",
+"\n",
+"//Simpsons 1/3rd Rule\n",
+"S=0;\n",
+"for i=1:3\n",
+"    if(i==1 | i==3)\n",
+"        S=S+y(i)\n",
+"    elseif(((i)/2)-fix((i)/2)==0)\n",
+"        S=S+4*y(i)\n",
+"    else\n",
+"        S=S+2*y(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/3\n",
+"printf('\n\nSimpsons 1/3rd Rule Sum = %g',S)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.5: Romberg_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.5\n",
+"//Romberg Method\n",
+"//Page no. 457\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=1/(1+x)')\n",
+"\n",
+"h=[0.5,0.25,0.125]\n",
+"for k=1:3\n",
+"    for i=0:h(k):1\n",
+"        x(i/h(k)+1)=i;\n",
+"        y(i/h(k)+1)=f(x(i/h(k)+1))\n",
+"    end\n",
+"    n=1+(1/h(k))\n",
+"    //trapezoidal rule\n",
+"    S=0;\n",
+"     for i=1:n\n",
+"        if(i==1 | i==n)\n",
+"            S=S+y(i)\n",
+"        else\n",
+"            S=S+2*y(i)\n",
+"        end\n",
+"    end\n",
+"    S=S*h(k)/2\n",
+"    printf('\n\nI(%g) = %g',h(k),S)\n",
+"    z(2*k-1,1)=S\n",
+"end\n",
+"for i=2:3\n",
+"    for k=1:4-i\n",
+"    z(k*2+i-2,i)=z(2*k-1+i,i-1)+(z(2*k-1+i,i-1)-z(2*k-3+i,i-1))/3\n",
+"end\n",
+"end\n",
+"\n",
+"printf('\n\n')\n",
+"disp(z,'The Table of values:')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.7: Gaussian_Quadrature_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.7\n",
+"//Gaussian Quadrature Formula\n",
+"//Page no. 463\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=cos(x)*log(x)')\n",
+"s=0;\n",
+"for i=0:2:2000\n",
+"    s=s+integrate('((-1)^(i/2))*(x^i)/factorial(i)*log(x)','x',0,1)\n",
+"end\n",
+"disp(s,'Till 1000 terms .... I =')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.8: Gauss_Legendre_Two_Point_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.8\n",
+"//Gauss Legendre Two Point Rule\n",
+"//Page no. 472\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=1/(x+3)')\n",
+"s=integrate('f(x)','x',-1,1)\n",
+"printf('By Direct Method, I = %g',s)\n",
+"s=f(-1/sqrt(3))+f(1/sqrt(3))\n",
+"printf('\n\n By Gauss-Legendre 2 point rule, I = %g',s)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 14.9: Gauss_Legendre_Three_Point_Rule.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 14.9\n",
+"//Gauss Legendre Three Point Rule\n",
+"//Page no. 473\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=1/(x+3)')\n",
+"s=integrate('f(x)','x',-1,1)\n",
+"printf('By Direct Method, I = %g',s)\n",
+"s=5/9*f(-sqrt(3/5))+8/9*f(0)+5/9*f(sqrt(3/5))\n",
+"printf('\n\n By Gauss-Legendre 3 point rule, I = %g',s)"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/15-Numerical_Solutions_of_Ordinary_Differential_Equations_Initial_Value_Problem.ipynb b/Numerical_Methods_Principles_by_Analysis/15-Numerical_Solutions_of_Ordinary_Differential_Equations_Initial_Value_Problem.ipynb
new file mode 100644
index 0000000..6ec0ca2
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/15-Numerical_Solutions_of_Ordinary_Differential_Equations_Initial_Value_Problem.ipynb
@@ -0,0 +1,948 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 15: Numerical Solutions of Ordinary Differential Equations Initial Value Problem"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.10: Heun_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.10\n",
+"//Heun Method\n",
+"//Page no. 517\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=y*2/x')\n",
+"y=2;\n",
+"h=0.25;\n",
+"for i=1:4\n",
+"    x=1+(i-1)*h\n",
+"    x1=x+h\n",
+"    ye=y+h*f(x,y)\n",
+"    y=y+h*(f(x,y)+f(x1,ye))/2\n",
+"    printf('\n  y(%g) = %g\n',x1,y)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.11: Midpoint_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.11\n",
+"//Midpoint Method\n",
+"//Page no. 518\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=y+x')\n",
+"y=1;\n",
+"h=0.2;\n",
+"printf('i\txi\tyi\tslope1\tslope2\ty(i+1)\n-----------------------------------------------\n')\n",
+"for i=1:3\n",
+"    x=(i-1)*h\n",
+"    s1=f(x,y);\n",
+"    s2=f(x+h/2,y+s1*h/2);\n",
+"    printf(' %i\t%g\t%g\t%g\t%g',i-1,x,y,s1,s2)\n",
+"    y=y+s2*h;\n",
+"    printf('\t%g\n',y)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.12: Modified_Midpoint_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.12\n",
+"//Modified Midpoint Method\n",
+"//Page no. 519\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=y+x')\n",
+"y=1;\n",
+"h=0.2;\n",
+"Z(1)=y;\n",
+"Z(2)=Z(1)+h*f(0,Z(1))\n",
+"printf('Z(%i) = %g',1,Z(2))\n",
+"for i=2:5\n",
+"    x=(i-1)*h;\n",
+"    Y(i-1)=(Z(i)+Z(i-1)+h*f(x,Z(i)))/2\n",
+"    Z(i+1)=Z(i-1)+2*h*f(x,Z(i))\n",
+"    printf('\n Y(%i) = %g\n\n\n Z(%i) = %g',i-1,Y(i-1),i,Z(i+1))\n",
+"end\n",
+"printf('\n\n\n y4 = %g',(4*Y(4)-Y(2))/3)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.13: Single_Step_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.13\n",
+"//Single Step Method\n",
+"//Page no. 521\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^2')\n",
+"deff('y=f1(x)','y=1/(1-x)')\n",
+"y=1;h=0.2;\n",
+"printf('n\tXn\tYn (by single-step method)\tYn (computed)\n-----------------------------------------------------------------\n')\n",
+"for i=1:6\n",
+"    x=(i-1)*h\n",
+"    if i<6 then\n",
+"        printf(' %i\t%.2f\t%.5f\t\t\t\t%.5f\n',i-1,x,y,f1(x))\n",
+"    else\n",
+"        printf(' %i\t%.2f\t%.5f\t\t\t\t \n',i-1,x,y)\n",
+"    end\n",
+"    y=y+h*f(y);\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.14: Second_Order_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.14\n",
+"//Second Order Runge Kutta Method\n",
+"//Page no. 525\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;\n",
+"//simple runge kutta method\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h,y+K1);\n",
+"y1=y+(K1+K2)/2\n",
+"printf('\ny(1.1) by simple runge kutta method = %g\n\n',y1)\n",
+"\n",
+"//euler cauchy method\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/2,y+K1/2);\n",
+"y1=y+(K1+K2)\n",
+"printf('y(1.1) by euler cauchy method = %g\n\n',y1)\n",
+"\n",
+"//optimal method\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+2*h/3,y+2*K1/3);\n",
+"y1=y+(K1+3*K2)/4\n",
+"printf('y(1.1) by optimal method = %g',y1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.15: Third_Order_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.15\n",
+"//Third Order Runge Kutta Method\n",
+"//Page no. 526\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;\n",
+"//scheme 1\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/2,y+K1/2);\n",
+"K3=h*f(x+h/2,y-K1+2*K2);\n",
+"y1=y+(K1+4*K2+K3)/6\n",
+"printf('\ny(1.1) by scheme 1 = %g\n\n',y1)\n",
+"\n",
+"//scheme 2\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/3,y+K1/3);\n",
+"K3=h*f(x+2*h/3,y+2*K2/3);\n",
+"y1=y+(K1+3*K3)/4\n",
+"printf('\ny(1.1) by scheme 2 = %.7f\n\n',y1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.16: Fourth_Order_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.16\n",
+"//Fourth Order Runge Kutta Method\n",
+"//Page no. 528\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/2,y+K1/2);\n",
+"K3=h*f(x+h/2,y+K2/2);\n",
+"K4=h*f(x+h,y+K3);\n",
+"disp(K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')\n",
+"y1=y+(K1+2*K2+2*K3+K4)/6\n",
+"printf('\ny(1.1) = %.8f\n\n',y1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.17: New_Variant_of_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.17\n",
+"//New Variant of Runge Kutta Method\n",
+"//Page no. 530\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/2,y+K1/2);\n",
+"K3=h*f(x+h/2,y+K2/2);\n",
+"K4=h*f(x+h,y+K3);\n",
+"K5=h*f(x+3*h/4,y+(5*K1+7*K2+13*K3-K4)/32)\n",
+"disp(K5,'K5 =',K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')\n",
+"y1=y+(K1+2*K2+2*K3+K5)/6\n",
+"printf('\ny(1.1) = %.8f\n\n',y1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.18: Runge_Kutta_Merson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.18\n",
+"//Runge Kutta Merson Method\n",
+"//Page no. 532\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x+y')\n",
+"y=1;x=0;h=0.1;\n",
+"printf('n\t Xn\t Yn\t K1\t K2\t K3\t K4\t K5\tY(n+1)\n----------------------------------------------------------------------')\n",
+"for i=0:14\n",
+"    K1=h*f(x,y);\n",
+"K2=h*f(x+h/3,y+K1/3);\n",
+"K3=h*f(x+h/3,y+(K1+K2)/6);\n",
+"K4=h*f(x+h/2,y+(K1+3*K3)/8);\n",
+"K5=h*f(x+h,y+(K1-3*K3+4*K4)/2)\n",
+"y1=y+(K1+4*K4+K5)/6\n",
+"printf('\n %i\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f',i,x,y,K1,K2,K3,K4,K5,y1)\n",
+"y=y1;\n",
+"x=x+h;\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.19: Runge_Kutta_Fehlberg_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.19\n",
+"//Runge Kutta Fehlberg Method\n",
+"//Page no. 535\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;\n",
+"K1=h*f(x,y);\n",
+"K2=h*f(x+h/4,y+K1/4);\n",
+"K3=h*f(x+3*h/8,y+3*(K1+3*K2)/32);\n",
+"K4=h*f(x+12*h/13,y+1932*K1/2197-7200*K2/2197+7296*K3/2197);\n",
+"K5=h*f(x+h,y+439*K1/216-8*K2+3680*K3/513-845*K4/4104)\n",
+"K6=h*f(x+h/2,y-8*K1/27+2*K2-3544*K3/2565+1859*K4/4104-11*K5/40)\n",
+"disp(K6,'K6 =',K5,'K5 =',K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')\n",
+"y1=y+(25*K1/216+1408*K3/2565+2197*K4/4104-K5/5)\n",
+"y11=y+(16*K1/135+6656*K3/12825+28561*K4/56430-9*K5/50+2*K6/55)\n",
+"printf('\ny(1.1) = %.9f\n\n',y1)\n",
+"printf('\ny~(1.1) = %.9f\n\n',y11)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.1: Ordinary_Differential_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.1\n",
+"//Ordinary Differential Equation\n",
+"//Page no. 503\n",
+"clc;clear;close;\n",
+"s=log(2)/log(1.02)\n",
+"disp(s,'Time Taken = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.20: Carp_Karp_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.20\n",
+"//Carp Karp Runge Kutta Method\n",
+"//Page no. 537\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;printf('\n')\n",
+"U=[0,1/5,3/10,3/5,1,7/8];\n",
+"v=[0,0,0,0,0;1/5,0,0,0,0;3/40,9/40,0,0,0;3/10,-9/10,6/5,0,0;-11/54,5/2,-70/27,35/27,0;1631/55296,175/512,575/13824,44275/110592,253/4096];\n",
+"a=[37/378,0,250/621,125/594,0,512/1771];\n",
+"a1=[2825/27648,0,18575/48384,13525/55296,277/14336,1/4];\n",
+"for l=1:5\n",
+"    K(1)=h*f(x,y);\n",
+"for i=2:6\n",
+"    k=0;\n",
+"    for j=1:i-1\n",
+"        k=k+v(i,j)*K(j)\n",
+"    end\n",
+"    K(i)=h*f(x+U(i)*h,y+k)\n",
+"end\n",
+"k=0;\n",
+"for i=1:6\n",
+"    k=k+a(i)*K(i)\n",
+"end\n",
+"y1=y+k;\n",
+"k=0;\n",
+"for i=1:6\n",
+"    k=k+a1(i)*K(i)\n",
+"end\n",
+"y11=y+k;\n",
+"for i=1:6\n",
+"    printf('K%i = %.9f\n',i,K(i))\n",
+"end\n",
+"printf('\ny(1.1) = Y%i = %.9f\n',l,y1)\n",
+"printf('y~(1.1) = Y%i~ = %.9f\n',l,y11)\n",
+"y=y1;\n",
+"printf('\n\n\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.21: Implicit_Runge_Kutta_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.21\n",
+"//Implicit Runge Kutta Method\n",
+"//Page no. 539\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x-y')\n",
+"y=1;x=1;h=0.1;printf('\n')\n",
+"U=[0,1/5];\n",
+"v=[0,0;1/2,1/2];\n",
+"a2=1;\n",
+"K(1)=h*f(x,y);\n",
+"K(2)=(x+h/2-y-K(1)/2)/(1/h-1/2)\n",
+"y1=y+(K(1)+a2*K(2))\n",
+"printf('\ny(1.1) = %.9f\n\n',y1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.22: Linear_Multi_Step_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.22\n",
+"//Linear Multi Step Method\n",
+"//Page no. 540\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x+y')\n",
+"y(1)=1;y(2)=1;x(1)=0;h=0.1;\n",
+"printf('n\tXn\t\tYn\t\tfn\n-----------------------------------------------\n 0\t%g\t\t%.3f\t\t%.3f\n',x(1),y(1),f(x(1),y(1)));\n",
+"for i=2:11\n",
+"    x(i)=(i-1)*h;\n",
+"    y(i+1)=(-y(i)-y(i-1)+h*(f(x(i),y(i))+f(x(i-1),y(i-1))))/2;\n",
+"    printf(' %i\t%.3f\t\t%.3f\t\t%.3f\n',i-1,x(i),y(i),f(x(i),y(i)))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.23: Milne_Simpson_Predictor_Corrector_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.23\n",
+"//Milne Simpson Predictor Corrector Method\n",
+"//Page no. 544\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=y+exp(x)')\n",
+"h=0.5;\n",
+"y=[1,1.824,3.718,7.722]\n",
+"for i=1:4\n",
+"    x=(i-1)*h;\n",
+"    f1(i)=f(x,y(i));\n",
+"    printf('\nf%i = %g',i-1,f1(i))\n",
+"end\n",
+"y41=y(1)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3\n",
+"f4=f(x+h,y41);\n",
+"y4=y(3)+h*(f4+4*f1(4)+f1(3))/3\n",
+"printf('\n\n\nPredictor = %.9f\n\n',y41)\n",
+"printf('Evaluator = %.9f\n\n',f4)\n",
+"printf('Corrector = %.9f',y4)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.24: Improved_Milne_Simpson_Predictor_Corrector_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.24\n",
+"//Improved Milne Simpson Predictor Corrector Method\n",
+"//Page no. 546\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x,y)','y=y-x^2')\n",
+"y(1)=1;h=0.25;x=0;\n",
+"printf('n\tXn\tYn\tfn\tY`n\tYn\tY`n+1\tm(n+1)\tv(n+1)\n------------------------------------------------------------------------\n')\n",
+"f1(1)=f(x,y(1));\n",
+"for i=1:3\n",
+"    K1=h*f(x,y(i));\n",
+"    K2=h*f(x+2*h/3,y(i)+2*K1/3);\n",
+"    y(i+1)=y(i)+(K1+3*K2)/4\n",
+"    printf(' %i\t%.3f\t%.3f\t%.3f\n',i-1,x,y(i),f1(i))\n",
+"    x=x+h\n",
+"    f1(i+1)=f(x,y(i+1))\n",
+"end\n",
+"Y31=0\n",
+"for i=3:10\n",
+"    Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3      //predictor\n",
+"    m4=Y41+28*(y(i+1)-Y31)/29   //modifier\n",
+"    v4=f(x+h,m4)     //evaluator\n",
+"    Y4=y(i)+h*(v4+4*f1(4)+f1(3))/3       //corrector\n",
+"    printf(' %i\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',i,x,y(i+1),f1(4),Y31,y(i+1),Y41,m4,v4)\n",
+"    y(i+2)=Y4\n",
+"    Y31=Y41;\n",
+"    f1(2)=f1(3);\n",
+"    f1(3)=f1(4);\n",
+"    f1(4)=f(x+h,y(i+2))\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.25: Hamming_Predictor_Corrector_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.25\n",
+"//Hamming Predictor Corrector Method\n",
+"//Page no. 548\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x,y)','y=y-x^2')\n",
+"y(1)=1;h=0.25;x=0;\n",
+"printf('n\tXn\tYn\tfn\tY`n\tYc(n)\tY`n+1\tm(n+1)\tv(n+1)\tYc(n+1)\n-----------------------------------------------------------------------------------------\n')\n",
+"f1(1)=f(x,y(1));\n",
+"for i=1:3\n",
+"    K1=h*f(x,y(i));\n",
+"    K2=h*f(x+2*h/3,y(i)+2*K1/3);\n",
+"    y(i+1)=y(i)+(K1+3*K2)/4\n",
+"    printf(' %i\t%.3f\t%.3f\t%.3f\n',i-1,x,y(i),f1(i))\n",
+"    x=x+h\n",
+"    f1(i+1)=f(x,y(i+1))\n",
+"end\n",
+"Y31=y(4);Yc=0\n",
+"for i=3:10\n",
+"    Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3  //predictor\n",
+"    m4=Y41+112*(Y31-Yc)/121    //modifier\n",
+"    v4=f(x+h,m4)            //evaluator\n",
+"    Y4c=(9*y(i+1)-y(i-1))/8+3*h*(v4+2*f1(4)-f1(3))/8     //corrector\n",
+"    Y4=Y4c+9*(Y41-Y4c)/121        //final value\n",
+"    printf(' %i\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',i,x,y(i+1),f1(4),Y31,Yc,Y41,m4,v4,Y4c)\n",
+"    y(i+2)=Y4\n",
+"    Y31=Y41;\n",
+"    f1(2)=f1(3);\n",
+"    f1(3)=f1(4);\n",
+"    f1(4)=f(x+h,y(i+2))\n",
+"    Yc=Y4c\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.26: Multi_Valued_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.26\n",
+"//Multi Valued Method\n",
+"//Page no. 553\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x,y)','y=2*x^2-y')\n",
+"h=0.1;x=0;y=-1;\n",
+"deff('y=f2(x,y)','y=4*x-f1(x,y)')\n",
+"deff('y=f3(x,y)','y=4-f2(x,y)')\n",
+"B=[1,1,1,1;0,1,2,3;0,0,1,3;0,0,0,1];\n",
+"y0=[y;h*f1(x,y);h^2*f2(x,y)/2;h^3*f3(x,y)/6]\n",
+"y01=y0;\n",
+"r=[0;1;3/4;1/6]\n",
+"\n",
+"disp(r,'If r = ')\n",
+"printf('\n\n-------------------------------------------------------------------------\nx = 0\t\t\tx = 0.1\t\t\t\tx = 0.2\n\t')\n",
+"for i=1:2\n",
+"    y11=B*y01\n",
+"    s(i)=h*(f1(x+h,y11(1)))-y11(2)\n",
+"    y1=y11+s(i)*r\n",
+"    if i==2 then\n",
+"        break\n",
+"    end\n",
+"    y2=y1;\n",
+"    y22=y11;\n",
+"    y01=y1\n",
+"end\n",
+"printf('\t   (s = %.5g)\t\t   (s = %.9f)\n-------------------------------------------------------------------------\n   Y0\t\t   Y`i\t\t   Y1\t\t   Y`2\t\t   Y2\n-------------------------------------------------------------------------\n',s(1),s(2))\n",
+"for i=1:4\n",
+"    printf('%.5f \t%.5f \t%.5f \t%.5f \t%.5f\n',y0(i),y22(i),y2(i),y11(i),y1(i))\n",
+"end\n",
+"y0=[y;h*f1(x,y);h^2*f2(x,y)/2;h^3*f3(x,y)/6]\n",
+"y01=y0;\n",
+"r=[5/12;1;3/4;1/6]\n",
+"disp(r,'If r = ')\n",
+"printf('\n\n-------------------------------------------------------------------------\nx = 0\t\t\tx = 0.1\t\t\t\tx = 0.2\n\t')\n",
+"for i=1:2\n",
+"    y11=B*y01\n",
+"    s(i)=h*(f1(x+h,y11(1)))-y11(2)\n",
+"    y1=y11+s(i)*r\n",
+"    if i==2 then\n",
+"        break\n",
+"    end\n",
+"    y2=y1;\n",
+"    y22=y11;\n",
+"    y01=y1\n",
+"end\n",
+"printf('\t   (s = %.5g)\t\t   (s = %.9f)\n-------------------------------------------------------------------------\n   Y0\t\t   Y`i\t\t   Y1\t\t   Y`2\t\t   Y2\n-------------------------------------------------------------------------\n',s(1),s(2))\n",
+"for i=1:4\n",
+"    printf('%.5f \t%.5f \t%.5f \t%.5f \t%.5f\n',y0(i),y22(i),y2(i),y11(i),y1(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.27: First_order_ODE.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.27\n",
+"//First order ODE\n",
+"//Page no. 558\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x,y1,y2)','y=y1*y2+x')\n",
+"deff('y=f2(x,y1,y2)','y=y1-x')\n",
+"h=0.2;x=0;y1=0;y2=1;\n",
+"//heun method\n",
+"printf('Heun Method:\n\n x\ty1\ty2\n-------------------------\n')\n",
+"Y=[y1;y2]\n",
+"for i=1:8\n",
+"    \n",
+"    F=[f1(x,Y(1),Y(2));f2(x,Y(1),Y(2))]\n",
+"    Y1=Y+h*F\n",
+"    x=x+h;\n",
+"    F1=[f1(x,Y1(1),Y1(2));f2(x,Y1(1),Y1(2))]\n",
+"    Y=Y+(h/2)*(F+F1)\n",
+"    printf(' %g\t%.3f\t%.3f\n',x-h,Y(1),Y(2))\n",
+"    \n",
+"end\n",
+"\n",
+"//classical runge kutta method\n",
+"printf('\n\n\nClassical Runge Kutta Method:\n\n n\tx\tYn\tK1\tK2\tK3\tK4\tY(n+1)\n-----------------------------------------------------------------\n')\n",
+"Y=[y1;y2];x=0;\n",
+"for i=1:6\n",
+"    K1=h*[f1(x,Y(1),Y(2));f2(x,Y(1),Y(2))]\n",
+"    K2=h*[f1(x+h/2,Y(1)+K1(1)/2,Y(2)+K1(2)/2);f2(x+h/2,Y(1)+K1(1)/2,Y(2)+K1(2)/2)]\n",
+"    K3=h*[f1(x+h/2,Y(1)+K2(1)/2,Y(2)+K2(2)/2);f2(x+h/2,Y(1)+K2(1)/2,Y(2)+K2(2)/2)]\n",
+"    K4=h*[f1(x+h,Y(1)+K3(1),Y(2)+K3(2));f2(x+h,Y(1)+K3(1),Y(2)+K3(2))]\n",
+"    Y1=Y+(K1+2*K2+2*K3+K4)/6\n",
+"    printf(' %i\t%.2f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n\t\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n---------------------------------------------------------------\n',i-1,x,Y(1),K1(1),K2(1),K3(1),K4(1),Y1(1),Y(2),K1(2),K2(2),K3(2),K4(2),Y1(2))\n",
+"    Y=Y1;\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.28: Differential_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.28\n",
+"//Differential Equation\n",
+"//Page no. 562\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x,y)','y=2*y^2/(1+x)')\n",
+"h=0.1;z(1)=-1;\n",
+"for i=1:11\n",
+"    printf('\nZ(%g) = %g\n',(i-1)/10,z(i))\n",
+"    z(i+1)=z(i)+h*f((i-1)/10,z(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.6: Taylor_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.6\n",
+"//Taylor Method\n",
+"//Page no. 510\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f1(x,y)','y=x^2+y^2')\n",
+"deff('y=f2(x,y)','y=2*x+2*y*f1(x,y)')\n",
+"deff('y=f3(x,y)','y=2+2*f1(x,y)^2+2*y*f2(x,y)')\n",
+"deff('y=f4(x,y)','y=6*f1(x,y)*f2(x,y)+2*y*f3(x,y)')\n",
+"h=0.2;\n",
+"for l=1:2\n",
+"    a=0;y=0;x=0;\n",
+"    printf('\n---------------\nh = %g\n---------------\n',h)\n",
+"    for i=1:4\n",
+"    x=a+(i-1)*h\n",
+"    k=0;\n",
+"    for j=1:4\n",
+"    if j==1 then\n",
+"        k=k+(h^j)*f1(x,y)/factorial(j)\n",
+"    elseif j==2\n",
+"        k=k+(h^j)*f2(x,y)/factorial(j)\n",
+"    elseif j==3\n",
+"        k=k+(h^j)*f3(x,y)/factorial(j)\n",
+"    else\n",
+"        k=k+(h^j)*f4(x,y)/factorial(j)\n",
+"    end\n",
+"end\n",
+"y=y+k;\n",
+"printf('\nx = %g\n\ny(%g) = %g\n\n',x,x+0.2,y)\n",
+"end\n",
+"h=h+0.2;\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.7: Picard_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.7\n",
+"//Picard Method\n",
+"//Page no. 511\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x^2+y^2')\n",
+"y(1)=0;\n",
+"for i=1:2\n",
+"    y(i+1)=y(1)+integrate('f(x,y(i))','x',0,i/10)\n",
+"    printf('\n y(%g) = %g\n',i/10,y(i+1))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.8: Euler_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.8\n",
+"//Euler Method\n",
+"//Page no. 513\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x+y')\n",
+"y(1)=1;\n",
+"h=0.1;\n",
+"for i=1:6\n",
+"    printf('\ny(%g) = %g\n',(i-1)/10,y(i))\n",
+"    y(i+1)=y(i)+h*f((i-1)/10,y(i))\n",
+"    \n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 15.9: Trapezium_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 15.9\n",
+"//Trapezium Method\n",
+"//Page no. 516\n",
+"clc;clear;close;\n",
+"deff('y=f(x,y)','y=x*y^2')\n",
+"y=1;\n",
+"h=0.2;\n",
+"y2=poly(0,'y2')\n",
+"for i=1:2\n",
+"    x=(i-1)*h;\n",
+"    x1=x+h\n",
+"    y1=roots(-y2+y+h*(f(x,y)+f(x1,y2))/2)\n",
+"    printf('\n  Y(%i) = %g  or  %g\n',i,y1(1),y1(2))\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/16-Numerical_Solutions_of_Ordinary_Differential_Equations_Boundary_Value_Problems.ipynb b/Numerical_Methods_Principles_by_Analysis/16-Numerical_Solutions_of_Ordinary_Differential_Equations_Boundary_Value_Problems.ipynb
new file mode 100644
index 0000000..1b738ec
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/16-Numerical_Solutions_of_Ordinary_Differential_Equations_Boundary_Value_Problems.ipynb
@@ -0,0 +1,397 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 16: Numerical Solutions of Ordinary Differential Equations Boundary Value Problems"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.1: Outline_of_Linear_Shooting_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.1\n",
+"//Outline of Linear Shooting Method\n",
+"//Page no. 572\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=x^2');\n",
+"h=0.5;X0=0;Y0=1;Z1=[-1,-1.5,-1.1771];i=1;Y1=Y0;\n",
+"for j=1:3\n",
+"    Z0=Z1(i);\n",
+"    i=i+1\n",
+"    Y0=1;\n",
+"    for n=1:2\n",
+"        printf('\nFor n = %i\n---------------------------\n',n-1)\n",
+"        K1(1)=h*Z0;\n",
+"        printf('\n K11 = %g',K1(1));\n",
+"        K1(2)=h*f(Y0);\n",
+"        printf('\n K12 = %g',K1(2));\n",
+"        K2=h*f(Y0+K1(2))\n",
+"        printf('\n K22 = %g',K2);\n",
+"        Z0=Z0+(K1(2)+K2)/2\n",
+"        printf('\n Z%i = %g',n,Z0);\n",
+"        K2=h*Z0;\n",
+"        printf('\n K21 = %g',K2);\n",
+"        Y0=Y0+(K1(1)+K2)/2\n",
+"        printf('\n Y%i = %g',n,Y0);\n",
+"        printf('\n\n\n')\n",
+"        if n==1 then\n",
+"            Y2=Y0\n",
+"        end\n",
+"    end\n",
+"    printf('\n\n\n')\n",
+"end\n",
+"printf('Hence the solution is y(%g) = %i, y(%g) = %.4f   and  y(%g) = %.1f',X0,Y1,X0+h,Y2,X0+2*h,Y0)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.2: Linear_Shooting_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.2\n",
+"//Linear Shooting Method\n",
+"//Page no. 576\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')\n",
+"deff('y=F1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')\n",
+"deff('y=F2(x,y,y1)','y=-x*y1+x^2*y')\n",
+"a=0;b=1;\n",
+"y0=1;y1=-1;n=5;\n",
+"h=(b-a)/n\n",
+"y=y0;y01=0;x=a;\n",
+"for i=0:5\n",
+"    yi1(1,i+1)=y\n",
+"    K1=h*y01;\n",
+"    R1=h*F1(x,y,y01);\n",
+"    K2=h*(y+R1/2);\n",
+"    R2=h*F1(x+h/2,y+K1/2,y01+R1/2)\n",
+"    K3=h*(y01+R2/2)\n",
+"    R3=h*F1(x+h/2,y+K2/2,y01+R2/2)\n",
+"    K4=h*(y+R3)\n",
+"    R4=h*F1(x+h,y+K3,y01+R3)\n",
+"    y=y+(K1+2*K2+2*K3+K4)/6\n",
+"    y01=y01+(R1+2*R2+2*R3+R4)/6\n",
+"    x=x+h\n",
+"end\n",
+"y=0;y01=1;x=a;\n",
+"for i=0:5\n",
+"    yi2(1,i+1)=y\n",
+"    K1=h*y01;\n",
+"    R1=h*F2(x,y,y01);\n",
+"    K2=h*(y+R1/2);\n",
+"    R2=h*F2(x+h/2,y+K1/2,y01+R1/2)\n",
+"    K3=h*(y01+R2/2)\n",
+"    R3=h*F2(x+h/2,y+K2/2,y01+R2/2)\n",
+"    K4=h*(y+R3)\n",
+"    R4=h*F2(x+h,y+K3,y01+R3)\n",
+"    y=y+(K1+2*K2+2*K3+K4)/6\n",
+"    y01=y01+(R1+2*R2+2*R3+R4)/6\n",
+"    x=x+h\n",
+"end\n",
+"for i=1:6\n",
+"    yi(i)=yi1(1,i)+((y1-yi1(6))/yi2(6))*yi2(i)\n",
+"end\n",
+"y=1;x=a;y01=y1\n",
+"for i=0:5\n",
+"    yir(1,i+1)=y;\n",
+"    K1=h*y01;\n",
+"    R1=h*f1(x,y,y01);\n",
+"    K2=h*(y+R1/2);\n",
+"    R2=h*f1(x+h/2,y+K1/2,y01+R1/2)\n",
+"    K3=h*(y01+R2/2)\n",
+"    R3=h*f1(x+h/2,y+K2/2,y01+R2/2)\n",
+"    K4=h*(y+R3)\n",
+"    R4=h*f1(x+h,y+K3,y01+R3)\n",
+"    y=y+(K1+2*K2+2*K3+K4)/6\n",
+"    y01=y01+(R1+2*R2+2*R3+R4)/6\n",
+"    x=x+h\n",
+"end\n",
+"x=a;\n",
+"printf('\n   ------------------------------------------------------------------------------------------------------\n\tx')\n",
+"for i=1:6\n",
+"    printf('\t%.1f\t',x)\n",
+"    x=x+h\n",
+"end\n",
+"printf('\n\ty')\n",
+"for i=1:6\n",
+"    printf('\t%.4f\t',yi(i))\n",
+"end\n",
+"printf('\n    by RK')\n",
+"for i=1:6\n",
+"    printf('\t%.4f\t',yir(i))\n",
+"end\n",
+"printf('\n   ------------------------------------------------------------------------------------------------------')\n",
+"printf('\n\n\nNote: Computation error in calculation of values by RK method performed in book')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.3: Multiple_Shooting_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.3\n",
+"//Multiple Shooting Method\n",
+"//Page no. 577\n",
+"clc;close;clear;\n",
+"\n",
+"h=0.25;x=0;y1=0;\n",
+"deff('y=f(x)','y=-(4*h^2)/(1+x)^2')\n",
+"deff('y=f1(x)','y=-2*(1+(h^2)/(1+x)^2)')\n",
+"\n",
+"for i=1:4\n",
+"    x=x+h\n",
+"    B(i)=f(x);\n",
+"    for j=1:4\n",
+"        if i==4 & i==j\n",
+"            A(i,j)=f1(x)+1/4\n",
+"            A(i,j-1)=2\n",
+"        elseif j==i then\n",
+"            A(i,j)=f1(x)\n",
+"            A(i,j+1)=1\n",
+"            if j-1~=0 then\n",
+"                A(i,j-1)=1\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"end\n",
+"y=inv(A)*B\n",
+"disp(B,'B =',A,'A = ')\n",
+"printf('\n\n\n x :')\n",
+"for i=1:5\n",
+"    printf('\t%.2f',x)\n",
+"    x=x+h\n",
+"end\n",
+"x=0;printf('\n y :\t%.2f',y1);\n",
+"for i=1:4\n",
+"    printf('\t%.4f',y(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.4: Finite_Difference_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.4\n",
+"//Finite Difference Method\n",
+"//Page no. 582\n",
+"clc;close;clear;\n",
+"\n",
+"x=0;h=0.25;q=-1;Y(1)=-2;Y(5)=1;\n",
+"printf('\n i\txi\tYi\tpi\tqi\tri\n-----------------------------------------------\n')\n",
+"for i=1:5\n",
+"    r(i)=-x^2\n",
+"    if i>1 & i<5 then\n",
+"        printf(' %i\t%g\t%s\t%g\t%i\t%g\n',i-1,x,'?',x,q,r(i))\n",
+"    else\n",
+"        printf(' %i\t%g\t%g\t%g\t%i\t%g\n',i-1,x,Y(i),x,q,r(i))\n",
+"    end\n",
+"    x=x+h\n",
+"end\n",
+"x=0;\n",
+"printf('-----------------------------------------------\n')\n",
+"for i=1:3\n",
+"    x=x+h\n",
+"    for j=1:3\n",
+"        if i==j then\n",
+"            A(i,j)=2+h^2*q\n",
+"        elseif i<j & abs(i-j)~=2\n",
+"            A(i,j)=-1+h*x/2\n",
+"        elseif i>j & abs(i-j)~=2\n",
+"            A(i,j)=-1-h*x/2\n",
+"        end\n",
+"    end\n",
+"    if i==3 then\n",
+"        B(i)=-h^2*r(i+1)+(-h*x/2+1)*Y(1+2*(i-1))\n",
+"    else\n",
+"        B(i)=-h^2*r(i+1)+(h*x/2+1)*Y(1+2*(i-1))\n",
+"    end\n",
+"    B(i)=(-1)^(i+1)*B(i)\n",
+"end\n",
+"disp(B,'B =',A,'A = ')\n",
+"y=inv(A)*B\n",
+"for i=1:3\n",
+"    Y(i+1)=y(i)\n",
+"end\n",
+"x=0;\n",
+"disp('The Solution is :',B,'B =',A,'A = ')\n",
+"printf(' x :')\n",
+"for i=1:5\n",
+"    printf('\t %.2f',x)\n",
+"    x=x+h\n",
+"end\n",
+"x=0;printf('\n y :');\n",
+"for i=1:5\n",
+"    printf('\t%.3f',Y(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.5: Non_Linear_Problem.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.5\n",
+"//Non Linear Problem\n",
+"//Page no. 584\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=2/(1+x)')\n",
+"Y=[1,0.75,0.75,0.75,0.5];h=0.25\n",
+"A=[-2,1,0;1,-2,1;0,1,-2];A_1=inv(A)\n",
+"disp(A_1,'Inverse of A =',A,'A =')\n",
+"printf('\nThe Solution of the system is: \n\n Iteration\t  Y0\t\t  Y1\t\t  Y2\t\t  Y3\t\t  Y4\n----------------------------------------------------------------------------------------')\n",
+"for i=0:6\n",
+"    printf('\n     %i',i)\n",
+"    for j=1:5\n",
+"        if j<4 & i~=0 then\n",
+"            Y(j+1)=y(j)\n",
+"        end\n",
+"        printf('\t\t%.4f',Y(j))\n",
+"    end\n",
+"    x=0;\n",
+"    for j=1:3\n",
+"        x=x+h\n",
+"        if j~=2 then\n",
+"            B(j)=h^2*f(x)*Y(j+1)^2-Y(1+2*(j-1))\n",
+"        else\n",
+"            B(j)=h^2*f(x)*Y(j+1)^2\n",
+"        end\n",
+"    end\n",
+"    y=A_1*B\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 16.6: Collocation_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 16.6\n",
+"//Collocation Method\n",
+"//Page no. 589\n",
+"clc;close;clear;\n",
+"\n",
+"h1=0.000001;h=0.25;x=0;\n",
+"Y(1)=0;Y(5)=0;\n",
+"deff('y=p(x)','y=1')\n",
+"deff('y=q(x)','y=-2/(1+x)^2')\n",
+"deff('y=f(x)','y=(2*x-4)/(1+x)^4')\n",
+"deff('y=fi(x,j)','y=(1-x)*x^j')\n",
+"deff('y=f1(x,y)','y=(-x+y)/h1')   //function for differentiation\n",
+"for i=1:4\n",
+"    x=x+h\n",
+"    for j=1:4\n",
+"        A(i,j)=p(x)*f1(f1(fi(x,j),fi(x+h1,j)),f1(fi(x+h1,j),fi(x+2*h1,j)))+f1(p(x),p(x+h1))*f1(fi(x,j),fi(x+h1,j))+q(x)*fi(x,j)\n",
+"    end\n",
+"end\n",
+"x=0;\n",
+"for i=1:4\n",
+"    x=x+h\n",
+"    B(i)=f(x)\n",
+"end\n",
+"disp(B,'B =',A,'A =')\n",
+"C=inv(A)*B\n",
+"x=0;\n",
+"for i=2:4\n",
+"    x=x+h;\n",
+"    for j=1:4\n",
+"        Y(i)=Y(i)+C(j)*fi(x,j)\n",
+"    end\n",
+"end\n",
+"disp(Y,'Solution Matrix Y = ')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/18-Numerical_Solutions_of_Parabolic_Partial_Differential_Equations.ipynb b/Numerical_Methods_Principles_by_Analysis/18-Numerical_Solutions_of_Parabolic_Partial_Differential_Equations.ipynb
new file mode 100644
index 0000000..c66c4b2
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/18-Numerical_Solutions_of_Parabolic_Partial_Differential_Equations.ipynb
@@ -0,0 +1,399 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 18: Numerical Solutions of Parabolic Partial Differential Equations"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 18.4: Forward_Difference_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 18.4\n",
+"//Forward Difference Method\n",
+"//Page no. 624\n",
+"clc;clear;close;\n",
+"\n",
+"h=0.2;k=0.02;\n",
+"r=k/h^2;\n",
+"printf('\n j\tt\t|\ti -->\t')\n",
+"for i=0:5\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n |\t|\t|\tx -->\t')\n",
+"for i=0:5\n",
+"    printf('%.3f\t',(i)/5)\n",
+"end\n",
+"printf('\n-------------------------------------------------------------------------------')\n",
+"for j=1:6\n",
+"    printf('\n %i\t%.3f\t|\t\t',j-1,(j-1)/50)\n",
+"    for i=1:6\n",
+"        if i==1 | i==6 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=sin(%pi*(i-1)/5)\n",
+"        else\n",
+"            u(j,i)=(u(j-1,i-1)+u(j-1,i+1))/2\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 18.5: Bender_Schmidt_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 18.5\n",
+"//Bender Schmidt Method\n",
+"//Page no. 625\n",
+"clc;clear;close;\n",
+"\n",
+"h=0.1;k=0.005;\n",
+"r=k/h^2;\n",
+"printf('\n j  |\ti -->\t')\n",
+"for i=0:10\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n |  |\tx -->\t')\n",
+"for i=0:10\n",
+"    printf('%.3f\t',(i)/10)\n",
+"end\n",
+"printf('\n------------------------------------------------------------------------------------------------------')\n",
+"for j=1:9\n",
+"    printf('\n %i  |\t\t',j-1)\n",
+"    for i=1:11\n",
+"        if i==1 | i==11 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=sin(%pi*(i-1)/10)\n",
+"        else\n",
+"            u(j,i)=u(j-1,i)/2+(u(j-1,i-1)+u(j-1,i+1))/4\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 18.6: Crank_Nicolson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 18.6\n",
+"//Crank Nicolson Method\n",
+"//Page no. 631\n",
+"clc;clear;close;\n",
+"h=1/2;k=1/8;\n",
+"r=k/h^2;\n",
+"for i=1:2:3\n",
+"    for j=1:9\n",
+"        if i==1 | j==1 then\n",
+"            u(i,j)=0;\n",
+"        end\n",
+"        if i==3 then\n",
+"            u(i,j)=(j-1)/8\n",
+"        end\n",
+"    end\n",
+"end\n",
+"a=[3,-1,0;-1,3,-1;0,-1,3];\n",
+"a=inv(a);\n",
+"for j=2:9\n",
+"        u(2,j)=(u(1,j-1)+2*u(2,j-1)+u(3,j-1)+u(1,j)+u(3,j))/6\n",
+"end\n",
+"u=u'\n",
+"printf('\nfor h = 1/2\n\n')\n",
+"printf('i\\j --> ')\n",
+"for i=1:3\n",
+"    printf('\t%i\t',i)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------\n')\n",
+"for i=1:9\n",
+"    printf('\n %i',i)\n",
+"    for j=1:3\n",
+"        printf('\t   %.9f',u(i,j))\n",
+"    end\n",
+"end\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"h=1/4;k=1/8;\n",
+"r=k/h^2;\n",
+"for i=1:4:5\n",
+"    for j=1:9\n",
+"        if i==1 | j==1 then\n",
+"            u(i,j)=0;\n",
+"        end\n",
+"        if i==5 then\n",
+"            u(i,j)=(j-1)/8\n",
+"        end\n",
+"    end\n",
+"end\n",
+"a=[3,-1,0;-1,3,-1;0,-1,3];\n",
+"a=inv(a);\n",
+"for j=2:9\n",
+"        b=[u(1,j-1)-u(2,j-1)+u(3,j-1)+u(1,j);u(2,j-1)-u(3,j-1)+u(4,j-1);u(3,j-1)-u(4,j-1)+u(5,j-1)+u(5,j)]\n",
+"    x=a*b\n",
+"    u(2,j)=x(1);u(3,j)=x(2);u(4,j)=x(3);\n",
+"end\n",
+"u=u'\n",
+"printf('\n\n\n\n\nfor h = 1/4\n\n')\n",
+"printf('i\\j --> ')\n",
+"for i=1:5\n",
+"    printf('\t%i\t',i)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------\n')\n",
+"for i=1:9\n",
+"    printf('\n %i',i)\n",
+"    for j=1:5\n",
+"        printf('\t   %.9f',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 18.7: Gauss_Seidel_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 18.7\n",
+"//Gauss Seidel Method\n",
+"//Page no. 637\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=4*x-4*x^2')\n",
+"h=0.2;k=0.04;\n",
+"r=k/h^2;\n",
+"printf('\n k\t|\ti -->\t')\n",
+"for i=0:5\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n |\t|\tx -->\t')\n",
+"for i=0:5\n",
+"    printf('%.2f\t',(i)/5)\n",
+"end\n",
+"printf('\n-------------------------------------------------------------------------------')\n",
+"for k=1:7\n",
+"    printf('\n %i\t|\t\t',k-1)\n",
+"    for i=1:6\n",
+"        if i==1 | i==6 then\n",
+"            u(k,i)=0;\n",
+"        elseif k==1 then\n",
+"            u(k,i)=f((i-1)/5)\n",
+"        else\n",
+"            u(k,i)=(u(k-1,i-1)+u(k-1,i+1))/2\n",
+"        end\n",
+"        printf('%.2f\t',u(k,i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 18.8: ADI_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 18.8\n",
+"//ADI Method\n",
+"//Page no. 642\n",
+"clc;clear;close;\n",
+"\n",
+"for i=1:4\n",
+"    for j=1:5\n",
+"        P(i,j)=20\n",
+"    end\n",
+"end\n",
+"r=1;k=0;\n",
+"for i=1:6\n",
+"    v1(i)=20\n",
+"    u1(i)=20\n",
+"end\n",
+"P1=[25,30,35,50,60;35,0,0,0,70;45,0,0,0,80;60,70,80,100,90]\n",
+"for i=1:4\n",
+"    printf('\n')\n",
+"    for j=1:5\n",
+"        printf('%i\t',P(i,j))\n",
+"    end\n",
+"    if i==2 then\n",
+"        printf('-->')\n",
+"    end\n",
+"    printf('\t')\n",
+"    for j=1:5\n",
+"        printf('%i\t',P1(i,j))\n",
+"        if i>1 & i<4 & j>1 & j<5 then\n",
+"            P1(i,j)=P(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"P1v=P1;P1h=P1;\n",
+"for i=1:6\n",
+"    for j=1:6\n",
+"        if i==j then\n",
+"            Av(i,j)=1+2*r\n",
+"        elseif abs(i-j)==1 & i+j~=5 & i+j~=9\n",
+"            Av(i,j)=-r\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for i=1:6\n",
+"    for j=1:6\n",
+"        if i==j then\n",
+"            Ah(i,j)=1+2*r\n",
+"        elseif abs(i-j)==1 & i+j~=7\n",
+"            Ah(i,j)=-r\n",
+"        end\n",
+"    end\n",
+"end\n",
+"n=8\n",
+"for l=1:n\n",
+"    k=0;\n",
+"for j=0:2\n",
+"    for i=1:2\n",
+"        if i==1 then\n",
+"            Bv(i+j+k)=r*P1h(i+1,j+1)+(1-2*r)*P1h(i+1,j+2)+r*P1h(i+1,j+3)+r*P1h(i,j+1)\n",
+"        else\n",
+"            Bv(i+j+k)=r*P1h(i+1,j+1)+(1-2*r)*P1h(i+1,j+2)+r*P1h(i+1,j+3)+r*P1h(i+2,j+1)\n",
+"        end\n",
+"    end\n",
+"    k=k+1;\n",
+"end\n",
+"k=0;\n",
+"Bh=[r*30+(1-2*r)*v1(1)+r*v1(4)+r*35;r*35+(1-2*r)*v1(3)+r*v1(5);r*v1(1)+(1-2*r)*v1(2)+r*v1(3)+r*(70);r*v1(1)+(1-2*r)*v1(2)+r*(70+45);r*v1(3)+(1-2*r)*v1(4)+r*80;r*v1(5)+(1-2*r)*v1(6)+r*(100+80)]\n",
+"     for i=1:6\n",
+"         v(i,l)=v1(i)\n",
+"     end\n",
+"     for i=1:6\n",
+"         u(i,l)=u1(i)\n",
+"     end\n",
+"     v1=inv(Av)*Bv\n",
+"     u1=inv(Ah)*Bh\n",
+"     k=1;\n",
+"     for i=2:3\n",
+"         for j=2:4\n",
+"             P1h(i,j)=u1(i+j+k-4)\n",
+"         end\n",
+"         k=k+2\n",
+"     end\n",
+"     k=0;\n",
+"     for j=2:4\n",
+"         for i=2:3\n",
+"             P1v(i,j)=v1(i+j+k-3)\n",
+"         end\n",
+"         k=k+1\n",
+"     end\n",
+"end\n",
+"printf('\n\n\n\nResults for Vertical Transverse in Celsius :\n')\n",
+"for i=1:7\n",
+"    printf('\n')\n",
+"    if i==1 then\n",
+"        printf('Itr -->')\n",
+"        for j=1:n\n",
+"        printf('\t  %i',j-1)\n",
+"    end\n",
+"    printf('\n----------------------------------------------------------------------')\n",
+"    else\n",
+"        printf(' v%i',i-1)\n",
+"        for j=1:n\n",
+"        printf('\t%.2f',v(i-1,j))\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\n\n\nResults for Horizontal Transverse in Celsius :\n')\n",
+"for i=1:7\n",
+"    printf('\n')\n",
+"    if i==1 then\n",
+"        printf('Itr -->')\n",
+"        for j=1:n\n",
+"        printf('\t  %i',j-1)\n",
+"    end\n",
+"    printf('\n----------------------------------------------------------------------')\n",
+"    else\n",
+"        printf(' u%i',i-1)\n",
+"        for j=1:n\n",
+"        printf('\t%.2f',u(i-1,j))\n",
+"        end\n",
+"    end\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/19-Numerical_Solutions_of_Hyperbolic_Partial_Differential_Equations.ipynb b/Numerical_Methods_Principles_by_Analysis/19-Numerical_Solutions_of_Hyperbolic_Partial_Differential_Equations.ipynb
new file mode 100644
index 0000000..831d59e
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/19-Numerical_Solutions_of_Hyperbolic_Partial_Differential_Equations.ipynb
@@ -0,0 +1,751 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 19: Numerical Solutions of Hyperbolic Partial Differential Equations"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.10: Non_Linear_1st_Order_Hyperboolic_Differential_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.10\n",
+"//Non Linear 1st Order Hyperboolic Differential Equation\n",
+"//Page no. 667\n",
+"clc;clear;close;\n",
+"\n",
+"c=-2;k=0.05;h=0.2;\n",
+"r=abs(c)*k/h;\n",
+"printf('\n i\t x\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n |\t |\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*k)\n",
+"end\n",
+"i=1;\n",
+"x=0;\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"for j=1:7\n",
+"    for i=1:6\n",
+"        if j==1 then\n",
+"            u(i,j)=exp(-x);\n",
+"            u(i+1,j)=exp(-(x+h));\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=u(i,j-1)-k*(u(i+1,j-1)^2-u(i-1,j-1)^2)/(4*h)+k^2*((u(i+1,j-1)+u(i,j-1))*(u(i+1,j-1)^2-u(i,j-1)^2)-(u(i,j-1)+u(i-1,j-1))*(u(i,j-1)^2-u(i-1,j-1)^2))/(8*h^2)\n",
+"    end\n",
+"    x=x+h\n",
+"    end\n",
+"end\n",
+"x=0;\n",
+"for i=1:6\n",
+"    printf('\n %i\t%.1f\t|\t\t',i-1,x)\n",
+"    for j=1:7\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.11: Finite_Difference_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.11\n",
+"//Finite Difference Method\n",
+"//Page no. 670\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=sin(%pi*x)')\n",
+"deff('y=g(x)','y=0')\n",
+"a=1;b=1;c=1;n=5;m=10;\n",
+"h=a/n;k=b/m;r=c*k/h;\n",
+"r1=r^2;r2=r1/2;s1=1-r1;s2=2*(1-r2)\n",
+"printf('\n i ')\n",
+"for i=1:n\n",
+"    printf('\t  %i',i)\n",
+"end\n",
+"printf('\n-----------------------------------------------\nfi')\n",
+"for i=1:n\n",
+"    f1(i)=f(h*(i-1))\n",
+"    printf('\t%.3f',f1(i))\n",
+"end\n",
+"printf('\ngi')\n",
+"for i=1:n\n",
+"    g1(i)=g(h*(i-1))\n",
+"    printf('\t  %g',g1(i))\n",
+"end\n",
+"printf('\n\n\n i / j --> ')\n",
+"for i=1:m\n",
+"    printf('\t  %i',i)\n",
+"end\n",
+"printf('\n-------------------------------------------------------------------------------------------------')\n",
+"for j=1:m\n",
+"    for i=1:n\n",
+"        if i==1 | i==n then\n",
+"            u(i,j)=0;\n",
+"        elseif j==1\n",
+"            u(i,j)=f1(i)\n",
+"        elseif j==2\n",
+"            u(i,j)=s1*f1(i)+k*g1(i)+r2*(f1(i+1)+f1(i-1))\n",
+"        else\n",
+"            u(i,j)=s2*u(i,j-1)+r1*u(i-1,j-1)+u(i+1,j-1)-u(i,j-2)\n",
+"        end\n",
+"        \n",
+"    end\n",
+"end\n",
+"for i=1:n\n",
+"    printf('\n %i\t',i)\n",
+"    for j=1:m\n",
+"        printf('\t%.3f',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.12: Hyperbolic_Partial_Differential_Equations.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.12\n",
+"//Hyperbolic Partial Differential Equations\n",
+"//Page no. 673\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=12*x')\n",
+"Ua(1)=0.25;\n",
+"Ua(2)=0.75\n",
+"A=[1,-2;1,2];\n",
+"x1=inv(A)*Ua;\n",
+"printf('Xb = %g   and   Tb = %g',x1(1),x1(2))\n",
+"A=[2,-1;2,1];\n",
+"B=[-7.5;-8.5];\n",
+"x2=inv(A)*B;\n",
+"printf('\n\n Pb = %g   and   Qb = %g',x2(1),x2(2))\n",
+"x1(1)=x1(1)-Ua(1)\n",
+"du=x1'*x2\n",
+"printf('\n\n dU = %g',du)\n",
+"Ub=f(Ua(1))+du;\n",
+"printf('\n\n Modified Ub = %g',Ub)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.13: Hyperbolic_Differential_Equations_in_2D_or_3D.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.13\n",
+"//Hyperbolic Differential Equations in 2D or 3D\n",
+"//Page no. 675\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x,y)','y=x*(2-x)*y*(2-y)')\n",
+"c2=3;k=0.4;h=0.4;c2=3;s2=0.5\n",
+"for l=0:11\n",
+"    if l==0 then\n",
+"        printf('\n t = %i\n\n i\t  x\t|\tj -->\t',l)\n",
+"    for i=0:5\n",
+"        printf('  %i\t',i)\n",
+"    end\n",
+"    printf('\n |\t  |\t|\ty -->\t')\n",
+"    for i=0:5\n",
+"         printf('%.3f\t',i*k)\n",
+"    end\n",
+"    x=0;\n",
+"     printf('\n---------------------------------------------------------------------------------------')\n",
+"     for i=1:6\n",
+"         y=0;\n",
+"        printf('\n %i\t%.3f\t|\t\t',i-1,x)\n",
+"        for j=1:6\n",
+"             if i==1 | i==6 then\n",
+"                u(i,j)=0;\n",
+"            elseif j==1 | j==6 then\n",
+"                u(i,j)=0\n",
+"            else\n",
+"                u(i,j)=f(x,y)\n",
+"        end\n",
+"            printf('%.3f\t',u(i,j))\n",
+"       y=y+k;\n",
+"        end\n",
+"    x=x+h\n",
+"end\n",
+"u2=u;\n",
+"else\n",
+"    printf('\n\n\n t = %i\n\n i\t  x\t|\tj -->\t',l)\n",
+"    for i=0:5\n",
+"        printf('  %i\t',i)\n",
+"    end\n",
+"    printf('\n |\t  |\t|\ty -->\t')\n",
+"    for i=0:5\n",
+"         printf('%.3f\t',i*k)\n",
+"    end\n",
+"    x=0;\n",
+"     printf('\n---------------------------------------------------------------------------------------')\n",
+"     for i=1:6\n",
+"         y=0;\n",
+"        printf('\n %i\t%.3f\t|\t\t',i-1,x)\n",
+"        for j=1:6\n",
+"             if i==1 | i==6 then\n",
+"                u(i,j)=0;\n",
+"            elseif j==1 | j==6 then\n",
+"                u(i,j)=0\n",
+"            elseif l==1\n",
+"                u(i,j)=s2*(u1(i+1,j)+u1(i-1,j)+u1(i,j+1)+u1(i,j-1)-4*u1(i,j))+2*u1(i,j)\n",
+"            else\n",
+"                u(i,j)=s2*(u1(i+1,j)+u1(i-1,j)+u1(i,j+1)+u1(i,j-1)-4*u1(i,j))+2*u1(i,j)-u2(i,j)\n",
+"        end\n",
+"            printf('%.4f\t',u(i,j))\n",
+"       y=y+k;\n",
+"        end\n",
+"    x=x+h\n",
+"    end\n",
+"end\n",
+"if l>1 then\n",
+"    u2=u1\n",
+"end\n",
+"u1=u;\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.3: Simple_Explicit_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.3\n",
+"//Simple Explicit Method\n",
+"//Page no. 658\n",
+"clc;clear;close;\n",
+"\n",
+"c=-2;dt=0.07;dx=0.2;\n",
+"r=abs(c)*dt/dx;\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"for j=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',(j-1)*dx,j-1)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.4: Simple_Implicit_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.4\n",
+"//Simple Implicit Method\n",
+"//Page no. 659\n",
+"clc;clear;close;\n",
+"\n",
+"c=-2;dt=0.07;dx=0.2;\n",
+"r=abs(c)*dt/dx;\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"for j=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',(j-1)*dx,j-1)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.5: Lax_Wendroff_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.5\n",
+"//Lax Wendroff Method\n",
+"//Page no. 660\n",
+"clc;clear;close;\n",
+"\n",
+"c=-2;dt=0.07;dx=0.2;\n",
+"r=abs(c)*dt/dx;\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"i=1;\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"for j=1:7\n",
+"    for i=1:6\n",
+"        if j==1 then\n",
+"            u(i,j)=0;\n",
+"            u(i+1,j)=0;\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=r*(r-1)*u(i+1,j-1)/2+(1-r^2)*u(i,j-1)+r*(1+r)*u(i-1,j-1)/2\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for i=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',(i-1)*dx,i-1)\n",
+"    for j=1:7\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.6: Wendroff_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.6\n",
+"//Wendroff Method\n",
+"//Page no. 661\n",
+"clc;clear;close;\n",
+"\n",
+"c=2;k=0.07;h=0.2;\n",
+"a=(h+k*c)/(h-k*c)\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*k)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"for i=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',(i-1)*h,i-1)\n",
+"    for j=1:7\n",
+"        if j==1 then\n",
+"            u(i,j)=0;\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=u(i-1,j-1)+(u(i,j-1)-u(i-1,j))/a\n",
+"        end\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.7: Leapfrog_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.7\n",
+"//Leapfrog Method\n",
+"//Page no. 662\n",
+"clc;clear;close;\n",
+"\n",
+"c=2;k=0.07;h=0.2;\n",
+"r=c*k/h\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*k)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"\n",
+"for j=1:7\n",
+"    for i=1:6\n",
+"        if j==1 | j==2 & i~=1 then\n",
+"            u(i,j)=0;\n",
+"            u(i+1,j)=0;\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=u(i,j-2)-r*(u(i+1,j-1)-u(i-1,j-1))\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for i=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',(i-1)*h,i-1)\n",
+"    for j=1:7\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.8: Variable_Coefficients.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.8\n",
+"//Variable Coefficients\n",
+"//Page no. 663\n",
+"clc;clear;close;\n",
+"\n",
+"//simple explicit method\n",
+"printf('\n\nBy Simple Explicit Method:\n\n')\n",
+"dt=0.05;dx=0.2;\n",
+"x=0;\n",
+"printf('\n i\t  x\t  r\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  \t\t\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n----------------------------------------------------------------------------------------------')\n",
+"for j=1:6\n",
+"    r=sqrt(1+2*x)*dt/dx;\n",
+"    printf('\n %i\t%.3f\t%.3f\t|\t\t',(j-1),x,r)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"        \n",
+"    end\n",
+"    x=x+dx\n",
+"end\n",
+"\n",
+"\n",
+"//simple implicit method\n",
+"printf('\n\n\nBy Simple Implicit Method:\n')\n",
+"c=-2;dt=0.05;dx=0.2;x=0\n",
+"printf('\n i\t  x\t  r\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  \t\t\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n----------------------------------------------------------------------------------------------')\n",
+"for j=1:6\n",
+"    r=sqrt(1+2*x)*dt/dx;\n",
+"    printf('\n %i\t%.3f\t%.3f\t|\t\t',(j-1),x,r)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=0;\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"    x=x+dx\n",
+"end\n",
+"\n",
+"\n",
+"//wendroff method\n",
+"printf('\n\n\nBy Wendroff Method:\n')\n",
+"k=0.05;h=0.2;\n",
+"x=0.1;\n",
+"printf('\n i\t  x\t  c\t  a\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  \t\t\t\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*k)\n",
+"end\n",
+"printf('\n-------------------------------------------------------------------------------------------------------')\n",
+"for i=1:6\n",
+"    c=sqrt(1+2*x);\n",
+"    a=(h+k*c)/(h-k*c)\n",
+"    printf('\n %i\t%.3f\t%.3f\t%.3f\t|\t\t',(i-1),x-h/2,c,a)\n",
+"    for j=1:7\n",
+"        if j==1 then\n",
+"            u(i,j)=0;\n",
+"            u(i+1,j)=0;\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=u(i-1,j-1)+(u(i,j-1)-u(i-1,j))/a\n",
+"        end\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 19.9: Inhomogeneous_1st_Order_Hyperboolic_Differential_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 19.9\n",
+"//Inhomogeneous 1st Order Hyperboolic Differential Equation\n",
+"//Page no. 665\n",
+"clc;clear;close;\n",
+"\n",
+"//simple explicit method\n",
+"printf('\n\nBy Simple Explicit Method:\n')\n",
+"c=-2;dt=0.07;dx=0.2;\n",
+"r=abs(c)*dt/dx;\n",
+"printf('\n  i\tx\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"x=0;\n",
+"for j=1:6\n",
+"    printf('\n %i\t%.1f\t|\t\t',j-1,x)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=exp(-x);\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)+dt*2*x\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"    x=x+dx\n",
+"end\n",
+"\n",
+"\n",
+"//simple implicit method\n",
+"printf('\n\n\nBy Simple Implicit Method:\n')\n",
+"c=-2;dt=0.07;dx=0.2;\n",
+"r=abs(c)*dt/dx;\n",
+"printf('\n  i\tx\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*dt)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"x=0;\n",
+"for j=1:6\n",
+"    printf('\n %i\t%.1f\t|\t\t',j-1,x)\n",
+"    for i=1:7\n",
+"        if i==1 then\n",
+"            u(j,i)=exp(-x);\n",
+"        elseif j==1 then\n",
+"            u(j,i)=1\n",
+"        else\n",
+"            u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)+dt*2*x\n",
+"        end\n",
+"        printf('%.3f\t',u(j,i))\n",
+"    end\n",
+"    x=x+dx\n",
+"end\n",
+"\n",
+"\n",
+"//wendroff method\n",
+"printf('\n\n\nBy Wendroff Method:\n')\n",
+"c=2;k=0.07;h=0.2;\n",
+"a=(h+k*c)/(h-k*c)\n",
+"printf('\n  x\ti\t|\tj -->\t')\n",
+"for i=0:6\n",
+"    printf('  %i\t',i)\n",
+"end\n",
+"printf('\n  |\t|\t|\tt -->\t')\n",
+"for i=0:6\n",
+"    printf('%.3f\t',i*k)\n",
+"end\n",
+"printf('\n---------------------------------------------------------------------------------------')\n",
+"x=0;\n",
+"for i=1:6\n",
+"    printf('\n %.1f\t%i\t|\t\t',x,i-1)\n",
+"    for j=1:7\n",
+"        if j==1 then\n",
+"            u(i,j)=exp(-x);\n",
+"        elseif i==1 then\n",
+"            u(i,j)=1\n",
+"        else\n",
+"            u(i,j)=u(i-1,j-1)+(u(i,j-1)-u(i-1,j))/a+(2*h*k)*(x+h/2)/(a*(h+c*k))\n",
+"        end\n",
+"        printf('%.3f\t',u(i,j))\n",
+"    end\n",
+"    x=x+h\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/2-Scope_of_Numerical_and_Mathematical_Methods.ipynb b/Numerical_Methods_Principles_by_Analysis/2-Scope_of_Numerical_and_Mathematical_Methods.ipynb
new file mode 100644
index 0000000..7652685
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/2-Scope_of_Numerical_and_Mathematical_Methods.ipynb
@@ -0,0 +1,84 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 2: Scope of Numerical and Mathematical Methods"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 2.4: Solving_Simultaneous_Linear_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 2.4\n",
+"//Solving Simultaneous Linear Equation\n",
+"//Page 36\n",
+"clc;close;clear;\n",
+"//eq1= 5x-331y=3.5\n",
+"//eq2= 6x-397y=5.2\n",
+"\n",
+"A=[5,-331;6,-397];\n",
+"B=[3.5;5.2];\n",
+"C=inv(A)*B;      //finding value by multiplying inverse with values\n",
+"disp(C(1,1),'Value of x=');\n",
+"disp(C(2,1),'Value of y=');"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 2.6: Integration.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 2.6\n",
+"//Integration\n",
+"//Page no. 36\n",
+"clc;clear;close;\n",
+"disp(integrate('1/x','x',exp(-4),1),'Integration Value=');    //performing integration with respect to dx"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/20-Numerical_Solutions_of_Elliptical_Partial_Differential_Equations.ipynb b/Numerical_Methods_Principles_by_Analysis/20-Numerical_Solutions_of_Elliptical_Partial_Differential_Equations.ipynb
new file mode 100644
index 0000000..010a912
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/20-Numerical_Solutions_of_Elliptical_Partial_Differential_Equations.ipynb
@@ -0,0 +1,467 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 20: Numerical Solutions of Elliptical Partial Differential Equations"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.1: Direct_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.1\n",
+"//Direct Method\n",
+"//Page no. 682\n",
+"clc;clear;close;\n",
+"h=1/3;\n",
+"A=[-4,1,1,0;1,-4,0,1;1,0,-4,1;0,1,1,-4]\n",
+"x=0;\n",
+"for i=1:4\n",
+"    x=x+h\n",
+"    if i==4 then\n",
+"        B(i,1)=0\n",
+"    else\n",
+"        B(i,1)=-1*sin(x*%pi)^2\n",
+"    end\n",
+"end\n",
+"disp(A,'A =')\n",
+"disp(B,'B =')\n",
+"U=inv(A)*B\n",
+"disp(U,'U =')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.2: Five_Point_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.2\n",
+"//Five Point Formula\n",
+"//Page no. 683\n",
+"clc;clear;close;\n",
+"\n",
+"A=[-4,1,1,0;1,0,-4,1;1,-4,0,1;0,1,1,-4];\n",
+"B=[-25;-150;-25;-150];\n",
+"u1=inv(A)*B;\n",
+"j=0;k=1\n",
+"for i=1:4\n",
+"    j=j+1;\n",
+"    printf('\nu%i%i = %g\n',k,j,u1(i))\n",
+"    if i==2 then\n",
+"        j=0;k=2\n",
+"    end\n",
+"end\n",
+"printf('\n\n  U = \n')\n",
+"for i=1:4\n",
+"    printf('\n')\n",
+"    for j=1:4\n",
+"        if j==1 then\n",
+"            u(i,j)=0\n",
+"        elseif j==4\n",
+"            u(i,j)=100\n",
+"        elseif (i==1 | i==4) & j==2\n",
+"            u(i,j)=25\n",
+"        elseif i==1 | i==4\n",
+"            u(i,j)=u(i,j-1)*2\n",
+"        else\n",
+"            u(i,j)=u1((j-1)*2-i+2)\n",
+"        end\n",
+"        printf('\t%g\t',u(i,j))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.3: Finite_Difference_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.3\n",
+"//Finite Difference Method\n",
+"//Page no. 685\n",
+"clc;clear;close;\n",
+"\n",
+"printf('Itr\t\t U11\t\t U21\t\t U12\t\t U22\n-----------------------------------------------------------------------\n')\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        if j==1 then\n",
+"            u(i,j)=0\n",
+"        elseif j==4\n",
+"            u(i,j)=100\n",
+"        elseif (i==1 | i==4) & j==2\n",
+"            u(i,j)=25\n",
+"        elseif i==1 | i==4\n",
+"            u(i,j)=u(i,j-1)*2\n",
+"        else\n",
+"            u(i,j)=0\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for k=0:17\n",
+"    printf('  %i\t\t%.3f\t\t%.3f\t\t%.3f\t\t%.3f\n',k,u(3,2),u(3,3),u(2,2),u(2,3))\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u1(i,j)=(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j))/4\n",
+"        end\n",
+"    end\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u(i,j)=u1(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"disp(u,'U = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.4: Seven_Point_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.4\n",
+"//Seven Point Formula\n",
+"//Page no. 686\n",
+"clc;clear;close;\n",
+"printf('Itr\t\t U111\t\t U211\t\t U121\t\t U221\n-----------------------------------------------------------------------\n')\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        for k=3:-1:1\n",
+"            if k==3 then\n",
+"                u(i,j,k)=100\n",
+"            elseif (i==1 | i==4 | j==1 | j==4) & k==2\n",
+"                u(i,j,k)=300\n",
+"            elseif k==2\n",
+"                u(i,j,k)=0\n",
+"            elseif (i==1 | i==4 | j==1 | j==4) & k==1\n",
+"                u(i,j,k)=500\n",
+"            else\n",
+"                u(i,j,k)=700\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"end\n",
+"k=2\n",
+"for l=0:14\n",
+"    printf('  %i\t\t%.3f\t\t%.3f\t\t%.3f\t\t%.3f\n',l,u(3,2,2),u(3,3,2),u(2,2,2),u(2,3,2))\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u1(i,j)=(u(i,j+1,k)+u(i,j-1,k)+u(i-1,j,k)+u(i+1,j,k)+u(i,j,k+1)+u(i,j,k-1))/6\n",
+"        end\n",
+"    end\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u(i,j,2)=u1(i,j)\n",
+"        end\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.5: Nine_Point_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.5\n",
+"//Nine Point Formula\n",
+"//Page no. 688\n",
+"clc;clear;close;\n",
+"\n",
+"printf('Itr\t\t U11\t\t U12\t\t U21\t\t U22\n-----------------------------------------------------------------------\n')\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        if j==1 then\n",
+"            u(i,j)=0\n",
+"        elseif j==4\n",
+"            u(i,j)=100\n",
+"        elseif (i==1 | i==4) & j==2\n",
+"            u(i,j)=25\n",
+"        elseif i==1 | i==4\n",
+"            u(i,j)=u(i,j-1)*2\n",
+"        else\n",
+"            u(i,j)=0\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for k=0:17\n",
+"    printf('  %i\t\t%.3f\t\t%.3f\t\t%.3f\t\t%.3f\n',k,u(3,2),u(2,2),u(3,3),u(2,3))\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u1(i,j)=(u(i+1,j-1)+u(i-1,j-1)+u(i+1,j+1)+u(i-1,j+1)+4*(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j)))/20\n",
+"        end\n",
+"    end\n",
+"    for i=3:-1:2\n",
+"        for j=2:3\n",
+"            u(i,j)=u1(i,j)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"disp(u,'The Solution of the System is = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.6: Five_Point_Formula.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.6\n",
+"//Five Point Formula\n",
+"//Page no. 689\n",
+"clc;clear;close;\n",
+"\n",
+"h=0.25;k=0.25;y=1;x=0;\n",
+"deff('x=f(y)','x=y^3')\n",
+"\n",
+"for i=1:5\n",
+"    x=0;\n",
+"    printf('\n%g\t|',y)\n",
+"    for j=1:5\n",
+"        if (i==1 | i==5)\n",
+"            u(i,j)=f(x)\n",
+"        elseif j==5\n",
+"            u(i,j)=f(x)\n",
+"        else\n",
+"            u(i,j)=0\n",
+"        end\n",
+"        x=x+k;\n",
+"        printf('%f\t',u(i,j))\n",
+"    end\n",
+"    y=y-h\n",
+"end\n",
+"printf('\n\t-------------------------------------------------------------------------\n')\n",
+"x=0;\n",
+"    for j=1:5\n",
+"        printf('\t   %g\t',x)\n",
+"        x=x+k\n",
+"    end\n",
+"printf('\n\n\n Itr\t U11\t U12\t U13\t U21\t U22\t U23\t U31\t U32\t U33\n-------------------------------------------------------------------------------\n')\n",
+"\n",
+"for l=0:20\n",
+"    y=0;\n",
+"    printf('  %i\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',l,u(4,2),u(4,3),u(4,4),u(3,2),u(3,3),u(3,4),u(2,2),u(2,3),u(2,4))\n",
+"    for i=4:-1:2\n",
+"        y=y+k\n",
+"        for j=2:4\n",
+"            u1(i,j)=(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j)-h^2*y)/4\n",
+"        end\n",
+"    end\n",
+"    for i=4:-1:2\n",
+"        for j=2:4\n",
+"            u(i,j)=u1(i,j)\n",
+"        end\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.7: Laplace_Distributio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.7\n",
+"//Laplace Distribution\n",
+"//Page no. 694\n",
+"clc;clear;close;\n",
+"\n",
+"dr=3;r0=4;dth=%pi/4;\n",
+"deff('y=f(u1,u2,u3,u4)','y=(u1+u3+(dr*(u3-u1))/(2*r0)+(u2+u4)*(dr/(r0*dth))^2)/(2*(1+(dr/(r0*dth))^2))')         //laplace distribution\n",
+"for i=1:8\n",
+"    U(i)=0;\n",
+"end\n",
+"printf('Itr\t  U1\t  U2\t  U3\t  U4\t  U5\t  U6\t  U7\t  U8\n-----------------------------------------------------------------------')\n",
+"for l=0:15\n",
+"    printf('\n  %i',l)\n",
+"    for i=1:8\n",
+"        if i==1 then\n",
+"            u1(i)=f(100,U(8),40,U(i+1))\n",
+"        elseif i==8\n",
+"            u1(i)=f(100,U(i-1),40,U(1))\n",
+"        else\n",
+"            u1(i)=f(100,U(i-1),40,U(i+1))\n",
+"        end\n",
+"        \n",
+"    end\n",
+"    for i=1:8\n",
+"        U(i)=u1(i)\n",
+"        printf('\t%.3f',U(i))\n",
+"    end\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 20.8: Spherical_Coordinate_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 20.8\n",
+"//Spherical Coordinate System\n",
+"//Page no. 697\n",
+"clc;clear;close;\n",
+"deff('y=cot(x)','y=1/tan(x)')\n",
+"dr=5;r0=50;dth=%pi/4;dfi=%pi/4;N=-10;Z=60;Nb=0;Zt=70;\n",
+"deff('y=f(u1,u2,u3,u4,u5,u6,th0)','y=((u1+u3)/dr^2+(u3-u1)/(r0*dr)+(u2+u4)/(r0*dth)^2+(u2*cot(th0)/(r0^2*dth)+(u5+u6)/(r0*sin(th0)*dfi)^2))/(2/dr^2+2/(r0*dth)^2+cot(th0)/(r0^2*dth)+2/(r0*sin(th0)*dfi)^2)')         //laplace distribution in spherical coordinate\n",
+"T1=40;T2=20;H1=35;H2=10;B1=5;B2=0;t1=240;t2=180;b1=100;b2=80;h1=210;h2=150\n",
+"printf('\n----------------------------------------------------------------------------\n')\n",
+"s=['T','H','B','t','h','b'];\n",
+"for i=1:8\n",
+"    if i<4 | i>6 then\n",
+"        T(1,i)=T1;\n",
+"        H(1,i)=H1;\n",
+"        B(1,i)=B1;\n",
+"        b(1,i)=b1;\n",
+"        t(1,i)=t1;\n",
+"        h(1,i)=h1;\n",
+"    else\n",
+"        T(1,i)=T2;\n",
+"        H(1,i)=H2;\n",
+"        b(1,i)=b2;\n",
+"        B(1,i)=B2;\n",
+"        t(1,i)=t2;\n",
+"        h(1,i)=h2;\n",
+"    end\n",
+"end\n",
+"h(1)=0;h(2)=0;\n",
+"Al=[T;H;B;t;h;b]\n",
+"for i=1:6\n",
+"    if i==1 then\n",
+"        printf('Temperature Distribution in Outer Sphere\n')\n",
+"        printf('----------------------------------------------------------------------------\n')\n",
+"    end\n",
+"    if i==4 then\n",
+"        printf('\nTemperature Distribution in Inner Sphere\n')\n",
+"        printf('----------------------------------------------------------------------------\n')\n",
+"    end\n",
+"    printf('\nPoint : ')\n",
+"    for j=1:8\n",
+"            printf('\t%s%i',s(i),j)\n",
+"    end\n",
+"    printf('\nTemperature : ')\n",
+"    for j=1:8\n",
+"        if (j==1 | j==2) & i==5 then\n",
+"            printf('\t%s','?')\n",
+"        else\n",
+"            printf('\t%i',Al(i,j))\n",
+"        end\n",
+"    end\n",
+"    printf('\n----------------------------------------------------------------------------')\n",
+"end\n",
+"th0=10^-30\n",
+"Uh1=f(1000,Al(5,8),Al(2,1),Al(5,2),Al(6,1),Al(4,1),th0)\n",
+"disp(Uh1,'Uh1 = ')\n",
+"th0=%pi/4;\n",
+"Uh2=f(1000,Uh1,Al(2,2),Al(5,3),Al(6,2),Al(4,2),th0)\n",
+"disp(Uh2,'Uh2 = ')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/21-Advances_in_Numerical_Methods_Using_Parallel_Computing_Paradigm.ipynb b/Numerical_Methods_Principles_by_Analysis/21-Advances_in_Numerical_Methods_Using_Parallel_Computing_Paradigm.ipynb
new file mode 100644
index 0000000..de8b791
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/21-Advances_in_Numerical_Methods_Using_Parallel_Computing_Paradigm.ipynb
@@ -0,0 +1,344 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 21: Advances in Numerical Methods Using Parallel Computing Paradigm"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 21.1: Parallel_Bisection_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 21.1\n",
+"//Parallel Bisection Method\n",
+"//Page no. 721\n",
+"clc;close;clear;\n",
+"\n",
+"deff('y=f(x)','y=x^2-cos(x)')\n",
+"a=0;b=1;e=0.0001;i=1;\n",
+"printf('Itr\ta\tb\th\t\tx0\t\tx1\t\tx2\t\tx3\t\tx4\t\tx5\n\t\t\t\t\ty0\t\ty1\t\ty2\t\ty3\t\ty4\t\ty5')\n",
+"printf('\n--------------------------------------------------------------------------------------------------------------------------------\n')\n",
+"while (abs(a-b)>=e)\n",
+"    \n",
+"\n",
+"    h=(b-a)/5;\n",
+"    y(1)=f(a);\n",
+"    x(1)=a;\n",
+"    printf(' %i\t%g\t%g\t%f\t%f',i,a,b,h,x(1))\n",
+"    for j=2:6\n",
+"        x(j)=x(j-1)+h;\n",
+"        y(j)=f(x(j));\n",
+"        if (y(j-1)*y(j)<0)\n",
+"                a=x(j-1);\n",
+"                b=x(j);\n",
+"        end\n",
+"        printf('\t%f',x(j))\n",
+"    end\n",
+"    printf('\n\t\t\t\t\t')\n",
+"    for j=1:6\n",
+"        printf('%f\t',y(j))\n",
+"    end\n",
+"    \n",
+"    printf('\n')\n",
+"    i=i+1;\n",
+"end\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 21.2: Lagrange_Interpolation_in_Parallel_Computing.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 21.2\n",
+"//Lagrange Interpolation in Parallel Computing\n",
+"//Page no. 723\n",
+"clc;close;clear;\n",
+"\n",
+"xi=[-1,0,2,5];\n",
+"yi=[9,5,3,15];\n",
+"s=['x=1','n=4','Data:','(-1,9)','(0,5)','(2,3)','(5,15)']\n",
+"for i=1:4\n",
+"    printf('\tProcessor\t')\n",
+"end\n",
+"printf('\n')\n",
+"for i=1:4\n",
+"    printf('\t   N%i\t\t',i)\n",
+"end\n",
+"printf('\n')\n",
+"for i=1:7\n",
+"    for j=1:4\n",
+"        printf('         %s\t\t',s(i))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"\n",
+"x=1;T=0;\n",
+"for k=0:3\n",
+"    p=yi(k+1)\n",
+"    for j=0:3\n",
+"        if(j~=k)\n",
+"            p=p*((x-xi(j+1))/(xi(k+1)-xi(j+1)))\n",
+"        end\n",
+"    end\n",
+"    T=T+p;\n",
+"    printf('\nT(%i) = %g',k+1,p)\n",
+"end\n",
+"printf('\n\nT = %g',T)\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 21.3: Trapezoidal_Rule_and_Simpsons_Rule_in_Parallel_Computing.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 21.3\n",
+"//Trapezoidal Rule and Simpsons Rule in Parallel Computing\n",
+"//Page no. 726\n",
+"clc;close;clear;\n",
+"n=8;a=0;b=8;\n",
+"h=(b-a)/n\n",
+"deff('y=f(x)','y=1/(1+x)')\n",
+"for i=0:8\n",
+"    x(i+1)=i;\n",
+"    y(i+1)=f(x(i+1))\n",
+"end\n",
+"printf('xi\t ')\n",
+"for i=1:9\n",
+"    printf('%i\t ',x(i))\n",
+"end\n",
+"printf('\n yi\t')\n",
+"for i=1:9\n",
+"    printf('1/%i\t',i)\n",
+"end\n",
+"\n",
+"//trapezoidal rule\n",
+"S=0;\n",
+"for i=1:9\n",
+"    if(i==1 | i==9)\n",
+"        S=S+y(i)\n",
+"    else\n",
+"        S=S+2*y(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/2\n",
+"printf('\n\nTrapezoidal Rule Sum = %g',S)\n",
+"\n",
+"//Simpsons 1/3rd Rule\n",
+"S=0;\n",
+"for i=1:9\n",
+"    if(i==1 | i==9)\n",
+"        S=S+y(i)\n",
+"    elseif(((i)/2)-fix((i)/2)==0)\n",
+"        S=S+4*y(i)\n",
+"    else\n",
+"        S=S+2*y(i)\n",
+"    end\n",
+"end\n",
+"S=S*h/3\n",
+"printf('\n\nSimpsons 1/3rd Rule Sum = %g',S)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 21.4: Parallel_Gauss_Seidel_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 21.4\n",
+"//Parallel Gauss-Seidel Method\n",
+"//Page no. 730\n",
+"clc;close;clear;\n",
+"A=[3,2;6,2];\n",
+"B=[2;3];\n",
+"x(1)=1/4;\n",
+"x(2)=1/5;\n",
+"e=0.002;\n",
+"old(1)=x(1);\n",
+"old(2)=x(2);\n",
+"new(1)=old(1);\n",
+"new(2)=old(2);\n",
+"printf('\t\tProcess 1\t\tProcess 2\n Itr\t\told\tnew1\t\told2\tnew2\n\n')\n",
+"printf('  %i\t\t%g\t%g\t\t%g\t%g\n',0,old(1),new(1),old(2),new(2))\n",
+"for i=1:4\n",
+"    printf('  %i',i)\n",
+"    for j=1:2\n",
+"        k=0;\n",
+"        for l=1:j-1\n",
+"            k=k-(A(j,l)*old(l));\n",
+"        end\n",
+"        m=0;\n",
+"        for l=j+1:2\n",
+"            m=m-(A(j,l)*old(l));\n",
+"        end\n",
+"        new(j)=(B(j)+k+m)/A(j,j)\n",
+"        printf('\t\t%.5g\t%.5g',old(j),new(j))\n",
+"    end\n",
+"    printf('\n')\n",
+"    old(1)=new(1)\n",
+"    old(2)=new(2)\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 21.5: Poissons_Partial_Differential_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 21.5\n",
+"//Poissons Partial Differential Equation\n",
+"//Page no. 733\n",
+"clc;clear;close;\n",
+"\n",
+"s=['st','nd','rd']\n",
+"for i=4:20\n",
+"    s(i)='th'\n",
+"end\n",
+"h=0.25;deff('y=f(x)','y=x^3');y=1;x=0;\n",
+"for i=1:6\n",
+"    \n",
+"    \n",
+"    if i~=6 then\n",
+"        printf('%g\t|',y)\n",
+"        y=y-h;\n",
+"        x=0;\n",
+"        for j=1:5\n",
+"            if i==1 | i==5 | j==5 then\n",
+"                P(i,j)=f(x)\n",
+"            else\n",
+"                P(i,j)=0\n",
+"            end\n",
+"        printf('%f\t',P(i,j))\n",
+"        x=x+h;\n",
+"        end\n",
+"    else\n",
+"        printf('---------------------------------------------------------------------------------\n\t')\n",
+"        x=0;\n",
+"        for j=1:5\n",
+"            printf('   %g\t\t',x)\n",
+"            x=x+h\n",
+"        end\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"\n",
+"printf('\n\n\n')\n",
+"\n",
+"for l=0:17\n",
+"    y=1;\n",
+"    if l~=0 then\n",
+"        printf('After the %i%s Iteration : \n------------------------------------------------------\n  %i',l,s(l),l)\n",
+"    for i=1:6\n",
+"        if i~=6 then\n",
+"            printf('\t%g',y)\n",
+"        y=y-h\n",
+"            for j=1:5\n",
+"            printf('\t%.3f',P(i,j))\n",
+"           end\n",
+"        else\n",
+"            x=0;\n",
+"            printf('\t')\n",
+"            for j=1:5\n",
+"                printf('\t%g',x)\n",
+"                x=x+h \n",
+"            end\n",
+"        end\n",
+"        printf('\n')\n",
+"    end\n",
+"    printf('------------------------------------------------------\n')\n",
+"end\n",
+"y=0;\n",
+"    for i=4:-1:2\n",
+"        y=y+h\n",
+"        for j=2:4\n",
+"            P1(i,j)=(P(i,j+1)+P(i,j-1)+P(i-1,j)+P(i+1,j)-h^2*y)/4\n",
+"        end\n",
+"    end\n",
+"    for i=4:-1:2\n",
+"        for j=2:4\n",
+"            P(i,j)=P1(i,j)\n",
+"        end\n",
+"    end\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/22-Numerical_Methods_Using_Neural_Networks.ipynb b/Numerical_Methods_Principles_by_Analysis/22-Numerical_Methods_Using_Neural_Networks.ipynb
new file mode 100644
index 0000000..6bcd6af
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/22-Numerical_Methods_Using_Neural_Networks.ipynb
@@ -0,0 +1,257 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 22: Numerical Methods Using Neural Networks"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.1: MLP_Algorithm.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.1\n",
+"//MLP Algorithm\n",
+"//Page no. 748\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=1/(1+exp(-x))')\n",
+"Wih=[0.1,-0.3;0.3,0.4];\n",
+"Who=[0.4;0.5]\n",
+"i=[0.2,0.6];\n",
+"t=0.7;\n",
+"a=10;\n",
+"for k=1:3\n",
+"    printf('\n\n\nAfter Iteration %i :\n\n',k)\n",
+"    disp(Wih,'Wih = ')\n",
+"    disp(Who,'Who = ')\n",
+"a1=i*Wih;\n",
+"disp(a1,'a = ')\n",
+"h=[f(a1(1)),f(a1(2))]\n",
+"disp(h,'h = ')\n",
+"b1=h*Who\n",
+"disp(b1,'b1 =')\n",
+"o=f(b1)\n",
+"disp(o,'o = ')\n",
+"d=o*(1-o)*(t-o)\n",
+"disp(d,'d =')\n",
+"for j=1:2\n",
+"    e(1,j)=h(j)*(1-h(j))*d*Who(j)\n",
+"end\n",
+"disp(e,'e =')\n",
+"dWho=a*h'*d;\n",
+"disp(dWho,'dWho =')\n",
+"Who=Who+dWho;\n",
+"dWih=a*i'*e;\n",
+"disp(dWih,'dWih =')\n",
+"Wih=Wih+dWih;\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.2: MLP.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.2\n",
+"//MLP\n",
+"//Page no. 758\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^3-x^2+x-1')\n",
+"printf('Input\t\tDesired\t\tNetwork\t\tError\n\t\t Output\t\t Output\n---------------------------------------------------------\n')\n",
+"in=[0.7572,0.7601,0.7620,1.4831,1.4874,1.4900,2.0913,2.0934,2.1006,2.8391,2.8496,2.8529,3.4555,3.4631,3.4654,4.1547,,4.1839,4.1874]\n",
+"n=[-0.3941,-0.3896,-0.3867,1.6054,1.6259,1.6391,5.8762,5.8969,5.9685,16.6462,16.8542,16.9188,31.7640,31.9928,32.0646,57.6220,58.9268,59.0866]\n",
+"for i=1:18\n",
+"    printf(' %.4f\t\t%.4f\t\t%.4f\t\t%.4f\n',in(i),f(in(i)),n(i),n(i)-f(in(i)))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.3: Bisection_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.3\n",
+"//Bisection Method\n",
+"//Page no. 764\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^3-x^2+x-1')\n",
+"printf('N01\tN02\tN11\tN12\tN21\tNet31\tO31\tN41\tN42\n------------------------------------------------------------------------\n')\n",
+"N01=[0,1,0.5,0.75,0.875,0.938,0.969,0.984,0.992,0.996,0.998,0.999,1,1]\n",
+"N02(1)=2\n",
+"for i=2:13\n",
+"    N02(i)=1;\n",
+"end\n",
+"for i=1:13\n",
+"    net31(i)=f(N01(i+1))*f(N01(i))\n",
+"    if net31(i)>0 then\n",
+"        O31(i)=1;\n",
+"    else\n",
+"        O31(i)=0;\n",
+"    end\n",
+"    N41(i)=(1-O31(i))*(N01(i))+O31(i)*N01(i+1)\n",
+"    N42(i)=(1-O31(i))*N01(i+1)+O31(i)*N02(i)\n",
+"    if i==2 then\n",
+"        printf('%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',0,N02(i),f(N01(i)),N01(i+1),f(N01(i+1)),net31(i),O31(i),N41(i),N42(i))\n",
+"    else\n",
+"    printf('%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',N01(i),N02(i),f(N01(i)),N01(i+1),f(N01(i+1)),net31(i),O31(i),N41(i),N42(i))\n",
+"end\n",
+"\n",
+"end\n",
+"printf('\n\nTherefore the solution is %.3f',N42(13))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.4: Hopfield_Neural_Network.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.4\n",
+"//Hopfield Neural Network\n",
+"//Page no. 766\n",
+"clc;clear;close;\n",
+"\n",
+"A=[1,2,1;-1,1,1;1,0,-1];\n",
+"disp(inv(A),'Inverse of A =',A,'A =')\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        k=0;\n",
+"        for l=1:3\n",
+"            k=k+A(i,l)*A(j,l)\n",
+"        end\n",
+"        T(i,j)=k;\n",
+"    end\n",
+"end\n",
+"disp(T,'T =')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.5: RBF_Network.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.5\n",
+"//RBF Network\n",
+"//Page no. 773\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=10*sin(x)')\n",
+"printf('Input\t\tDesired\t\tNetwork\t\tError\n\t\t Output\t\t Output\n---------------------------------------------------------\n')\n",
+"in=[0.7053,0.7060,0.7097,1.5056,1.5103,1.5377,2.2481,2.2514,2.2599,3.7076,3.7229,3.7364,5.0002,5.0022,5.0028,6.3749,6.3799,6.3886]\n",
+"n=[6.4828,6.4883,6.5164,9.9786,9.9816,9.9944,7.7926,7.7718,7.7180,-5.3625,-5.4910,-5.6034,-9.5884,-9.5828,-9.5809,0.9163,0.9663,1.0527]\n",
+"for i=1:18\n",
+"    printf(' %.4f\t\t%.4f\t\t%.4f\t\t%.4f\n',in(i),f(in(i)),n(i),f(in(i))-n(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 22.7: First_Order_ODE.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 22.7\n",
+"//First Order ODE\n",
+"//Page no. 783\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=(exp(-x^2/2))/(1+x+x^3)')\n",
+"printf('Test Points\tActual Solution \tEstimated Solution\tError\n   x\t\twa(x)\t\t\twt(x)\t\t\tdw(x)\n------------------------------------------------------------------------\n')\n",
+"x=[0.1054,0.1091,0.2693,0.2703,0.3067,0.3088,0.4268,0.4284,0.5098,0.5139];\n",
+"e=[0.1027,0.1063,0.2513,0.2522,0.2832,0.2849,0.3792,0.3805,0.4398,0.4427]\n",
+"for i=1:10\n",
+"    printf(' %.4f \t%.4f  \t\t%.4f\t\t\t%.4f\t\n',x(i),(1-f(x(i))),e(i),-e(i)+(1-f(x(i))))\n",
+"end\n",
+"printf('\n\n\nExperimental result varying from calculated result')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/3-Errors_and_Their_Propagation.ipynb b/Numerical_Methods_Principles_by_Analysis/3-Errors_and_Their_Propagation.ipynb
new file mode 100644
index 0000000..9fd0544
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/3-Errors_and_Their_Propagation.ipynb
@@ -0,0 +1,178 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 3: Errors and Their Propagation"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 3.1: Limiting_Error.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 3.1\n",
+"//Limiting Error\n",
+"//Page no. 45\n",
+"clc;clear;close;\n",
+"R=1000;\n",
+"e=0.1*1000;        //limiting error calculation\n",
+"printf('Magnitude of the Resistor resistence (R) =\n%i <= R <= %i',R-e,R+e)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 3.2: Known_Error.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 3.2\n",
+"//Known Error\n",
+"//Page no. 46\n",
+"clc;clear;close;\n",
+"l=28;d=5;\n",
+"v=%pi*l*(d/2)^2;\n",
+"printf('\nVolume of Cylinder= %f cu. cm',v);\n",
+"re_d=0.1;re_l=-0.5;\n",
+"re_v=2*re_d+re_l;               //relative error computation\n",
+"printf('\n\nRelative error in volume= %f %%',re_v);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 3.3: Absolute_Relative_and_Percentage_Errors.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 3.3\n",
+"//Absolute, Relative and Percetage Errors\n",
+"//Page no. 48\n",
+"clc;clear;close;\n",
+"x=0.00006;x1=0.00005;\n",
+"ex=x-x1;            //absolute error\n",
+"Ex=ex/x1;       //relative error\n",
+"px=100*Ex;     //percentage error  \n",
+"printf('\nAbsolute Error= %f\nRelative Error= %f\nPercentage Error= %f %%',ex,Ex,px);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 3.4: Absolute_Relative_and_Percentage_Errors.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 3.4\n",
+"//Absolute, Relative and Percetage Errors\n",
+"//Page no. 48\n",
+"clc;clear;close;\n",
+"x=100500;x1=100000;\n",
+"ex=x-x1;            //absolute error\n",
+"Ex=ex/x1;       //relative error\n",
+"px=100*Ex;     //percentage error  \n",
+"printf('\nAbsolute Error= %f\nRelative Error= %f\nPercentage Error= %f %%',ex,Ex,px);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 3.5: Absolute_Relative_and_Percentage_Errors.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 3.5\n",
+"//Absolute, Relative and Percentage Errors\n",
+"//Page no. 52\n",
+"clc;clear;close;\n",
+"x=9.12345;y=7.654321;\n",
+"x1=9.1234;y1=7.6543;      //on a 5 decimal computer\n",
+"ex=x-x1;            //absolute error of x\n",
+"ey=y-y1;            //absolute error of y\n",
+"z1=x1+y1;\n",
+"printf('\nAbsolute Error in x= %f',ex);\n",
+"printf('\nAbsolute Error in y= %f',ey);\n",
+"printf('\nAddition on a 5 decimal computer yields= %.5g',z1);\n",
+"z2=16.777;\n",
+"printf('\nAbsolute Total Error= %f',x+y-z2);\n",
+"printf('\nAbsolute Propagated Error= %f',x+y-z1);\n",
+"printf('\nAbsolute Round-off Error= %.4g',z1-z2);\n",
+"printf('\nRealtive Total Error= %.4g',(x+y-z2)/(x+y));\n",
+"printf('\nRelative Propagated Error= %.2g',(x+y-z1)/(x+y));\n",
+"printf('\nRelative Round-off Error= %.3g',(z1-z2)/(x+y));\n",
+"printf('\nBound on the propagated relative error= %f',2*10^-4);\n",
+"printf('\nBound on the total relative error= %f',3*10^-4);\n",
+"printf('\nAs we can see that both the propagated and total relative error are less than their bound values')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/4-Programming_Tools_and_Techniques.ipynb b/Numerical_Methods_Principles_by_Analysis/4-Programming_Tools_and_Techniques.ipynb
new file mode 100644
index 0000000..ca962cb
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/4-Programming_Tools_and_Techniques.ipynb
@@ -0,0 +1,143 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 4: Programming Tools and Techniques"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 4.1: Quadratic_Equatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 4.1\n",
+"//Quadratic Equation\n",
+"//Page no. 96\n",
+"clc;clear;close;\n",
+"a=input('Enter value of a= ');\n",
+"b=input('Enter vlaue of b= ');\n",
+"c=input('Enter value of c= ');\n",
+"x1=(-1*b+sqrt((b^2)-4*a*c))/(2*a);    //1st root\n",
+"x2=(-1*b-sqrt((b^2)-4*a*c))/(2*a);    //2nd root\n",
+"printf('\n1st Root= %f', x1);\n",
+"printf('\n2nd Root= %f', x2);"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 4.2: Database_Management.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 4.2\n",
+"//Database Management\n",
+"//Page no. 112\n",
+"clc;clear;close;\n",
+"M=[12,25,21,35;25,7,23,29;10,27,7,36;26,26,26,35;29,0,23,30];   //marks\n",
+"\n",
+"//calculation of composite score\n",
+"for i=1:5,\n",
+"    j=1;k=0;\n",
+"    max1=M(i,j);\n",
+"    if(max1<M(i,j+1))\n",
+"        max1=M(i,j+1)\n",
+"    else\n",
+"        k=1;\n",
+"    end,\n",
+"    \n",
+"        if(M(i,j+2)>M(i,j+k))\n",
+"        max2=M(i,j+2);\n",
+"    else\n",
+"        max2=M(i,j);\n",
+"    end,\n",
+"       CS(i,1)=max1+max2+M(i,4);\n",
+"end\n",
+"\n",
+"I=['Reg. No.','Name of Students','Test 1','Test 2','Test 3','Final';\n",
+"'CS/01','C.V.Rajan','12','25','21','35';\n",
+"'CS/02','B.X.Roy','25','07','23','29';\n",
+"'CS/03','P.C.Sasikumar','10','27','07','36';\n",
+"'CS/04','B.D.Box','26','26','26','35';\n",
+"'CS/05','K.K.Mukherjee','29','0','23','30';]\n",
+"printf('\n')\n",
+"for i=1:6\n",
+"    for j=1:6\n",
+"        if(j>2)\n",
+"                printf('\t')\n",
+"            end\n",
+"            \n",
+"        printf('%s  ',I(i,j));\n",
+"        if(i~=1)\n",
+"            if(j>2)\n",
+"                printf('\t')\n",
+"            end\n",
+"            printf('    ')\n",
+"            \n",
+"        end\n",
+"        if(i==1 & j==6)\n",
+"            printf('Composite Score\n')\n",
+"        end\n",
+"        \n",
+"    end\n",
+"    \n",
+"    if(i~=1)\n",
+"    printf('%i\n',CS(i-1,1));\n",
+"end\n",
+"\n",
+"end\n",
+"//disp(CS,'Composite Score',I);\n",
+"max1=CS(1,1);j=1;\n",
+"for i=2:5\n",
+"    if(max1<CS(i,1))\n",
+"        max1=CS(i,1);j=i;\n",
+"    end,\n",
+"end\n",
+"printf('\n\nTopper is:\n%s\t%s\t%s',I(1,1),I(1,2),'Composite Score')\n",
+"printf('\nCS/0%i\t\t%s\t\t\t%i',j,I(j+1,2),CS(j,1))"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/5-Solutions_of_Algebraic_and_Transcendental_Equations.ipynb b/Numerical_Methods_Principles_by_Analysis/5-Solutions_of_Algebraic_and_Transcendental_Equations.ipynb
new file mode 100644
index 0000000..55b874c
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/5-Solutions_of_Algebraic_and_Transcendental_Equations.ipynb
@@ -0,0 +1,1738 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 5: Solutions of Algebraic and Transcendental Equations"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.10: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.10\n",
+"//Newton Raphson Method\n",
+"//Page no. 167\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x*exp(-x)')\n",
+"deff('x=f1(x)','x=exp(-x)-x*exp(-x)')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=2;e=0.00001\n",
+"for i=1:11\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, this is not convergent (i.e.) divergent')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.11: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.11\n",
+"//Newton Raphson Method\n",
+"//Page no. 167\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x^3-x-3')\n",
+"deff('x=f1(x)','x=3*x^2-1')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=0;e=0.00001\n",
+"for i=1:11\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, it is cyclic in nature')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.12: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.12\n",
+"//Newton Raphson Method\n",
+"//Page no. 168\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=atan(x)')\n",
+"deff('x=f1(x)','x=1/(1+x^2)')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=1.45;e=0.00001\n",
+"for i=1:12\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.5g   \t\t%.5g\t\t%.5g \t\t%.5g \t\t%.5g\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, it is divergent')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.13: Secant_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.13\n",
+"//Secant Method\n",
+"//Page no. 170\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=exp(x)-3*x-sin(x)')\n",
+"deff('x=f1(x)','x=exp(x)-3-cos(x)')\n",
+"printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')\n",
+"printf('----------------------------------------------------------------------------------------------------------\n')\n",
+"x0=0.567123008;x1=1;e=0.00001\n",
+"for i=1:9\n",
+"    x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))\n",
+"    e1=abs(x0-x2)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),x1,f(x1),x2,e1)\n",
+"    x0=x1;\n",
+"    x1=x2\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, the root is %.10f',x2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.14: Kizner_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.14\n",
+"//Kizner Method\n",
+"//Page no. 172\n",
+"clc;clear;close;\n",
+"h2=0.00001\n",
+"deff('x=f(x)','x=2*x-3-cos(x)')\n",
+"deff('y=f1(x,y)','y=h2/(-x+y)')      //function for differentiation\n",
+"printf('n\th\tc\txn\t\tf(xn)\t\tF(xn)\t\tk1\t\t v\t\tXn+1\n')\n",
+"printf('--------------------------------------------------------------------------------------------------------------------\n')\n",
+"x0=2;e=0.00001;h=0.5;c=0.5;\n",
+"for i=1:11\n",
+"    h1=-f(x0);\n",
+"    F=f1(f(x0),f(x0+h2))\n",
+"    k1=h1*F/2;\n",
+"    v=h*f(x0)/(c*(f(x0+c+h)-f(x0+c)))-k1/c;\n",
+"    a=0;\n",
+"    for j=0:3\n",
+"        a=a+(v^j)/factorial(j+1)\n",
+"    end\n",
+"    x1=x0+k1*a\n",
+"    printf(' %i\t%g\t%g\t%.6f\t%.6f\t%.6f\t%.8f\t %.5f\t%.6f\n',i-1,h,c,x0,f(x0),F,k1,v,x1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, the solution is %.10f',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.15: Brent_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.15\n",
+"//Brent Method\n",
+"//Page no. 173\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=x^2+x-2')\n",
+"x1=0;x2=0.5;x3=2;\n",
+"r=f(x2)/f(x3);s=f(x2)/f(x1);t=f(x1)/f(x3);\n",
+"q=(t-1)*(r-1)*(s-1);\n",
+"p=r*t*(s-1)*(x2-x3)-s*(1-r)*(x2-x1)+(t*s-r)*x2\n",
+"printf('Root is : %.10g',x2+(p/q))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.19: Horner_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.19\n",
+"//Horner Method\n",
+"//Page no. 177\n",
+"clc;clear;close;\n",
+"deff('y=f(x,a1,a2,a3,a4)','y=a1*x^3+a2*x^2+a3*x+a4')\n",
+"\n",
+"k=1;m=2;\n",
+"a=[4;-13;-31;-275];\n",
+"for i=1:10\n",
+"    s=1;\n",
+"    si=f(s,a(1),a(2),a(3),a(4))*abs(1/f(s,a(1),a(2),a(3),a(4)))\n",
+"    while 1\n",
+"        a1=f(s,a(1),a(2),a(3),a(4))*abs(1/f(s,a(1),a(2),a(3),a(4)))\n",
+"        if si~=a1 then\n",
+"            d(i)=s-1\n",
+"            break\n",
+"        end\n",
+"        si=a1;\n",
+"        s=s+1;\n",
+"    end \n",
+"    b(1)=a(1)\n",
+"    for j=1:3\n",
+"        for k=1:4-j\n",
+"            b(k+1)=a(k+1)+b(k)*d(i)\n",
+"            a(k+1)=b(k+1)\n",
+"        end\n",
+"    end\n",
+"    for j=1:3\n",
+"        a(j+1)=10^j*a(j+1)\n",
+"    end\n",
+"end\n",
+"printf('The positive root is %i.',d(1))\n",
+"for i=2:10\n",
+"    printf('%i',d(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.1: Bisection_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.1\n",
+"//Bisection Method\n",
+"//Page no. 145\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=2^x-3*x')\n",
+"x1=0;x2=2;e=0.001;i=0;\n",
+"printf('Iteration\tx1\t\tx2\t\tz\t\tf(z)\n')\n",
+"printf('--------------------------------------------------------------------------\n')\n",
+"while abs(x1-x2)>e\n",
+"    z=(x1+x2)/2\n",
+"    printf('     %i\t\t%f\t%f\t%f\t%f\n',i,x1,x2,z,f(z))\n",
+"    if f(z)*f(x1)>0\n",
+"        x1=z\n",
+"    else\n",
+"        x2=z\n",
+"    end\n",
+"    i=i+1\n",
+"end\n",
+"printf('\n\nThe solution of this equation is %g after %i Iterations',z,i-1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.20: Laguerre_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.20\n",
+"//Laguerre Method\n",
+"//Page no. 180\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=x^3+x^2+10*x-20')\n",
+"deff('y=f1(x)','y=3*x^2+2*x+10')\n",
+"deff('y=f2(x)','y=6*x+2')\n",
+"n=3;\n",
+"printf('i\tn\txi\t\tP(x)\t\tP1(x)\t\tP2(x)\t\tProot\t\tNroot\n')\n",
+"printf('---------------------------------------------------------------------------------------------------------\n')\n",
+"xi=1\n",
+"for i=0:9\n",
+"    Proot=xi-(n*f(xi))/(f1(xi)+sqrt((n-1)*f1(xi)^2-n*f(xi)*f2(xi)))\n",
+"    Nroot=xi-(n*f(xi))/(f1(xi)-sqrt((n-1)*f1(xi)^2-n*f(xi)*f2(xi)))\n",
+"    printf(' %i\t%i\t%f\t%f\t%f\t%f\t%f\t%f\n',i,n,xi,f(xi),f1(xi),f2(xi),Proot,Nroot)\n",
+"    xi=Proot\n",
+"end\n",
+"printf('\n\nProot = %f\n\nNroot = %f',Proot,Nroot)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.21: Mullers_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.21\n",
+"//Mullers Method\n",
+"//Page no. 182\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^3-x-4')\n",
+"zi=[1;2;3];\n",
+"s=['i','z2','z0','z1','f2','f0','f1','a0','a1','a2','zr+','zr-']\n",
+"li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))\n",
+"hi(1)=zi(3,1)-zi(2,1);\n",
+"for i=2:6\n",
+"    for j=1:3\n",
+"       fz(j,i-1)=f(zi(j,i-1))\n",
+"    end\n",
+"    di(i-1)=1+li(i-1)\n",
+"    gi(i-1)=fz(1,i-1)*li(i-1)^2-fz(2,i-1)*di(i-1)^2+fz(3,i-1)*(li(i-1)+di(i-1))\n",
+"    D1(i-1)=gi(i-1)+sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    D2(i-1)=gi(i-1)-sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    if abs(D1(i-1))>abs(D2(i-1)) then\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)\n",
+"    else\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)\n",
+"    end\n",
+"    hi(i)=li(i)*hi(i-1);\n",
+"    z(i-1)=zi(3,i-1)+hi(i)\n",
+"    for j=1:2\n",
+"        zi(j,i)=zi(j+1,i-1)\n",
+"    end\n",
+"    zi(3,i)=z(i-1)\n",
+"end\n",
+"for i=1:12\n",
+"    if i==1 then\n",
+"        printf(s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t\t%i',j-1)\n",
+"        end\n",
+"    elseif i<=4\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',zi(i-1,j))\n",
+"        end\n",
+"    elseif i<=7\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',fz(i-4,j))\n",
+"        end\n",
+"    elseif i<=8\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',li(j))\n",
+"        end\n",
+"    elseif i<=9\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',di(j))\n",
+"        end\n",
+"    elseif i<=10\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',gi(j))\n",
+"        end\n",
+"    elseif i<=11\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',z(j))\n",
+"        end\n",
+"    elseif i<=12\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',zi(j))\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\nAt the end of the %i iteration, the root of the equation is %.10f',j-2,z(j))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.22: Mullers_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.22\n",
+"//Mullers Method\n",
+"//Page no. 183\n",
+"clc;clear;close;\n",
+"\n",
+"deff('y=f(x)','y=x^3-x-4')\n",
+"zi=[1;2;3];\n",
+"s=['i','z0','z1','z2','f0','f1','f2','li','di','gi','li+1','hi','hi+1','zi+1','D+','D_']\n",
+"li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))\n",
+"hi(1)=zi(3,1)-zi(2,1);\n",
+"for i=2:6\n",
+"    for j=1:3\n",
+"       fz(j,i-1)=f(zi(j,i-1))\n",
+"    end\n",
+"    di(i-1)=1+li(i-1)\n",
+"    gi(i-1)=fz(1,i-1)*li(i-1)^2-fz(2,i-1)*di(i-1)^2+fz(3,i-1)*(li(i-1)+di(i-1))\n",
+"    D1(i-1)=gi(i-1)+sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    D2(i-1)=gi(i-1)-sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    if abs(D1(i-1))>abs(D2(i-1)) then\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)\n",
+"    else\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)\n",
+"    end\n",
+"    hi(i)=li(i)*hi(i-1);\n",
+"    z(i-1)=zi(3,i-1)+hi(i)\n",
+"    for j=1:2\n",
+"        zi(j,i)=zi(j+1,i-1)\n",
+"    end\n",
+"    zi(3,i)=z(i-1)\n",
+"end\n",
+"for i=1:16\n",
+"    if i==1 then\n",
+"        printf(s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t\t%i',j-1)\n",
+"        end\n",
+"    elseif i<=4\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',zi(i-1,j))\n",
+"        end\n",
+"    elseif i<=7\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',fz(i-4,j))\n",
+"        end\n",
+"    elseif i<=8\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',li(j))\n",
+"        end\n",
+"    elseif i<=9\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',di(j))\n",
+"        end\n",
+"    elseif i<=10\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',gi(j))\n",
+"        end\n",
+"    elseif i<=11\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',li(j+1))\n",
+"        end\n",
+"    elseif i<=12\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',hi(j))\n",
+"        end\n",
+"        elseif i<=13\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',hi(j+1))\n",
+"        end\n",
+"        elseif i<=14\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',z(j))\n",
+"        end\n",
+"        elseif i<=15\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',D1(j))\n",
+"        end\n",
+"        elseif i<=16\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',D2(j))\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\nAt the end of the %ith iteration, the root of the equation is %.10f',j-1,z(j))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.23: Bairstow_Hitchcock_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.23\n",
+"//Bairstow Hitchcock Method\n",
+"//Page no. 187\n",
+"clc;clear;close;\n",
+"deff('y=f(x,p,q)','y=x^2+p*z+q')\n",
+"a=[1,-1,1,-1,1]\n",
+"a=a';a=[a,a,a,a,a]\n",
+"printf('Iteration-->')\n",
+"for i=1:5\n",
+"    printf('\t%i\t',i)\n",
+"end\n",
+"printf('\n------------------------------------------------------------------------------------------')\n",
+"p(1,1)=-1.2;q(1,1)=0.95;\n",
+"s=['b1','b2','b3','b4','c1','c2','c3','c4','c','dp','dq','p','q']\n",
+"//s1=[b1;b2;b3;b4;c1;c2;c3;c4;c;dp;dq;p;q]\n",
+"for i=1:5\n",
+"    b(1,i)=0;b(2,i)=a(1,i);c(1,i)=0;c(2,i)=a(1,i);\n",
+"       for k=1:4\n",
+"           b(k+2,i)=a(k+1,i)-p(1,i)*b(k+1,i)-q(1,i)*b(k,i)\n",
+"           c(k+2,i)=b(k+2,i)-p(1,i)*c(k+1,i)-q(1,i)*c(k,i)\n",
+"       end\n",
+"      cb(1,i)=c(6,i)-b(6,i);\n",
+"      dq(1,i)=(b(6,i)*c(4,i)-b(5,i)*cb(1,i))/(c(4,i)^2-cb(1,i)*c(3,i))\n",
+"       dp(1,i)=(b(5,i)*c(4,i)-b(6,i)*c(3,i))/(c(4,i)^2-cb(1,i)*c(3,i))\n",
+"     p(1,i+1)=p(1,i)+dp(1,i);q(1,i+1)=q(1,i)+dq(1,i);\n",
+"end\n",
+"for j=1:13\n",
+"  printf('\n     %s\t\t',s(j))\n",
+"  if j<5 then\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',b(j+2,i))\n",
+"      end\n",
+"  elseif j<9 then\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',c(j-2,i))\n",
+"      end\n",
+"  elseif j<10\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',cb(1,i))\n",
+"      end\n",
+"      elseif j<11\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',dp(1,i))\n",
+"      end\n",
+"      elseif j<12\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',dq(1,i))\n",
+"      end\n",
+"      elseif j<13\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',p(1,i+1))\n",
+"      end\n",
+"      else\n",
+"      for i=1:5\n",
+"          printf('%.9f\t',q(1,i+1))\n",
+"      end\n",
+"  end\n",
+"end\n",
+"z=poly(0,'z');\n",
+"a=f(z,p(1,i+1),q(1,i+1));\n",
+"printf('\n\nRoots for Quadratic Equation Q = ')\n",
+"disp(a)\n",
+"a=roots(a)\n",
+"printf('\n\tare\n')\n",
+"disp(a(1))\n",
+"disp(a(2))\n",
+"\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.24: Bernoulli_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.24\n",
+"//Bernoulli Method\n",
+"//Page no. 189\n",
+"clc;clear;close;\n",
+"\n",
+"a=[1,-8,-15,10];\n",
+"for i=1:2\n",
+"    c(i)=0;\n",
+"end\n",
+"c(3)=1;\n",
+"for k=4:13\n",
+"   c(k)=-(a(2)*c(k-1)+a(3)*c(k-2)+a(4)*c(k-3))\n",
+"   r(k-3)=c(k)/c(k-1) \n",
+"end\n",
+"disp(c,'Ck Values')\n",
+"disp(r,'Rk Values')\n",
+"disp(r(k-3),'Therefore the exact root is = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.25: Graeffe_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.25\n",
+"//Graeffe Method\n",
+"//Page no. 191\n",
+"clc;clear;close;\n",
+"\n",
+"a=[1,-6,11,-6]\n",
+"k=0;\n",
+"for k=2:6\n",
+"    for i=1:4\n",
+"        a(k,i)=(-1)^(i-1)*(a(k-1,i))^2\n",
+"        j=1;\n",
+"        while i+j<5 & i+j>2\n",
+"            a(k,i)=a(k,i)+(-1)^(i-j-1)*2*(a(k-1,i-j))*a(k-1,i+j)\n",
+"            break\n",
+"            j=j+1;\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\t\t\t\ta1\t\t\t\ta2\t\t\t\ta3\n k\ta0\ta1\t\t--\t\ta2\t\t--\t\ta3\t\t--\t\n\t\t\t\ta0\t\t\t\ta1\t\t\t\ta2')\n",
+"printf('\n----------------------------------------------------------------------------------------------------\n')\n",
+"for i=1:4\n",
+"    printf(' %i\t%g\t%.4g\t\t%.5g\t\t%.9g\t\t%.8g\t%g\t\t%.10g\n',i-1,a(i,1),a(i,2),abs(a(i,2)/a(i,1))^(1/(2^(i-1))),a(i,3),abs(a(i,3)/a(i,2))^(1/(2^(i-1))),a(i,4),abs(a(i,4)/a(i,3))^(1/(2^(i-1))))\n",
+"end\n",
+"for i=5:6\n",
+"    printf(' %i\t%g\t%.4g\t%.5g\t\t%.9g\t%.8g\t%.7g\t%.10g\n',i-1,a(i,1),a(i,2),abs(a(i,2)/a(i,1))^(1/(2^(i-1))),a(i,3),abs(a(i,3)/a(i,2))^(1/(2^(i-1))),a(i,4),abs(a(i,4)/a(i,3))^(1/(2^(i-1))))\n",
+"end\n",
+"printf('\n\nThe Absolute Values of the roots are %g, %.8g and %g',abs(a(i,2)/a(i,1))^(1/(2^(i-1))),abs(a(i,3)/a(i,2))^(1/(2^(i-1))),abs(a(i,4)/a(i,3))^(1/(2^(i-1))))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.26: QD_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.26\n",
+"//QD Method\n",
+"//Page no. 194\n",
+"clc;clear;close;\n",
+"\n",
+"a=[32,-48,18,-1]\n",
+"for i=1:5\n",
+"    e(i,1)=0;\n",
+"    e(i,4)=0;\n",
+"end\n",
+"q(1,1)=-a(2)/a(1);\n",
+"q(1,2)=0;q(1,3)=0;\n",
+"e(1,2)=a(3)/a(2);\n",
+"e(1,3)=a(4)/a(3);\n",
+"for i=2:16\n",
+"    for j=1:3\n",
+"        q(i,j)=e(i-1,j+1)+q(i-1,j)-e(i-1,j)\n",
+"    end\n",
+"    for j=1:2\n",
+"        e(i,j+1)=e(i-1,j+1)*q(i,j+1)/q(i,j)\n",
+"    end\n",
+"end\n",
+"printf('e0\t\tq1\t\te1\t\tq2\t\te2\t\tq3\t\te3\n')\n",
+"printf('------------------------------------------------------------------------------------------------------------\n')\n",
+"for i=1:14\n",
+"    for j=1:3\n",
+"        printf('\t\t%.10f\t',q(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"    for j=1:4\n",
+"        printf('%.10f\t\t\t',e(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\t\t%.10f\t\t\t%.10f\t\t\t%.10f\n',q(15,1),q(15,2),q(15,3))\n",
+"printf('\nThe exact roots are \t%.10f    and    %.10f',q(15,1),q(15,3))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.27: Linear_Iteration_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.27\n",
+"//Linear Iteration Method\n",
+"//Page no. 198\n",
+"clc;clear;close;\n",
+"\n",
+"deff('x=f(x)','x=20/(x^2+2*x+10)')\n",
+"printf('n\tx\t\tf(x)\n')\n",
+"printf('-------------------------------------\n')\n",
+"x=1;\n",
+"for i=1:19\n",
+"    printf(' %i\t%.10f\t%.10f\n',i,x,f(x))\n",
+"    x1=x;\n",
+"    x=f(x);\n",
+"end\n",
+"printf('\n\nx = %.10f',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.28: Aitkens_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.28\n",
+"//Aitkens Method\n",
+"//Page no. 199\n",
+"clc;clear;close;\n",
+"\n",
+"deff('x=f(x)','x=20/(x^2+2*x+10)')\n",
+"printf('n\tx0\t\tx1\t\tx2\t\tx3\t\ty\t\tdx0\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=1;e=0.0001\n",
+"for i=1:3\n",
+"    x1=f(x0);x2=f(x1);x3=f(x2);\n",
+"    y=x3-((x3-x2)^2)/(x3-2*x2+x1)\n",
+"    dx0=y-x0;\n",
+"    \n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i,x0,x1,x2,x3,y,dx0)\n",
+"    x0=y;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,y)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.29: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.29\n",
+"//Newton Raphson Method\n",
+"//Page no. 199\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x^3+2*x^2+10*x-20')\n",
+"deff('x=f1(x)','x=3*x^2+4*x+10')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=01;e=0.00001\n",
+"for i=1:4\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.2: Bisection_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.2\n",
+"//Bisection Method\n",
+"//Page no. 147\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=x^x-2*x+2')\n",
+"x1=0;x2=2;e=0.001;i=0;\n",
+"printf('Iteration\tx1\t\tx2\t\tz\t\tf(z)\n')\n",
+"printf('--------------------------------------------------------------------------\n')\n",
+"while abs(x1-x2)>e\n",
+"    z=(x1+x2)/2\n",
+"    printf('     %i\t\t%f\t%f\t%f\t%f\n',i,x1,x2,z,f(z))\n",
+"    if f(z)*f(x1)>0\n",
+"        x1=z\n",
+"    else\n",
+"        x2=z\n",
+"    end\n",
+"    i=i+1\n",
+"end\n",
+"printf('\n\nThe solution of this equation is %g after %i Iterations',z,i-1)\n",
+"\n",
+"printf('\n\n\nNote : There are computational errors in the answer given by the book for this example')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.31: Secant_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.31\n",
+"//Secant Method\n",
+"//Page no. 200\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=(x-0.6)*(x-1.3)^2*(x-2)^3+0.01234*log(x)')\n",
+"printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')\n",
+"printf('----------------------------------------------------------------------------------------------------------\n')\n",
+"x0=0.1;x1=1.2;e=0.00001\n",
+"for i=1:7\n",
+"    x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))\n",
+"    e1=abs(x0-x2)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),x1,f(x1),x2,e1)\n",
+"    x0=x1;\n",
+"    x1=x2\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, the root is %.10f',x2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.32: Regula_Falsi_Newton_Raphson_and_Mullers_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.32\n",
+"//Regula Falsi, Newton Raphson and Mullers Method\n",
+"//Page no. 201\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x^5-3.7*x^4+7.4*x^3-10.8*x^2+10.8*x-6.8')\n",
+"deff('x=f1(x)','x=5*x^4-4*3.7*x^3+3*7.4*x^2-21.6*x+10.8')\n",
+"//newton raphson\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=1.5;e=0.00001\n",
+"for i=1:4\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation by newton raphshon after %i Iterations is %.10f\n\n\n',i,x1)\n",
+"\n",
+"//regula falsi\n",
+"x1=1;x2=2;e=0.00001\n",
+"printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)')\n",
+"printf('\n-------------------------------------------------------------------------------------------------\n')\n",
+"for i=0:7\n",
+"    x3=x2*f(x1)/(f(x1)-f(x2))+x1*f(x2)/(f(x2)-f(x1))\n",
+"    printf(' %i\t%f\t%f\t%f\t%f\t%f\t%f\n',i,x1,f(x1),x2,f(x2),x3,f(x3))\n",
+"    if f(x1)*f(x3)>0 then\n",
+"        x1=x3\n",
+"    else\n",
+"        x2=x3\n",
+"    end\n",
+"    if abs(f(x3))<e then\n",
+"        break\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore the solution by regula falsi method after %i iterations is %.10g',i,x3)\n",
+"\n",
+"//mullers method\n",
+"zi=[1;2;3];\n",
+"s=['i','z0','z1','z2','f0','f1','f2','li','di','gi','li+1','hi','hi+1','zi+1','D+','D_']\n",
+"li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))\n",
+"hi(1)=zi(3,1)-zi(2,1);\n",
+"for i=2:6\n",
+"    for j=1:3\n",
+"       fz(j,i-1)=f(zi(j,i-1))\n",
+"    end\n",
+"    di(i-1)=1+li(i-1)\n",
+"    gi(i-1)=fz(1,i-1)*li(i-1)^2-fz(2,i-1)*di(i-1)^2+fz(3,i-1)*(li(i-1)+di(i-1))\n",
+"    D1(i-1)=gi(i-1)+sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    D2(i-1)=gi(i-1)-sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    if abs(D1(i-1))>abs(D2(i-1)) then\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)\n",
+"    else\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)\n",
+"    end\n",
+"    hi(i)=li(i)*hi(i-1);\n",
+"    z(i-1)=zi(3,i-1)+hi(i)\n",
+"    for j=1:2\n",
+"        zi(j,i)=zi(j+1,i-1)\n",
+"    end\n",
+"    zi(3,i)=z(i-1)\n",
+"end\n",
+"printf('\n\n ')\n",
+"for i=1:16\n",
+"    if i==1 then\n",
+"        printf(s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t\t %i',j-1)\n",
+"        end\n",
+"        printf('\n----------------------------------------------------------------------------------------------------------------------------------')\n",
+"    elseif i<=4\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',zi(i-1,j))\n",
+"        end\n",
+"    elseif i<=7\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',fz(i-4,j))\n",
+"        end\n",
+"    elseif i<=8\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',li(j))\n",
+"        end\n",
+"    elseif i<=9\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',di(j))\n",
+"        end\n",
+"    elseif i<=10\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',gi(j))\n",
+"        end\n",
+"    elseif i<=11\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',li(j+1))\n",
+"        end\n",
+"    elseif i<=12\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',hi(j))\n",
+"        end\n",
+"        elseif i<=13\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',hi(j+1))\n",
+"        end\n",
+"        elseif i<=14\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',z(j))\n",
+"        end\n",
+"        elseif i<=15\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',D1(j))\n",
+"        end\n",
+"        elseif i<=16\n",
+"        printf('\n %s',s(i))\n",
+"        for j=1:5\n",
+"            printf('\t\t%.10f',D2(j))\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\nAt the end of the %ith iteration by mullers method, the root of the equation is %.10f',j-1,z(j))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.33: Newton_Raphson_and_Mullers_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.33\n",
+"//Newton Raphson and Mullers Method\n",
+"//Page no. 202\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x^4-8*x^3+18*x^2+0.12*x-24.24')\n",
+"deff('x=f1(x)','x=4*x^3-24*x^2+36*x+0.12')\n",
+"\n",
+"//newton raphson\n",
+"x9=[1.5,2.5,2.7,3.1;4,5,14,10]\n",
+"for h=1:4\n",
+"    x0=x9(1,h);e=0.00001\n",
+"for i=1:x9(2,h)\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\nThe solution of this equation by newton raphshon after %i Iterations is %.5f\n',i,x1)\n",
+"end\n",
+"\n",
+"//mullers method\n",
+"zx=[1,2,2.7,3.1;2,3,3.7,4.1;3,4,4.7,5.1]\n",
+"zi=[1;2;3];\n",
+"s=['i','z0','z1','z2','f0','f1','f2','li','di','gi','li+1','hi','hi+1','zi+1','D+','D_']\n",
+"li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))\n",
+"hi(1)=zi(3,1)-zi(2,1);\n",
+"for i=2:4\n",
+"    for j=1:3\n",
+"       fz(j,i-1)=f(zi(j,i-1))\n",
+"    end\n",
+"    di(i-1)=1+li(i-1)\n",
+"    gi(i-1)=fz(1,i-1)*li(i-1)^2-fz(2,i-1)*di(i-1)^2+fz(3,i-1)*(li(i-1)+di(i-1))\n",
+"    D1(i-1)=gi(i-1)+sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    D2(i-1)=gi(i-1)-sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))\n",
+"    if abs(D1(i-1))>abs(D2(i-1)) then\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)\n",
+"    else\n",
+"        li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)\n",
+"    end\n",
+"    hi(i)=li(i)*hi(i-1);\n",
+"    z(i-1)=zi(3,i-1)+hi(i)\n",
+"    for j=1:2\n",
+"        zi(j,i)=zi(j+1,i-1)\n",
+"    end\n",
+"    zi(3,i)=z(i-1)\n",
+"end\n",
+"printf('\n\nAt the end of the %ith iteration by mullers method, the root of the equation is %.10f',j+2,z(j))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.34: QD_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.34\n",
+"//QD Method\n",
+"//Page no. 202\n",
+"clc;clear;close;\n",
+"a=[1,2,10,-20]\n",
+"for i=1:5\n",
+"    e(i,1)=0;\n",
+"    e(i,4)=0;\n",
+"end\n",
+"q(1,1)=-a(2)/a(1);\n",
+"q(1,2)=0;q(1,3)=0;\n",
+"e(1,2)=a(3)/a(2);\n",
+"e(1,3)=a(4)/a(3);\n",
+"for i=2:7\n",
+"    for j=1:3\n",
+"        q(i,j)=e(i-1,j+1)+q(i-1,j)-e(i-1,j)\n",
+"    end\n",
+"    for j=1:2\n",
+"        e(i,j+1)=e(i-1,j+1)*q(i,j+1)/q(i,j)\n",
+"    end\n",
+"end\n",
+"printf('e0\t\tq1\t\te1\t\tq2\t\te2\t\tq3\t\te3\n')\n",
+"printf('------------------------------------------------------------------------------------------------------------\n')\n",
+"for i=1:7\n",
+"    for j=1:3\n",
+"        printf('\t\t%.10f\t',q(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"    for j=1:4\n",
+"        printf('%.10f\t\t\t',e(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\t\t%.10f\t\t\t%.10f\t\t\t%.10f\n',q(7,1),q(7,2),q(7,3))\n",
+"printf('\nThe exact roots are \t%.10f    and    %.10f',q(7,1),q(7,3))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.35: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.35\n",
+"//Newton Raphson Method\n",
+"//Page no. 203\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x^3-30*x^2+2552')\n",
+"deff('x=f1(x)','x=3*x^2-60*x')\n",
+"//newton raphson\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=10;e=0.00001\n",
+"for i=1:4\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThus the ball is submerged upto height of %.10f cm\n\n\n',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.36: Secant_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.36\n",
+"//Secant Method\n",
+"//Page no. 204\n",
+"clc;clear;close;\n",
+"a=8670;c=10^-8;t2=1.4*10^-4;\n",
+"deff('x=f(x)','x=-t2+log((1-2*x/a)/(2-x/a))*(a*x*c)/(a+x)')\n",
+"\n",
+"printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')\n",
+"printf('----------------------------------------------------------------------------------------------------------\n')\n",
+"x0=20000;x1=25000;e=0.00001\n",
+"for i=1:8\n",
+"    x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))\n",
+"    e1=abs(x0-x2)\n",
+"    printf(' %i\t%f\t%.10f\t%f\t%.10f\t%f\t%.10f\n',i-1,x0,f(x0),x1,f(x1),x2,e1)\n",
+"    x0=x1;\n",
+"    x1=x2\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, Rb = %.10f ohm',x2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.37: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.37\n",
+"//Newton Raphson Method\n",
+"//Page no. 204\n",
+"clc;clear;close;\n",
+"p=1.1;T=250;R=0.082;a=3.6;b=0.043;\n",
+"deff('y=f(v)','y=p*v^3-(b*p+R*T)*v^2+a*v-a*b')\n",
+"deff('y=f1(v)','y=3*p*v^2-2*(b*p+R*T)*v')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=0.1;e=0.00001\n",
+"for i=1:10\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, Volume v = %.10f ltr',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.38: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.38\n",
+"//Newton Raphson Method\n",
+"//Page no. 205\n",
+"clc;clear;close;\n",
+"deff('y=f(p)','y=p^3-9*p^2+33*p-65')\n",
+"deff('y=f1(p)','y=3*p^2-18*p+33')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=6;e=0.00001\n",
+"for i=1:10\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, Market Price at equilibrium = Rs. %.f',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.39: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.39\n",
+"//Newton Raphson Method\n",
+"//Page no. 205\n",
+"clc;clear;close;\n",
+"deff('y=f(v)','y=v^3-20*v+30')\n",
+"deff('y=f1(v)','y=3*v^2-20')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=10;e=0.00001\n",
+"for i=1:10\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, sides are  = %.5f m x %.5f m x %.5f m',x1,x1,20/x1^2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.3: Regula_Falsi_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.3\n",
+"//Regula Falsi Method\n",
+"//Page no. 149\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=x^3-3*x-5')\n",
+"x1=2;x2=3;e=0.00001\n",
+"printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)')\n",
+"printf('\n-------------------------------------------------------------------------------------------------\n')\n",
+"for i=0:19\n",
+"    x3=x2*f(x1)/(f(x1)-f(x2))+x1*f(x2)/(f(x2)-f(x1))\n",
+"    printf(' %i\t%f\t%f\t%f\t%f\t%f\t%f\n',i,x1,f(x1),x2,f(x2),x3,f(x3))\n",
+"    if f(x1)*f(x3)>0 then\n",
+"        x1=x3\n",
+"    else\n",
+"        x2=x3\n",
+"    end\n",
+"    if abs(f(x3))<e then\n",
+"        break\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore the solution is %.10g',x3)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.40: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.40\n",
+"//Newton Raphson Method\n",
+"//Page no. 206\n",
+"clc;clear;close;\n",
+"deff('y=f(F)','y=-10*F^3-21*F+10')\n",
+"deff('y=f1(F)','y=-21-30*F^2')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=1;e=0.00001\n",
+"for i=1:10\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.6f\t%.5f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\t\t\t\t\t2\n Therefore, Magnetic Flux = %.5f Wb m',x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.4: Ridders_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.4\n",
+"//Ridders Method\n",
+"//Page no. 153\n",
+"clc;clear;close;\n",
+"deff('y=f(x)','y=x^3-3*x-5')\n",
+"x1=2;x2=3;e=0.00001\n",
+"printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)\t   sign\t  x4')\n",
+"printf('\n----------------------------------------------------------------------------------------------------------\n')\n",
+"for i=0:8\n",
+"    x3=(x1+x2)/2\n",
+"    a=f(x1)-f(x2);\n",
+"    s=a*abs(1/a)\n",
+"    x4=x3+(x3-x2)*(s*f(x3))/sqrt(f(x3)-f(x1)*f(x2))\n",
+"    printf(' %i\t%f\t%f\t%f\t%f\t%f\t%f    %i\t%f\n',i,x1,f(x1),x2,f(x2),x3,f(x3),s,x4)\n",
+"    if f(x1)*f(x4)>0 then\n",
+"        x1=x4\n",
+"    else\n",
+"        x2=x4\n",
+"    end\n",
+"    if abs(f(x4))<e then\n",
+"        break\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation is %g after %i Iterations',x4,i)\n",
+"printf('\n\n\nThere are computation error in the answers given by the book in this example\n\n(value of x1 is used instead of x2)')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.5: General_Iterative_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.5\n",
+"//General Iterative Method\n",
+"//Page no. 154\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=sqrt(3+5/x)')\n",
+"printf('n\tx\t\tf(x)\n')\n",
+"printf('------------------------------------\n')\n",
+"x=2;\n",
+"for i=1:8\n",
+"    printf(' %i\t%.10f\t%.10f\n',i,x,f(x))\n",
+"    x=f(x);\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.6: Linear_Iterative_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.6\n",
+"//Linear Iterative Method\n",
+"//Page no. 159\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=1+sin(x)/10')\n",
+"printf('n\tx\t\tf(x)\n')\n",
+"printf('-------------------------------------\n')\n",
+"x=0;\n",
+"for i=1:7\n",
+"    printf(' %i\t%.10f\t%.10f\n',i,x,f(x))\n",
+"    x=f(x);\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.7: Aitkens_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.7\n",
+"//Aitkens Method\n",
+"//Page no. 161\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=exp(-x)')\n",
+"printf('n\tx0\t\tx1\t\tx2\t\tx3\t\ty\t\tdx0\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=0.5;e=0.0001\n",
+"for i=1:3\n",
+"    x1=f(x0);x2=f(x1);x3=f(x2);\n",
+"    y=x3-((x3-x2)^2)/(x3-2*x2+x1)\n",
+"    dx0=y-x0;\n",
+"    \n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i,x0,x1,x2,x3,y,dx0)\n",
+"    x0=y;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,y)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.8: Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.8\n",
+"//Newton Raphson Method\n",
+"//Page no. 163\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=x-exp(-x)')\n",
+"deff('x=f1(x)','x=1+exp(-x)')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=0.5;e=0.00001\n",
+"for i=1:4\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x1)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 5.9: Modified_Newton_Raphson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 5.9\n",
+"//Modified Newton Raphson Method\n",
+"//Page no. 165\n",
+"clc;clear;close;\n",
+"deff('x=f(x)','x=exp(x)-3*x-sin(x)')\n",
+"deff('x=f1(x)','x=exp(x)-3-cos(x)')\n",
+"printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')\n",
+"printf('-----------------------------------------------------------------------------------------------------\n')\n",
+"x0=0;e=0.00001\n",
+"for i=1:4\n",
+"    x1=x0-f(x0)/f1(x0)\n",
+"    e1=abs(x0-x1)\n",
+"    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)\n",
+"    x0=x1;\n",
+"    if abs(x0)<e then\n",
+"        break;\n",
+"    end\n",
+"end\n",
+"printf('\n\nTherefore, the root is %.10f',x1)"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/6-Numerical_Methods_of_Linear_Equations_Direct_Methods.ipynb b/Numerical_Methods_Principles_by_Analysis/6-Numerical_Methods_of_Linear_Equations_Direct_Methods.ipynb
new file mode 100644
index 0000000..31322e6
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/6-Numerical_Methods_of_Linear_Equations_Direct_Methods.ipynb
@@ -0,0 +1,504 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 6: Numerical Methods of Linear Equations Direct Methods"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.10: Solving_Matrices.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.10\n",
+"//Solving Matrices\n",
+"//Page no. 244\n",
+"clc;close;clear;\n",
+"warning('off')\n",
+"for i=1:7\n",
+"    s=0;\n",
+"    for j=1:7\n",
+"        A(i,j)=360360/(i+j)\n",
+"    end\n",
+"    B(i,1)=1;\n",
+"end\n",
+"X=inv(A)*B\n",
+"disp(360360*X,'The Solution by 360360*X= ')\n",
+"disp(X,'Final Solution = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.1: Gaussian_Elimination_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.1\n",
+"//Gaussian Elimination Method\n",
+"//Page no. 220\n",
+"clc;clear;close;\n",
+"\n",
+"A=[5,10,1,28;1,1,1,6;4,8,3,29];           //augmented matrix\n",
+"\n",
+"//triangularization\n",
+"for i=1:4\n",
+"    B(1,i)=A(1,i)\n",
+"    B(2,i)=A(2,i)-(A(2,1)/A(1,1))*A(1,i)\n",
+"    B(3,i)=A(3,i)-(A(3,1)/A(1,1))*A(1,i)\n",
+"end\n",
+"disp(A,'Augmented Matrix=')\n",
+"disp(B,'Triangulated Matrix=')\n",
+"//back substitution\n",
+"x(3)=B(3,4)/B(3,3);\n",
+"printf('\nx(3)=%f\n',x(3))\n",
+"for i=2:-1:1\n",
+"    k=0\n",
+"    for j=i+1:3\n",
+"       k=k+B(i,j)*x(j)\n",
+"    end\n",
+"    x(i)=(1/B(i,i))*(B(i,4)-k)\n",
+"     printf('\nx(%i)=%f\n',i,x(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.2: Gaussian_Elimination_Method_for_TriDiagonal_System.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.2\n",
+"//Gaussian Elimination Method for Tri-Diagonal System\n",
+"//Page no. 222\n",
+"clc;clear;close;\n",
+"\n",
+"//equation matrix\n",
+"A=[1,2,0,0;2,3,-1,0;0,4,2,3;0,0,2,-1];\n",
+"K=[5;5;11;10];i=1;\n",
+"\n",
+"//initialization\n",
+"w(1)=A(1,2)/A(1,1);\n",
+"g(1)=K(1)/A(1,1);\n",
+"printf('\nw(%i)=%f',i,w(i));printf('\ng(%i)=%f',i,g(i))\n",
+"\n",
+"//computation\n",
+"for i=2:3\n",
+"    w(i)=(A(i,i+1))/(A(i,i)-A(i,i-1)*w(i-1))\n",
+"    g(i)=(K(i)-A(i,i-1)*g(i-1))/(A(i,i)-A(i,i-1)*w(i-1))\n",
+"    printf('\nw(%i)=%f',i,w(i))\n",
+"    printf('\ng(%i)=%f',i,g(i))\n",
+"end\n",
+"i=4\n",
+"m=-2\n",
+"g(i)=m*(K(i)-A(i,i-1)*g(i-1))/(A(i,i)-A(i,i-1)*w(i-1))\n",
+"x(i)=g(i)\n",
+"printf('\ng(%i)=%f',i,g(i))\n",
+"printf('\n\nx(%i)=%f',i,x(i))\n",
+"\n",
+"//solution\n",
+"for i=3:-1:1\n",
+"    x(i)=g(i)-w(i)*x(i+1)\n",
+"    printf('\n\nx(%i)=%f',i,x(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.3: Gauss_Jordan_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.3\n",
+"//Gauss-Jordan Method\n",
+"//Page no. 224\n",
+"\n",
+"clc;clear;close;\n",
+"\n",
+"A=[5,10,1,28;4,8,3,29;1,1,1,6];     //augmented matrix\n",
+"\n",
+"for i=1:3\n",
+"    j=i\n",
+"    while (A(i,i)==0 & j<=3)\n",
+"        for k=1:4\n",
+"            B(1,k)=A(j+1,k)\n",
+"            A(j+1,k)=A(i,k)\n",
+"            A(i,k)=B(1,k)\n",
+"        end\n",
+"        disp(A)\n",
+"        j=j+1\n",
+"    end\n",
+"    disp(A)\n",
+"    for k=4:-1:i\n",
+"        A(i,k)=A(i,k)/A(i,i)\n",
+"    end\n",
+"    disp(A)\n",
+"    for k=1:3\n",
+"        if(k~=i) then\n",
+"           l=A(k,i)/A(i,i)\n",
+"           for m=i:4\n",
+"               A(k,m)=A(k,m)-l*A(i,m)\n",
+"           end\n",
+"        end\n",
+"       \n",
+"    end\n",
+"    disp(A)\n",
+"end\n",
+"\n",
+"for i=1:3\n",
+"    printf('\nx(%i) = %g\n',i,A(i,4))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.4: Gaussian_Elimination_Method_without_Pivoting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.4\n",
+"//Gaussian Elimination Method without Pivoting\n",
+"//Page no. 227\n",
+"clc;clear;close;\n",
+"\n",
+"A=[0.3*10^-11,1,0.7;1,1,0.9];           //augmented matrix\n",
+"\n",
+"//triangularization\n",
+"for i=1:3\n",
+"    B(1,i)=A(1,i)\n",
+"    B(2,i)=A(2,i)-(A(2,1)/A(1,1))*A(1,i)\n",
+"end\n",
+"disp(A,'Augmented Matrix=')\n",
+"disp(B,'Triangulated Matrix=')\n",
+"\n",
+"//back substitution\n",
+"x(2)=B(2,3)/B(2,2);\n",
+"printf('\nx(2)=%f\n',x(2))\n",
+"for i=1:-1:1\n",
+"    k=0\n",
+"    for j=i+1:2\n",
+"       k=k+B(i,j)*x(j)\n",
+"    end\n",
+"    x(i)=(1/B(i,i))*(B(i,3)-k)\n",
+"     printf('\nx(%i)=%f\n',i,x(i))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.5: Dolittle_Factorization_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.5\n",
+"//Dolittle Factorization Method\n",
+"//Page no. 233\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,1,1;1,3,1;1,1,4];\n",
+"printf('\tL\t\t  *\t\tU\t\t  =\t\tA')\n",
+"U(2,1)=0;U(3,1)=0;U(3,2)=0;\n",
+"L(1,2)=0;L(1,3)=0;L(2,3)=0;\n",
+"for i=1:3\n",
+"    L(i,i)=1\n",
+"end\n",
+"for i=1:3\n",
+"    U(1,i)=A(1,i)\n",
+"end\n",
+"L(2,1)=1/U(1,1);\n",
+"for i=2:3\n",
+"    U(2,i)=A(2,i)-U(1,i)*L(2,1);\n",
+"end\n",
+"L(3,1)=1/U(1,1);\n",
+"L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);\n",
+"U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);\n",
+"printf('\n')\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%.2f\t',L(i,j))\n",
+"    end\n",
+"    \n",
+"    if(i==2)\n",
+"        printf('  *     ')\n",
+"    else\n",
+"        printf('\t')\n",
+"    end\n",
+"    \n",
+"    for j=1:3\n",
+"        printf('%.2f\t',U(i,j))\n",
+"    end\n",
+"    if(i==2)\n",
+"        printf('  =     ')\n",
+"    else\n",
+"        printf('\t')\n",
+"    end\n",
+"    for j=1:3\n",
+"        printf('%.2f\t',A(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.6: Trangularization_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.6\n",
+"//Trangularization Method\n",
+"//Page no. 236\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,1,1;1,3,1;1,1,4];\n",
+"B=[7;10;15];\n",
+"printf('A can be factorizaed as follows:\n')\n",
+"printf('\tL\t\t  *\t\tU\t\t  =\t\tA')\n",
+"U(2,1)=0;U(3,1)=0;U(3,2)=0;\n",
+"L(1,2)=0;L(1,3)=0;L(2,3)=0;\n",
+"for i=1:3\n",
+"    L(i,i)=1\n",
+"end\n",
+"for i=1:3\n",
+"    U(1,i)=A(1,i)\n",
+"end\n",
+"L(2,1)=1/U(1,1);\n",
+"for i=2:3\n",
+"    U(2,i)=A(2,i)-U(1,i)*L(2,1);\n",
+"end\n",
+"L(3,1)=1/U(1,1);\n",
+"L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);\n",
+"U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);\n",
+"printf('\n')\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%.2f\t',L(i,j))\n",
+"    end\n",
+"    \n",
+"    if(i==2)\n",
+"        printf('  *     ')\n",
+"    else\n",
+"        printf('\t')\n",
+"    end\n",
+"    \n",
+"    for j=1:3\n",
+"        printf('%.2f\t',U(i,j))\n",
+"    end\n",
+"    if(i==2)\n",
+"        printf('  =     ')\n",
+"    else\n",
+"        printf('\t')\n",
+"    end\n",
+"    for j=1:3\n",
+"        printf('%.2f\t',A(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\nY=U*X')\n",
+"    Y=inv(L)*B\n",
+"    X=inv(U)*Y\n",
+"printf('\n\nX=')\n",
+"for i=1:3\n",
+"    printf('\n   %i',X(i,1))\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.7: Wilkinson_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.7\n",
+"//Wilkinson Method\n",
+"//Page no. 240\n",
+"clc;clear;close;\n",
+"\n",
+"A=[0.3*10^5,0.212,0.332;0.216,0.376,0.477;0.173,0.663,0.626];\n",
+"B=[0.235;0.128;0.285];\n",
+"X=inv(A)\n",
+"disp(X*B,'Final Solution = ')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.8: Choleskys_Factorizatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.8\n",
+"//Cholesky's Factorization\n",
+"//Page no. 243\n",
+"clc;clear;close;\n",
+"\n",
+"A=[1,2,3;2,5,8;3,8,22];\n",
+"U(2,1)=0;U(3,1)=0;U(3,2)=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            k=0;\n",
+"            for m=1:i-1\n",
+"               k=k+U(m,i)^2; \n",
+"            end\n",
+"            U(i,j)=sqrt(A(i,j)-k)\n",
+"        end\n",
+"        if(j>i)\n",
+"            k=0;\n",
+"            for m=1:i-1\n",
+"                k=k+U(m,j)*U(m,i);\n",
+"            end\n",
+"            U(i,j)=(A(i,j)-k)/U(i,i)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"disp(U,'Required Matrix (U)=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 6.9: Complex_System_of_Linear_Equation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 6.9\n",
+"//Complex System of Linear Equation\n",
+"//Page no. 244\n",
+"clc;clear;close;\n",
+"\n",
+"for i=1:7\n",
+"    s=0;\n",
+"    for j=1:7\n",
+"        A(i,j)=j^i\n",
+"        s=s+(-1)^(j+1)*A(i,j)\n",
+"    end\n",
+"    B(i,1)=s;\n",
+"end\n",
+"X=inv(A)*B\n",
+"disp(X,'The Solution = ')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/7-Numerical_Solutions_for_Matrix_Inversion.ipynb b/Numerical_Methods_Principles_by_Analysis/7-Numerical_Solutions_for_Matrix_Inversion.ipynb
new file mode 100644
index 0000000..8588c3b
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/7-Numerical_Solutions_for_Matrix_Inversion.ipynb
@@ -0,0 +1,451 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 7: Numerical Solutions for Matrix Inversion"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.1: Gauss_Jordan_Two_Array_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.1\n",
+"//Gauss-Jordan Two Array Method\n",
+"//Page no. 254\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,6,1;3,9,2;0,-1,3];   //matrix\n",
+"C=eye(3,3);               //Unit Matrix\n",
+"for i=1:3                  //interchange of row 1 and 2\n",
+"    B(1,i)=A(1,i);\n",
+"    A(1,i)=A(2,i);\n",
+"    A(2,i)=B(1,i);\n",
+"    B(2,i)=C(1,i);\n",
+"    C(1,i)=C(2,i);\n",
+"    C(2,i)=B(2,i);\n",
+"end\n",
+"printf('\n')\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)/3;\n",
+"    C(1,i)=C(1,i)/3;\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(2,i)=A(2,i)-2*A(1,i);\n",
+"    C(2,i)=C(2,i)-2*C(1,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3        //interchange of row 2 and 3\n",
+"    B(1,i)=A(2,i);\n",
+"    A(2,i)=A(3,i);\n",
+"    A(3,i)=B(1,i);\n",
+"    B(2,i)=C(2,i);\n",
+"    C(2,i)=C(3,i);\n",
+"    C(3,i)=B(2,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(2,i)=-1*A(2,i);\n",
+"    C(2,i)=-1*C(2,i);\n",
+"end\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)-3*A(2,i);\n",
+"    C(1,i)=C(1,i)-3*C(2,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(3,i)=-3*A(3,i);\n",
+"    C(3,i)=-3*C(3,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)-A(3,i)*(29/3);\n",
+"    C(1,i)=C(1,i)-29*C(3,i)/3;\n",
+"end\n",
+"for i=1:3\n",
+"    A(2,i)=A(2,i)+A(3,i)*3;\n",
+"    C(2,i)=C(2,i)+C(3,i)*3;\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"disp(C,'Inverse Matrix of A')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.2: Inverse_in_Place_without_Pivoting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.2\n",
+"//Inverse in Place without Pivoting\n",
+"//Page no. 256\n",
+"clc;clear;close;\n",
+"\n",
+"A=[3,-6,7;9,0,-5;5,-8,6];   //matrix\n",
+"B=[3,-6,7;9,0,-5;5,-8,6];   //copied matrix\n",
+"for i=1:3\n",
+"    printf('\n\nStage %i',i);\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            B(i,j)=1/B(i,j);\n",
+"        else\n",
+"            B(i,j)=A(i,j)/A(i,i);\n",
+"        end,\n",
+"    end\n",
+"    disp(B)\n",
+"        for j=1:3\n",
+"            for k=1:3\n",
+"                if(i~=j)\n",
+"                    B(j,k)=A(j,k)-A(j,i)*B(i,k);\n",
+"                end,\n",
+"            end\n",
+"        end\n",
+"        disp(B)\n",
+"    for j=1:3\n",
+"        if(i~=j)\n",
+"            B(j,i)=-1*A(j,i)*B(i,i);\n",
+"        end,\n",
+"        \n",
+"    end\n",
+"    disp(B)\n",
+"    A=B;\n",
+"end\n",
+"disp(B,'Inverse of Matrix A=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.3: Inverse_in_Place_with_Pivoting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.3\n",
+"//Inverse in Place with Pivoting\n",
+"//Page no. 258\n",
+"clc;clear;close;\n",
+"\n",
+"A=[3,-6,7;9,0,-5;5,-8,6];     //matrix\n",
+"B=[3,-6,7;9,0,-5;5,-8,6];      //copied matrix\n",
+"\n",
+"for i=1:3\n",
+"    printf('\n\nStage %i',i)\n",
+"    if(i<3)\n",
+"        for j=1:3         //interchange of rows\n",
+"            C(i,j)=A(i,j);\n",
+"            A(i,j)=A(i+1,j);\n",
+"            A(i+1,j)=C(i,j);\n",
+"            C(i,j)=B(i,j);\n",
+"            B(i,j)=B(i+1,j);\n",
+"            B(i+1,j)=C(i,j);\n",
+"        end\n",
+"    end\n",
+"    disp(B)\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            B(i,j)=1/B(i,j);\n",
+"        else\n",
+"            B(i,j)=A(i,j)/A(i,i);\n",
+"        end,\n",
+"    end\n",
+"        for j=1:3\n",
+"            for k=1:3\n",
+"                if(i~=j)\n",
+"                    B(j,k)=A(j,k)-A(j,i)*B(i,k);\n",
+"                end,\n",
+"            end\n",
+"        end\n",
+"    for j=1:3\n",
+"        if(i~=j)\n",
+"            B(j,i)=-1*A(j,i)*B(i,i);\n",
+"        end,\n",
+"        \n",
+"    end\n",
+"    disp(B)\n",
+"    A=B;\n",
+"end\n",
+"for j=1:3      //interchange of column 2 and 3\n",
+"    C(j,1)=A(j,2);\n",
+"    A(j,2)=A(j,3);\n",
+"    A(j,3)=C(j,1);\n",
+"end\n",
+"for j=1:3      //interchange of column 2 and 1\n",
+"    C(j,1)=A(j,2);\n",
+"    A(j,2)=A(j,1);\n",
+"    A(j,1)=C(j,1);\n",
+"end\n",
+"disp(A,'Inverse of Matrix A=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.4: Inverse_of_Triangular_Matrices.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.4\n",
+"//Inverse of Triangular Matrices\n",
+"//Page no. 260\n",
+"clc;clear;close;\n",
+"\n",
+"R=[2,4,-4,0;0,3,-3,-3;0,0,4,2;0,0,0,3];    //matrix R\n",
+"for i=4:-1:1\n",
+"    for j=4:-1:1\n",
+"        if(i>j)\n",
+"            Y(i,j)=0;\n",
+"        end\n",
+"        if(i==j)\n",
+"            Y(i,j)=1/R(i,j);\n",
+"        end\n",
+"        if(i<j)\n",
+"            l=0;\n",
+"            for k=i+1:j\n",
+"                l=l-R(i,k)*Y(k,j);\n",
+"            end\n",
+"            Y(i,j)=l/R(i,i);\n",
+"        end    \n",
+"    end\n",
+"end\n",
+"disp(Y,'Inverse of Matrix R=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.5: Inverse_of_Complex_Matrices.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.5\n",
+"//Inverse of Complex Matrices\n",
+"//Page no. 262\n",
+"clc;clear;close;\n",
+"\n",
+"A=[1,-1,0;2,3,4;0,1,2];\n",
+"B=[1,1,3;1,3,-3;-2,-4,-4];\n",
+"P=A+%i*B;\n",
+"disp(P,'Matrix P=')\n",
+"disp(A,'Matrix A=');disp(B,'Matrix B=');\n",
+"A1=inv(A);B1=inv(B);\n",
+"disp(A1,'Inverse of Matrix A=');\n",
+"disp(B1,'Inverse of Matrix B=');\n",
+"B1A=B1*A;disp(B1A,'Inverse(B)*A=');\n",
+"AB1A_B=A*B1A+B;disp(AB1A_B,'A*Inverse(B)*A+B=');\n",
+"AB1A_B1=inv(AB1A_B);disp(AB1A_B1,'Inverse(A*Inverse(B)*A+B)=');\n",
+"X=B1A*AB1A_B1;disp(X,'X=');\n",
+"Y=-1*AB1A_B1;disp(Y,'Y=');\n",
+"Q=X+%i*Y;disp(Q,'Inverse of Matrix P=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.6: Iterative_Procedure.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.6\n",
+"//Iterative Procedure\n",
+"//Page no. 265\n",
+"clc;clear;close;\n",
+"\n",
+"    A=[3,1,3/2;-5/4,-1/4,-3/4;-1/4,-1/4,-1/4];\n",
+"disp(A,'Matrix A=');\n",
+"B=[1,1,3.5;1,3,-3;-2,-3,-4];\n",
+"disp(B,'Assumed Matrix B=');\n",
+"e=0.1;\n",
+"\n",
+"//iterations\n",
+"E1=e;k=1;\n",
+"while(E1>=e)\n",
+"    printf('\n\n\nIteration %i\n',k)\n",
+"C=B*(2*eye(3,3)-A*B);disp(C,'Matrix C=');\n",
+"E=A*C-eye(3,3);disp(E,'Matrix E=');\n",
+"B=C;printf('\nInverse of Matrix A after %i iterations=',k);disp(B);\n",
+"E1=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        E1=E1+E(i,j)^2;\n",
+"    end\n",
+"end\n",
+"E1=sqrt(E1);\n",
+"k=k+1;\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/8-Numerical_Solutions_of_Linear_Systems_of_Equations_Iterative_Methods.ipynb b/Numerical_Methods_Principles_by_Analysis/8-Numerical_Solutions_of_Linear_Systems_of_Equations_Iterative_Methods.ipynb
new file mode 100644
index 0000000..1881c60
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/8-Numerical_Solutions_of_Linear_Systems_of_Equations_Iterative_Methods.ipynb
@@ -0,0 +1,666 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 8: Numerical Solutions of Linear Systems of Equations Iterative Methods"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.1: Jacobi_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.1\n",
+"//Jacobi Method\n",
+"//Page no. 273\n",
+"clc;clear;close;\n",
+"\n",
+"A=[8,-3,2;4,11,-1;6,3,12];        //equation matrix\n",
+"B=[20;33;36]                     //solution matrix\n",
+"for i=0:19\n",
+"    X(i+1,1)=i;\n",
+"end\n",
+"for i=2:4\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:19\n",
+"    for i=1:3\n",
+"        k=0;\n",
+"        for j=1:3\n",
+"            if(i~=j)\n",
+"                k=k-A(i,j)*X(r,j+1);\n",
+"            end\n",
+"        end\n",
+"        X(r+1,i+1)=(k+B(i,1))/A(i,i);\n",
+"    end\n",
+"end\n",
+"printf('   r\t   x(r)\t\ty(r)\t     z(r)');\n",
+"printf('\n    ------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 18 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(19,2),X(19,3),X(19,4))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.2: Gauss_Seidel_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.2\n",
+"//Gauss-Seidel Method\n",
+"//Page no. 274\n",
+"clc;clear;close;\n",
+"\n",
+"A=[8,-3,2;4,11,-1;6,3,12];        //equation matrix\n",
+"B=[20;33;36]                     //solution matrix\n",
+"for i=0:10\n",
+"    X(i+1,1)=i;\n",
+"end\n",
+"for i=2:4\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:10\n",
+"    for i=1:3\n",
+"        k1=0;\n",
+"        for j=1:i-1\n",
+"            \n",
+"                k1=k1-A(i,j)*X(r+1,j+1);\n",
+"            \n",
+"        end\n",
+"        k2=0;\n",
+"        for j=i+1:3\n",
+"            \n",
+"                k2=k2-A(i,j)*X(r,j+1);\n",
+"            \n",
+"        end\n",
+"        X(r+1,i+1)=(k1+k2+B(i,1))/A(i,i);\n",
+"    end\n",
+"end\n",
+"printf('   r\t   x(r)\t\ty(r)\t     z(r)');\n",
+"printf('\n    ------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 9 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(10,2),X(10,3),X(10,4))"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.3: SOR_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.3\n",
+"//SOR Method\n",
+"//Page no. 275\n",
+"clc;clear;close;\n",
+"\n",
+"A=[5,2,1;-1,4,2;2,-3,10];\n",
+"B=[-12;20;3];\n",
+"w=0.9;\n",
+"for i=0:13\n",
+"    X(i+1,1)=i;\n",
+"end\n",
+"X(1,2)=-2.4;\n",
+"X(1,3)=5;\n",
+"X(1,4)=0.3;\n",
+"for r=1:13\n",
+"    for i=1:3\n",
+"        k1=0;\n",
+"        for j=1:i-1\n",
+"            \n",
+"                k1=k1-A(i,j)*X(r+1,j+1);\n",
+"            \n",
+"        end\n",
+"        k2=0;\n",
+"        for j=i+1:3\n",
+"            \n",
+"                k2=k2-A(i,j)*X(r,j+1);\n",
+"            \n",
+"        end\n",
+"        X(r+1,i+1)=(1-w)*X(r,i+1)+(w*k1+w*k2+w*B(i,1))/A(i,i);\n",
+"    end\n",
+"end\n",
+"printf('   r\t   x(r)\t\ty(r)\t     z(r)');\n",
+"printf('\n    ------------------------------------');\n",
+"disp(X);\n",
+"printf('\n\nAfter 12 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(13,2),X(13,3),X(13,4));"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.4: Gauss_Seidel_Point_Iterative_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.4\n",
+"//Gauss-Seidel Point Iterative Method\n",
+"//Page no. 278\n",
+"clc;clear;close;\n",
+"\n",
+"\n",
+"A=[10,1,0,0,0,-1;1,10,1,0,0,0;2,0,20,1,0,0;0,0,1,10,-1,0;0,3,0,0,30,3;0,0,0,2,-2,20];        //equation matrix\n",
+"B=[5;10;10;0;0;5]                     //solution matrix\n",
+"for i=1:6\n",
+"    for j=1:6\n",
+"        if(A(j,j)==0)\n",
+"            for k=1:6\n",
+"                C(j,k)=A(j,k);\n",
+"                A(j,k)=A(j+1,k);\n",
+"                A(j+1,k)=C(j,k);\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for i=0:7\n",
+"    X(i+1,1)=i;\n",
+"end\n",
+"for i=2:7\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:7\n",
+"    for i=1:6\n",
+"        k1=0;\n",
+"        for j=1:i-1\n",
+"            \n",
+"                k1=k1-A(i,j)*X(r+1,j+1);\n",
+"            \n",
+"        end\n",
+"        k2=0;\n",
+"        for j=i+1:6\n",
+"            \n",
+"                k2=k2-A(i,j)*X(r,j+1);\n",
+"            \n",
+"        end\n",
+"        X(r+1,i+1)=(k1+k2+B(i,1))/A(i,i);\n",
+"    end\n",
+"end\n",
+"printf('   r     ');\n",
+"for i=1:6\n",
+"    printf('x%i           ',i);\n",
+"end\n",
+"printf('\n    --------------------------------------------------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 6 iterations exact solution is:\n');\n",
+"for i=1:6\n",
+"    printf('x%i=%f     ',i,X(7,i+1));\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.5: Gauss_Seidel_Point_Iterative_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.5\n",
+"//Gauss-Seidel Point Iterative Method\n",
+"//Page no. 279\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,3,-4,1;1,-2,-5,1;5,-3,1,-4;10,2,-1,2];       //equation matrix\n",
+"B=[3;2;1;-4];          //solution matrix\n",
+"\n",
+"//transformation of the equations\n",
+"for i=1:4\n",
+"    A1(1,i)=A(4,i);\n",
+"    B1(1,1)=B(4,1);\n",
+"end\n",
+"for i=1:4\n",
+"    A1(3,i)=A(2,i);\n",
+"    B1(3,1)=B(2,1);\n",
+"end\n",
+"for i=1:4\n",
+"    A1(2,i)=A(1,i)-A(2,i);\n",
+"    B1(2,1)=B(1,1)-B(2,1);\n",
+"end\n",
+"for i=1:4\n",
+"    A1(4,i)=2*A(1,i)-A(2,i)+2*A(3,i)-A(4,i);\n",
+"    B1(4,1)=2*B(1,1)-B(2,1)+2*B(3,1)-B(4,1);\n",
+"end\n",
+"\n",
+"//printing of transformed equations\n",
+"printf('\nTransformed Equations are=\n\n')\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        printf('(%ix(%i))',A1(i,j),j);\n",
+"        if(j<4)\n",
+"            printf(' + ')\n",
+"        end\n",
+"    end\n",
+"    printf('= %i\n',B1(i,1));\n",
+"end\n",
+"\n",
+"for i=1:4\n",
+"    for j=1:4\n",
+"        if(A(j,j)==0)\n",
+"            for k=1:4\n",
+"                C(j,k)=A(j,k);\n",
+"                A(j,k)=A(j+1,k);\n",
+"                A(j+1,k)=C(j,k);\n",
+"            end\n",
+"        end\n",
+"    end\n",
+"end\n",
+"for i=0:12\n",
+"    X(i+1,1)=i;\n",
+"end\n",
+"for i=2:5\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:12\n",
+"    for i=1:4\n",
+"        k1=0;\n",
+"        for j=1:i-1\n",
+"            \n",
+"                k1=k1-A1(i,j)*X(r+1,j+1);\n",
+"            \n",
+"        end\n",
+"        k2=0;\n",
+"        for j=i+1:4\n",
+"            \n",
+"                k2=k2-A1(i,j)*X(r,j+1);\n",
+"            \n",
+"        end\n",
+"        X(r+1,i+1)=(k1+k2+B1(i,1))/A1(i,i);\n",
+"    end\n",
+"end\n",
+"printf('\n\n    r     ');\n",
+"for i=1:4\n",
+"    printf('x%i           ',i);\n",
+"end\n",
+"printf('\n    ------------------------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 11 iterations exact solution is:\n');\n",
+"for i=1:4\n",
+"    printf('x%i=%f     ',i,X(12,i+1));\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.6: Block_Jacobi_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.6\n",
+"//Block Jacobi Method\n",
+"//Page no. 281\n",
+"clc;clear;close;\n",
+"\n",
+"A=[10,1,0,0,0,-1;1,10,1,0,0,0;2,0,20,1,0,0;0,0,1,10,-1,0;0,3,0,0,30,3;0,0,0,2,-2,20];        //equation matrix\n",
+"B=[5;10;10;0;0;5]                     //solution matrix\n",
+"disp(B,'B=',A,'A=')\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        A11(i,j)=A(i,j);\n",
+"    end\n",
+"    B1(i,1)=B(i,1);\n",
+"end\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        A12(i,j)=A(i,j+3);\n",
+"    end\n",
+"end\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        A21(i,j)=A(i+3,j);\n",
+"    end\n",
+"end\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        A22(i,j)=A(i+3,j+3);\n",
+"    end\n",
+"    B2(i,1)=B(i+3,1);\n",
+"end\n",
+"disp(B2,'B2=',B1,'B1=',A22,'A22=',A21,'A21=',A12,'A12=',A11,'A11=');\n",
+"A11_1=inv(A11);A22_1=inv(A22);\n",
+"disp(A22_1,'Inverse of A22=',A11_1,'Inverse of A11=')\n",
+"for i=1:3\n",
+"    X1(i,1)=0;\n",
+"    X2(i,1)=0;\n",
+"end\n",
+"for r=1:2\n",
+"    X11=A11_1*(-1*A12*X2+B1);\n",
+"    X22=A22_1*(-1*A21*X1+B2);\n",
+"    X1=X11;\n",
+"    X2=X22;\n",
+"    disp(X1,'X1=')\n",
+"    disp(X2,'X2=')\n",
+"end\n",
+"for i=1:6\n",
+"    if(i<4)\n",
+"        X(i,1)=X1(i,1);\n",
+"    else\n",
+"        X(i,1)=X2(i-3,1);\n",
+"    end\n",
+"end    \n",
+"disp(X,'X=')\n",
+"printf('\n\n\nNote : There is a computation error in calculation of X1(2)')\n",
+"    \n",
+"        \n",
+"    "
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.7: Block_Gauss_Seidel_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.7\n",
+"//Block Gauss-Seidel Method\n",
+"//Page no. 283\n",
+"clc;clear;close;\n",
+"\n",
+"A=[10,1,0,0,0,-1;1,10,1,0,0,0;2,0,20,1,0,0;0,0,1,10,-1,0;0,3,0,0,30,3;0,0,0,2,-2,20];        //equation matrix\n",
+"B=[5;10;10;0;0;5]                     //solution matrix\n",
+"disp(B,'B=',A,'A=')\n",
+"\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A11(i,j)=A(i,j);\n",
+"    end\n",
+"    B1(i,1)=B(i,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A12(i,j)=A(i,j+2);\n",
+"    end\n",
+"    B2(i,1)=B(i+2,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A13(i,j)=A(i,j+4);\n",
+"    end\n",
+"    B3(i,1)=B(i+4,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A21(i,j)=A(i+2,j);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A22(i,j)=A(i+2,j+2);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A23(i,j)=A(i+2,j+4);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A31(i,j)=A(i+4,j);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A32(i,j)=A(i+4,j+2);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A33(i,j)=A(i+4,j+4);\n",
+"    end\n",
+"end\n",
+"disp(B3,'B3=',B2,'B2=',B1,'B1=',A33,'A33=',A32,'A32=',A31,'A31=',A23,'A23=',A22,'A22=',A21,'A21=',A13,'A13=',A12,'A12=',A11,'A11=');\n",
+"A11_1=inv(A11);A22_1=inv(A22);A33_1=inv(A33);\n",
+"disp(A33_1,'Inverse of Matrix A33=',A22_1,'Inverse of Matrix A22=',A11_1,'Inverse of Matrix A11=');\n",
+"for i=1:2\n",
+"    X1(i,1)=0;\n",
+"    X2(i,1)=0;\n",
+"    X3(i,1)=0;\n",
+"end\n",
+"for i=1:6\n",
+"    X(i,1)=i-1;\n",
+"end\n",
+"for i=2:7\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:5\n",
+"    X11=A11_1*(-1*A12*X2+(-1)*A13*X3+B1);\n",
+"    X22=A22_1*(-1*A21*X11+(-1)*A23*X3+B2);\n",
+"    X33=A33_1*(-1*A31*X11+(-1)*A32*X22+B3);\n",
+"    X1=X11;\n",
+"    X2=X22;\n",
+"    X3=X33;\n",
+"    disp(X3,'X3=',X2,'X2=',X1,'X1=')\n",
+"    for i=2:7\n",
+"        if(i<4)\n",
+"            X(r+1,i)=X1(i-1,1);\n",
+"        end\n",
+"        if(i<6 & i>3)\n",
+"            X(r+1,i)=X2(i-3,1);\n",
+"        end\n",
+"        if(i<8 & i>5)\n",
+"            X(r+1,i)=X3(i-5,1);\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\nIteration');\n",
+"for i=1:6\n",
+"    printf('    x%i       ',i);\n",
+"end\n",
+"printf('\n    --------------------------------------------------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 4 iterations exact solution is:\n');\n",
+"for i=1:6\n",
+"    printf('x%i=%f     ',i,X(5,i+1));\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 8.8: Block_SOR_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 8.8\n",
+"//Block SOR Method\n",
+"//Page no. 284\n",
+"clc;clear;close;\n",
+"\n",
+"\n",
+"A=[10,1,0,0,0,-1;1,10,1,0,0,0;2,0,20,1,0,0;0,0,1,10,-1,0;0,3,0,0,30,3;0,0,0,2,-2,20];        //equation matrix\n",
+"B=[5;10;10;0;0;5]                     //solution matrix\n",
+"disp(B,'B=',A,'A=')\n",
+"w=0.8\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A11(i,j)=A(i,j);\n",
+"    end\n",
+"    B1(i,1)=B(i,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A12(i,j)=A(i,j+2);\n",
+"    end\n",
+"    B2(i,1)=B(i+2,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A13(i,j)=A(i,j+4);\n",
+"    end\n",
+"    B3(i,1)=B(i+4,1);\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A21(i,j)=A(i+2,j);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A22(i,j)=A(i+2,j+2);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A23(i,j)=A(i+2,j+4);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A31(i,j)=A(i+4,j);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A32(i,j)=A(i+4,j+2);\n",
+"    end\n",
+"end\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        A33(i,j)=A(i+4,j+4);\n",
+"    end\n",
+"end\n",
+"disp(B3,'B3=',B2,'B2=',B1,'B1=',A33,'A33=',A32,'A32=',A31,'A31=',A23,'A23=',A22,'A22=',A21,'A21=',A13,'A13=',A12,'A12=',A11,'A11=');\n",
+"A11_1=inv(A11);A22_1=inv(A22);A33_1=inv(A33);\n",
+"disp(A33_1,'Inverse of Matrix A33=',A22_1,'Inverse of Matrix A22=',A11_1,'Inverse of Matrix A11=');\n",
+"for i=1:2\n",
+"    X1(i,1)=0;\n",
+"    X2(i,1)=0;\n",
+"    X3(i,1)=0;\n",
+"end\n",
+"for i=1:7\n",
+"    X(i,1)=i-1;\n",
+"end\n",
+"for i=2:7\n",
+"    X(1,i)=0;\n",
+"end\n",
+"for r=1:6\n",
+"    X11=A11_1*((1-w)*X1+(-1)*w*A12*X2+(-1)*w*A13*X3+w*B1);\n",
+"    X22=A22_1*((1-w)*X2+(-1)*w*A21*X11+(-1)*w*A23*X3+w*B2);\n",
+"    X33=A33_1*((1-w)*X3+(-1)*w*A31*X11+(-1)*w*A32*X22+w*B3);\n",
+"    X1=X11;\n",
+"    X2=X22;\n",
+"    X3=X33;\n",
+"    disp(X3,'X3=',X2,'X2=',X1,'X1=')\n",
+"    for i=2:7\n",
+"        if(i<4)\n",
+"            X(r+1,i)=X1(i-1,1);\n",
+"        end\n",
+"        if(i<6 & i>3)\n",
+"            X(r+1,i)=X2(i-3,1);\n",
+"        end\n",
+"        if(i<8 & i>5)\n",
+"            X(r+1,i)=X3(i-5,1);\n",
+"        end\n",
+"    end\n",
+"end\n",
+"printf('\n\nIteration');\n",
+"for i=1:6\n",
+"    printf('    x%i       ',i);\n",
+"end\n",
+"printf('\n    --------------------------------------------------------------------------------')\n",
+"disp(X)\n",
+"printf('\n\nAfter 5 iterations exact solution is:\n');\n",
+"for i=1:6\n",
+"    printf('x%i=%f     ',i,X(6,i+1));\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}
diff --git a/Numerical_Methods_Principles_by_Analysis/9-Linear_Least_Squares_Problem.ipynb b/Numerical_Methods_Principles_by_Analysis/9-Linear_Least_Squares_Problem.ipynb
new file mode 100644
index 0000000..0e7132d
--- /dev/null
+++ b/Numerical_Methods_Principles_by_Analysis/9-Linear_Least_Squares_Problem.ipynb
@@ -0,0 +1,479 @@
+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 9: Linear Least Squares Problem"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.1: Moore_Penrose_Generalized_Inverse.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.1\n",
+"//Moore-Penrose Generalized Inverse\n",
+"//Page no. 292\n",
+"clc;clear;close;\n",
+"\n",
+"AT=[3,0,3;0,3,3];\n",
+"A=AT';           //transpose\n",
+"I=inv(AT*A);       //inverse\n",
+"disp(I,'Inverse of AT*A=',AT*A,'AT*A=',A,'A=',AT,'AT=');\n",
+"A#=I*AT;\n",
+"disp(A#,'Moore-Penrose Generalized Inverse of A=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.2: Curve_Fitting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.2\n",
+"//Curve Fitting\n",
+"//Page no. 293\n",
+"clc;clear;close;\n",
+"x(1)=0.25;\n",
+"for i=2:6\n",
+"    x(1,i)=x(1,i-1)+0.25;\n",
+"end               //x values\n",
+"y(1,1)=3.1;y(1,2)=1.7;y(1,3)=1;y(1,4)=0.68;y(1,5)=0.42;y(1,6)=0.26; //y values\n",
+"\n",
+"//construction of normal equations\n",
+"for i=1:6\n",
+"    Y(1,i)=log10(y(1,i));\n",
+"end\n",
+"Ex=0;\n",
+"for i=1:6\n",
+"    Ex=Ex+x(1,i);\n",
+"end\n",
+"EY=0;\n",
+"for i=1:6\n",
+"    EY=EY+Y(1,i);\n",
+"end\n",
+"Ex2=0;\n",
+"for i=1:6\n",
+"    Ex2=Ex2+x(1,i)^2;\n",
+"end\n",
+"ExY=0;\n",
+"for i=1:6\n",
+"    ExY=ExY+x(1,i)*Y(1,i);\n",
+"end\n",
+"printf('E x(k)\t\t y(k)\t\tE Y(k)\t\tE x2(k)\t\tE x(k)*Y(k)')\n",
+"printf('\n----------------------------------------------------------------------------')\n",
+"for i=1:6\n",
+"    printf('\n%f\t%f\t%f\t%f\t%f',x(1,i),y(1,i),Y(1,i),x(1,i)^2,x(1,i)*Y(1,i))\n",
+"end\n",
+"printf('\n----------------------------------------------------------------------------')\n",
+"printf('\n%f\t%f\t%f\t%f\t%f',Ex,0,EY,Ex2,ExY)\n",
+"printf('\n----------------------------------------------------------------------------\n\n')\n",
+"A=[6,Ex;Ex,Ex2];      //system of normal equations\n",
+"B=[EY;ExY];\n",
+"X=inv(A)*B;\n",
+"a=exp(X(1,1));\n",
+"b=-1*X(2,1);\n",
+"for i=1:2\n",
+"    for j=1:2\n",
+"        printf('%f    ',A(i,j))\n",
+"    end\n",
+"    if(i==1)\n",
+"        printf('  *')\n",
+"    end\n",
+"    \n",
+"    printf('\ta%i',i);\n",
+"    if(i==1)\n",
+"        printf('  =')\n",
+"    end\n",
+"    \n",
+"    printf('\t%f\n',B(i,1))\n",
+"end\n",
+"printf('\n\na1=%f\na2=%f\n\na=%f\nb=%f\n\n',X(1,1),X(2,1),a,b)\n",
+"printf('The fitted curve is:\n            %fx\ny=%f e',b,a)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.3: Gram_Schmidt_Orthogonalization_or_Orthonormalization_Process.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.3\n",
+"//Gram-Schmidt Orthogonalization/Orthonormalization Process\n",
+"//Page no. 294\n",
+"clc;clear;close;\n",
+"deff('y=f(x,a)','y=sqrt(x(1,a)^2+x(2,a)^2+x(3,a)^2+x(4,a)^2)');\n",
+"deff('y=f1(g,a,h,b)','y=g(1,a)*h(1,b)+g(2,a)*h(2,b)+g(3,a)*h(3,b)+g(4,a)*h(4,b)');\n",
+"\n",
+"U=[1/sqrt(3),-2/sqrt(7),1,0,0,0;0,1/sqrt(7),0,1,0,0;1/sqrt(3),1/sqrt(7),0,0,1,0;-1/sqrt(3),-1/sqrt(7),0,0,0,1];\n",
+"for i=1:4\n",
+"        V(i,1)=U(i,1);\n",
+"end\n",
+"for i=1:4\n",
+"    if(f(V,1)~=0)\n",
+"        W(i,1)=V(i,1)/f(V,1);\n",
+"    else\n",
+"        W(i,1)=0;\n",
+"    end \n",
+"end\n",
+"for j=2:6\n",
+"    for i=1:4\n",
+"        for l=1:4\n",
+"            k(l,1)=0;\n",
+"        end\n",
+"        for l=1:j-1\n",
+"            for m=1:4\n",
+"                w(m,1)=W(m,l);\n",
+"            end\n",
+"            k=k-(f1(U,j,W,l))*w;\n",
+"        end\n",
+"        V(i,j)=U(i,j)+k(i,1);\n",
+"    end\n",
+"    for i=1:4\n",
+"        if(j~=4)\n",
+"            if(f(V,j)~=0)\n",
+"                W(i,j)=V(i,j)/f(V,j);\n",
+"            else\n",
+"                W(i,j)=0;\n",
+"            end \n",
+"        else\n",
+"            W(i,j)=0;\n",
+"        end\n",
+"    end\n",
+"    \n",
+"end\n",
+"disp(U,'U=')\n",
+"disp('W=')\n",
+"printf('\n')\n",
+"for i=1:4\n",
+"    for j=1:6\n",
+"        printf('%.4f\t\t',W(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"disp('V=')\n",
+"printf('\n')\n",
+"for i=1:4\n",
+"    for j=1:6\n",
+"        printf('%.4f\t\t',V(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.4: QR_Decompositio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.4\n",
+"//QR Decomposition\n",
+"//Page no. 296\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,1,1;1,3,1;1,1,4];\n",
+"B=A*A';\n",
+"disp(B,'AT*A=')\n",
+"//cholesky factorization to find R\n",
+"R(2,1)=0;R(3,1)=0;R(3,2)=0;     \n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            k=0;\n",
+"            for m=1:i-1\n",
+"               k=k+R(m,i)^2; \n",
+"            end\n",
+"            R(i,j)=sqrt(B(i,j)-k)\n",
+"        end\n",
+"        if(j>i)\n",
+"            k=0;\n",
+"            for m=1:i-1\n",
+"                k=k+R(m,j)*R(m,i);\n",
+"            end\n",
+"            R(i,j)=(B(i,j)-k)/R(i,i)\n",
+"        end\n",
+"    end\n",
+"end\n",
+"//cholesky factorization end\n",
+"disp(R,'Upper Triangular Matrix (R)=')\n",
+"R_1=inv(R);\n",
+"disp(R_1,'Inverse of R')\n",
+"Q=A*R_1;\n",
+"disp(Q,'Orthogonal Matrix Q=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.5: Vector_Computatio.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.5\n",
+"//Vector Computation\n",
+"//Page no. 299\n",
+"clc;clear;close;\n",
+"\n",
+"X=[2,3,0,1];\n",
+"n=X(1);\n",
+"for i=2:4\n",
+"    if(n<X(i))\n",
+"        n=X(i);\n",
+"    end\n",
+"end\n",
+"printf('\nMaximum Value (n)=%i\n',n)\n",
+"for i=1:4\n",
+"    X(i)=X(i)/n;\n",
+"end\n",
+"disp(X,'Normalized X=')\n",
+"k=0;\n",
+"for i=1:4\n",
+"    k=k+X(i)^2;\n",
+"end\n",
+"sigma=X(1)*abs(1/X(1))*sqrt(k);\n",
+"printf('\nsigma=%f\n',sigma);\n",
+"X(1)=X(1)+sigma;\n",
+"printf('\nModified x1 = %g\n',X(1))\n",
+"for i=1:4\n",
+"    U(1,i)=X(i);\n",
+"end\n",
+"disp(U,'U=')\n",
+"p=sigma*X(1);sigma=n*sigma;\n",
+"printf('\n p = %f\n\n sigma = %f',p,sigma);\n",
+"printf('\n\n\nNote : There is a computation error in calculation of U1')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.6: House_Holder_Transformation.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.6\n",
+"//House Holder Transformation\n",
+"//Page no. 300\n",
+"clc;clear;close;\n",
+"\n",
+"A=[4,2,1;2,5,-2;1,-2,7]\n",
+"disp(A,'A=')\n",
+"k=0;\n",
+"for j=2:3\n",
+"    k=k+A(j,1)^2;\n",
+"end\n",
+"a=A(2,1)*abs(1/A(2,1))*sqrt(k);\n",
+"disp(a,'alpha=')\n",
+"U=[0;a+A(2,1);A(3,1)];\n",
+"disp(U,'U=')\n",
+"U1=U'*U;\n",
+"disp(U1,'UT*U=')\n",
+"U2=U*U';\n",
+"disp(U2,'U*UT=')\n",
+"P=eye(3,3)-(2*U2)/U1;\n",
+"disp(P,'P=');\n",
+"B=P*A*P;\n",
+"disp(B,'B=');\n",
+"printf('\n\n\nThere are computation error in the answers given by the book in this example\n\n(a22 value error in U*UT)')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.7: Givens_QR_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.7\n",
+"//Givens QR Method\n",
+"//Page no. 303\n",
+"clc;clear;close;\n",
+"\n",
+"A=[4,2,1;2,5,-2;1,-2,7]\n",
+"deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"deff('y=s(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"disp(A,'A=')\n",
+"R=A;Q=eye(3,3);\n",
+"m=1;\n",
+"for j=1:2\n",
+"    for i=j+1:3\n",
+"        for k=1:3             //C matrix evaluation\n",
+"            for l=1:3\n",
+"                if(k==l)\n",
+"                    if(k==i | k==j)\n",
+"                        C(k,l)=c(i,j)\n",
+"                    else\n",
+"                        C(k,l)=1\n",
+"                    end\n",
+"                end\n",
+"                if(k>l)\n",
+"                    if(k==i & l==j)\n",
+"                        C(k,l)=-1*s(i,j)\n",
+"                    else\n",
+"                        C(k,l)=0\n",
+"                    end\n",
+"                end\n",
+"                if(k<l)\n",
+"                    if(k==j & l==i)\n",
+"                        C(k,l)=s(i,j)\n",
+"                    else\n",
+"                        C(k,l)=0\n",
+"                    end\n",
+"                end\n",
+"            end\n",
+"        end\n",
+"        printf('\n\n Iteration %i',m)\n",
+"        m=m+1\n",
+"        disp(C,'C=');\n",
+"        R=C*R;\n",
+"        Q=Q*C';\n",
+"        disp(Q,'Q=',R,'R=')\n",
+"    end\n",
+"end\n",
+"disp(Q*R,'Q*R=A=')            //verification"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.8: Recursive_Least_Square_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 9.8\n",
+"//Recursive Least-Square Method\n",
+"//Page no. 308\n",
+"clc;clear;close;\n",
+"\n",
+"A0=[3,0;0,3;3,3];\n",
+"B0=[2;2;2];\n",
+"A1=[6,3];B1=[6];\n",
+"A0T=A0';\n",
+"G0=A0T*A0;\n",
+"disp(G0,'G0=')\n",
+"G0_1=inv(G0);\n",
+"disp(G0_1,'Inverse of G0=')\n",
+"X0=G0_1*A0T*B0;\n",
+"disp(X0,'X0=')\n",
+"\n",
+"//by recursive least square algorithm\n",
+"G1=G0+A1'*A1;\n",
+"disp(G1,'G1=');\n",
+"G1_1=inv(G1);\n",
+"disp(G1_1,'Inverse of G1')\n",
+"X1=X0+G1_1*A1'*(B1-A1*X0);\n",
+"disp(X1,'X1=')\n",
+"\n",
+"//verification\n",
+"A=[3,0;0,3;3,3;6,3];\n",
+"B=[2;2;2;6];\n",
+"AT=A';\n",
+"G=AT*A;\n",
+"disp(G,'G=')\n",
+"G_1=inv(G);\n",
+"disp(G_1,'Inverse of G=')\n",
+"X=G_1*AT*B;\n",
+"disp(X,'X=')\n",
+"disp('Thus X and X1 are Same')"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}