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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /1332 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '1332')
440 files changed, 7198 insertions, 0 deletions
diff --git a/1332/CH1/EX1.1/1_1.pdf b/1332/CH1/EX1.1/1_1.pdf Binary files differnew file mode 100755 index 000000000..ce963f2c0 --- /dev/null +++ b/1332/CH1/EX1.1/1_1.pdf diff --git a/1332/CH1/EX1.1/1_1.sce b/1332/CH1/EX1.1/1_1.sce new file mode 100755 index 000000000..e8854653d --- /dev/null +++ b/1332/CH1/EX1.1/1_1.sce @@ -0,0 +1,34 @@ +//Example 1.1
+//Conversion to Decimal System
+//Page no. 4
+clc;close;clear;
+function [s]=bas2dec(x,b)
+ xi=int(x)
+ xd=x-int(x)
+ s=0
+ for i=1:10
+ xi=xi/10
+ s=s+(10*(xi-fix(xi))*b^(i-1))
+ xi=int(xi)
+ if(xi==0)
+ break
+ end
+ end
+ for i=1:1
+ xd=xd*10;
+ s=s+(ceil(xd)/b^(i))
+ xd=xd-fix(xd)
+ if(xd==0)
+ break
+ end
+ end
+endfunction
+
+//conversion from hexadecimal to decimal system
+disp(hex2dec('1A2C'),'1A2C='); //inbuit function
+
+//conversion from hexadecimal to decimal system
+disp(bas2dec(428.5,8),'428.5=') //inline function
+
+//conversion from hexadecimal to decimal system
+disp(bas2dec(120.1,3),'120.1=') //inline function
\ No newline at end of file diff --git a/1332/CH1/EX1.10/1_10.pdf b/1332/CH1/EX1.10/1_10.pdf Binary files differnew file mode 100755 index 000000000..6d388d1f5 --- /dev/null +++ b/1332/CH1/EX1.10/1_10.pdf diff --git a/1332/CH1/EX1.10/1_10.sce b/1332/CH1/EX1.10/1_10.sce new file mode 100755 index 000000000..8b6535023 --- /dev/null +++ b/1332/CH1/EX1.10/1_10.sce @@ -0,0 +1,21 @@ +//Example 1.10
+//Conversion to Binary System and to Base N
+//Page no. 9
+clc;close;clear;
+
+b=dec2bin(oct2dec('1753'))
+disp(b,'Binary form of 1753 is ='); //inbuilt function
+b=dec2hex(oct2dec('1753'))
+disp(b,'Hexadecimal form of 1753 is ='); //inbuilt function
+//conversion from octal to binary
+b=dec2bin(hex2dec('A478'))
+disp(b,'Binary form of A478 is ='); //inbuilt function
+b=dec2oct(hex2dec('A478'))
+disp(b,'Octal form of A478 is ='); //inbuilt function
+//conversion from octal to binary
+s=dec2bin(oct2dec('3'));
+s1=dec2bin(oct2dec('154')); //inbuilt function
+printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)
+s=dec2hex(oct2dec('3'));
+s1=dec2hex(oct2dec('154')); //inbuilt function
+printf('\n\n Hexadecimal form of 3.154 is = \n\n %s.%s',s,s1)
\ No newline at end of file diff --git a/1332/CH1/EX1.13/1_13.pdf b/1332/CH1/EX1.13/1_13.pdf Binary files differnew file mode 100755 index 000000000..94c1f386a --- /dev/null +++ b/1332/CH1/EX1.13/1_13.pdf diff --git a/1332/CH1/EX1.13/1_13.sce b/1332/CH1/EX1.13/1_13.sce new file mode 100755 index 000000000..ceb644727 --- /dev/null +++ b/1332/CH1/EX1.13/1_13.sce @@ -0,0 +1,45 @@ +//Example 1.13
+//1s compliment and 2s compliment
+//Page no. 11
+clc;close;clear;
+
+function [x1]=com1(x) //function for 1s compliment
+ for i=8:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ if(floor((xd*10)+0.1)==1)
+ x1(1,i)=0;
+ else
+ x1(1,i)=1;
+ end
+ x=x-xd;
+ end
+endfunction
+function [x1]=com2(x) //function for 2s compliment()
+ for i=8:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ if(int((xd*10)+0.1)==1)
+ x1(1,i)=0;
+ else
+ x1(1,i)=1;
+ end
+ end
+ for i=8:-1:1
+ if (x1(1,i)==0) then
+ x1(1,i)=1;
+ break;
+ else
+ x1(1,i)=0;
+ end
+
+ end
+endfunction
+a=[00010011,01110110,11101101,10000001,10000000,00000000];
+for i=1:6
+ printf('1s Compliment of %.8i=',a(i));
+ disp(com1(a(i)))
+ printf('2s Compliment of %.8i=',a(i));
+ disp(com2(a(i)))
+ printf('\n\n')
+end
\ No newline at end of file diff --git a/1332/CH1/EX1.14/1_14.pdf b/1332/CH1/EX1.14/1_14.pdf Binary files differnew file mode 100755 index 000000000..459a93984 --- /dev/null +++ b/1332/CH1/EX1.14/1_14.pdf diff --git a/1332/CH1/EX1.14/1_14.sce b/1332/CH1/EX1.14/1_14.sce new file mode 100755 index 000000000..1702ff6ec --- /dev/null +++ b/1332/CH1/EX1.14/1_14.sce @@ -0,0 +1,23 @@ +//Example 1.14
+//1s compliment
+//Page no. 12
+clc;close;clear;
+
+function [x1]=com1(x) //function for 1s compliment
+ for i=8:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ if(floor((xd*10)+0.1)==1)
+ x1(1,i)=0;
+ else
+ x1(1,i)=1;
+ end
+ x=x-xd;
+ end
+endfunction
+a=[00010011,01110110,11101101,10000001,10000000,00000000];
+for i=1:6
+ printf('1s Compliment of %.8i=',a(i));
+ disp(com1(a(i)))
+ printf('\n\n')
+end
\ No newline at end of file diff --git a/1332/CH1/EX1.15/1_15.pdf b/1332/CH1/EX1.15/1_15.pdf Binary files differnew file mode 100755 index 000000000..5b07ed2c5 --- /dev/null +++ b/1332/CH1/EX1.15/1_15.pdf diff --git a/1332/CH1/EX1.15/1_15.sce b/1332/CH1/EX1.15/1_15.sce new file mode 100755 index 000000000..bbad2a1b2 --- /dev/null +++ b/1332/CH1/EX1.15/1_15.sce @@ -0,0 +1,74 @@ +//Example 1.15
+//Addition and Subtraction
+//Page no. 13
+clc;clear;close;
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ for i=1:10
+ x1(1,i)=0
+ end
+ for i=10:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=0;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+ disp(x1,'Addition of 173 and 141= ')
+endfunction
+function [x1]=sub(x,y) //function for subtraction of binaries
+ c=0;
+ for i=1:10
+ x1(1,i)=0
+ end
+ for i=10:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ elseif floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==1
+ x1(1,i)=1;c=1;
+ end
+ end
+ end
+ disp(x1,'Subtraction of 45 from 228= ')
+endfunction
+add(10101101,10001101)
+sub(11100100,00101101)
\ No newline at end of file diff --git a/1332/CH1/EX1.16/1_16.pdf b/1332/CH1/EX1.16/1_16.pdf Binary files differnew file mode 100755 index 000000000..450055383 --- /dev/null +++ b/1332/CH1/EX1.16/1_16.pdf diff --git a/1332/CH1/EX1.16/1_16.sce b/1332/CH1/EX1.16/1_16.sce new file mode 100755 index 000000000..3c6264461 --- /dev/null +++ b/1332/CH1/EX1.16/1_16.sce @@ -0,0 +1,45 @@ +//Example 1.16
+//Addition
+//Page no. 14
+clc;close;clear;
+
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ printf('Addition of %.4i and %.4i= ',x,y)
+ for i=1:4
+ x1(1,i)=0
+ end
+ for i=4:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=1;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+
+ disp(x1)
+endfunction
+add(0010,0101);
+add(1110,1011);
+add(1110,0101);
+add(0010,1011);
+add(1110,0010);
+add(0000,0000);
\ No newline at end of file diff --git a/1332/CH1/EX1.17/1_17.pdf b/1332/CH1/EX1.17/1_17.pdf Binary files differnew file mode 100755 index 000000000..89ea001d2 --- /dev/null +++ b/1332/CH1/EX1.17/1_17.pdf diff --git a/1332/CH1/EX1.17/1_17.sce b/1332/CH1/EX1.17/1_17.sce new file mode 100755 index 000000000..c0940b0f8 --- /dev/null +++ b/1332/CH1/EX1.17/1_17.sce @@ -0,0 +1,46 @@ +//Example 1.17
+//Addition
+//Page no. 14
+clc;close;clear;
+
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ printf('Addition of %.4i and %.4i= ',x,y)
+ for i=1:5
+ x1(1,i)=0
+ end
+ for i=5:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=1;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+
+ disp(x1)
+endfunction
+
+add(0010,0101);
+add(1101,1010);
+add(1101,0101);
+add(0010,1010);
+add(1101,0010);
+add(1111,0000);
\ No newline at end of file diff --git a/1332/CH1/EX1.18/1_18.pdf b/1332/CH1/EX1.18/1_18.pdf Binary files differnew file mode 100755 index 000000000..46a1381c3 --- /dev/null +++ b/1332/CH1/EX1.18/1_18.pdf diff --git a/1332/CH1/EX1.18/1_18.sce b/1332/CH1/EX1.18/1_18.sce new file mode 100755 index 000000000..1d6b6c395 --- /dev/null +++ b/1332/CH1/EX1.18/1_18.sce @@ -0,0 +1,43 @@ +//Example 1.18
+//Addition
+//Page no. 15
+clc;close;clear;
+
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ printf('Addition of %.4i and %.4i= ',x,y)
+ for i=1:5
+ x1(1,i)=0
+ end
+ for i=5:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=1;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+
+ disp(x1)
+endfunction
+
+add(0100,0101);
+add(1100,1011);
+add(1000,1000);
\ No newline at end of file diff --git a/1332/CH1/EX1.19/1_19.pdf b/1332/CH1/EX1.19/1_19.pdf Binary files differnew file mode 100755 index 000000000..fa8f21a66 --- /dev/null +++ b/1332/CH1/EX1.19/1_19.pdf diff --git a/1332/CH1/EX1.19/1_19.sce b/1332/CH1/EX1.19/1_19.sce new file mode 100755 index 000000000..0d9e5e9ba --- /dev/null +++ b/1332/CH1/EX1.19/1_19.sce @@ -0,0 +1,46 @@ +//Example 1.19
+//Addition
+//Page no. 15
+clc;close;clear;
+
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ printf('Addition of %.4i and %.4i= ',x,y)
+ for i=1:5
+ x1(1,i)=0
+ end
+ for i=5:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=1;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+
+ disp(x1)
+endfunction
+
+add(0010,0101);
+add(11110,11011);
+add(1000,0101);
+add(00010,11011);
+add(11110,00010);
+add(11111,0000);
\ No newline at end of file diff --git a/1332/CH1/EX1.2/1_2.pdf b/1332/CH1/EX1.2/1_2.pdf Binary files differnew file mode 100755 index 000000000..45cf31c95 --- /dev/null +++ b/1332/CH1/EX1.2/1_2.pdf diff --git a/1332/CH1/EX1.2/1_2.sce b/1332/CH1/EX1.2/1_2.sce new file mode 100755 index 000000000..a21b1a190 --- /dev/null +++ b/1332/CH1/EX1.2/1_2.sce @@ -0,0 +1,7 @@ +//Example 1.2
+//Conversion Using Shortcut Method
+//Page no. 4
+clc;close;clear;
+A=10;C=12;
+d=(((1)*16+A)*16+2)*16+C;
+disp(d,'Decimal form of 1A2C is =');
\ No newline at end of file diff --git a/1332/CH1/EX1.20/1_20.pdf b/1332/CH1/EX1.20/1_20.pdf Binary files differnew file mode 100755 index 000000000..786f5532d --- /dev/null +++ b/1332/CH1/EX1.20/1_20.pdf diff --git a/1332/CH1/EX1.20/1_20.sce b/1332/CH1/EX1.20/1_20.sce new file mode 100755 index 000000000..de212a826 --- /dev/null +++ b/1332/CH1/EX1.20/1_20.sce @@ -0,0 +1,40 @@ +//Example 1.20
+//Subtraction
+//Page no. 16
+clc;close;clear;
+function [x1]=add(x,y) //function for addition of binaries
+ c=0;
+ for i=1:5
+ x1(1,i)=0
+ end
+ for i=5:-1:1
+ x=x/10;
+ xd=x-fix(x)
+ x=x-xd;
+ y=y/10;
+ yd=y-fix(y)
+ y=y-yd;
+ if c==1 then
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=1;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=1;c=0;
+ else
+ x1(1,i)=0;c=0;
+ end
+ else
+ if floor((xd*10)+0.1)==1 & floor((yd*10)+0.1)==1 then
+ x1(1,i)=0;c=1;
+ elseif floor((xd*10)+0.1)==0 & floor((yd*10)+0.1)==0
+ x1(1,i)=0;c=0;
+ else
+ x1(1,i)=1;c=0;
+ end
+ end
+ end
+ disp(x1,'Addition of 173 and 141= ')
+endfunction
+
+add(0100,1011);
+add(1100,0101);
+add(1000,1000);
\ No newline at end of file diff --git a/1332/CH1/EX1.23/1_23.pdf b/1332/CH1/EX1.23/1_23.pdf Binary files differnew file mode 100755 index 000000000..3559f7052 --- /dev/null +++ b/1332/CH1/EX1.23/1_23.pdf diff --git a/1332/CH1/EX1.23/1_23.sce b/1332/CH1/EX1.23/1_23.sce new file mode 100755 index 000000000..8c63eb008 --- /dev/null +++ b/1332/CH1/EX1.23/1_23.sce @@ -0,0 +1,36 @@ +//Example 1.23
+//Multiplication
+//Page no. 18
+clc;clear;close;
+
+function [x1]=mul(x,y)
+ for i=1:8
+ x1(1,i)=0
+ end
+ printf('Multiplication of %.4i and %.4i = ',x,y)
+ x=x*y;
+ c=0;
+ for i=8:-1:1
+ x=x/10;
+ xd=floor((x-fix(x))*10+0.1)
+ if c==1 then
+ if xd==0 then
+ x1(1,i)=1;c=0
+ elseif xd==1
+ x1(1,i)=0;
+ c=1;
+ elseif xd==2
+ x1(1,i)=1;c=1;
+ end
+ else
+ if xd==0 | xd==1 then
+ x1(1,i)=xd;c=0
+ elseif xd==2
+ x1(1,i)=0;
+ i=i-1;c=1;
+ end
+ end
+ end
+ disp(x1)
+endfunction
+mul(1110,1011);
\ No newline at end of file diff --git a/1332/CH1/EX1.24/1_24.pdf b/1332/CH1/EX1.24/1_24.pdf Binary files differnew file mode 100755 index 000000000..b4f9870a4 --- /dev/null +++ b/1332/CH1/EX1.24/1_24.pdf diff --git a/1332/CH1/EX1.24/1_24.sce b/1332/CH1/EX1.24/1_24.sce new file mode 100755 index 000000000..3495a2234 --- /dev/null +++ b/1332/CH1/EX1.24/1_24.sce @@ -0,0 +1,36 @@ +//Example 1.24
+//Multiplication
+//Page no. 18
+clc;clear;close;
+
+function [x1]=mul(x,y)
+ for i=1:8
+ x1(1,i)=0
+ end
+ printf('Multiplication of %.4i and %.4i = ',x,y)
+ x=x*y;
+ c=0;
+ for i=8:-1:1
+ x=x/10;
+ xd=floor((x-fix(x))*10+0.1)
+ if c==1 then
+ if xd==0 then
+ x1(1,i)=1;c=0
+ elseif xd==1
+ x1(1,i)=0;
+ c=1;
+ elseif xd==2
+ x1(1,i)=1;c=1;
+ end
+ else
+ if xd==0 | xd==1 then
+ x1(1,i)=xd;c=0
+ elseif xd==2
+ x1(1,i)=0;
+ i=i-1;c=1;
+ end
+ end
+ end
+ disp(x1)
+endfunction
+mul(1110,1011);
\ No newline at end of file diff --git a/1332/CH1/EX1.25/1_25.pdf b/1332/CH1/EX1.25/1_25.pdf Binary files differnew file mode 100755 index 000000000..a50214e41 --- /dev/null +++ b/1332/CH1/EX1.25/1_25.pdf diff --git a/1332/CH1/EX1.25/1_25.sce b/1332/CH1/EX1.25/1_25.sce new file mode 100755 index 000000000..36aa499e0 --- /dev/null +++ b/1332/CH1/EX1.25/1_25.sce @@ -0,0 +1,84 @@ +//Example 1.25
+//Division
+//Page no. 19
+clc;close;clear;
+function [co]=com(x,y)
+ co=1;
+ for i=1:length(x)
+ if x(i)>y(i) then
+ break
+ elseif x(i)==y(i)
+ continue
+ else
+ co=0;break
+ end
+ end
+endfunction
+function [x1]=sub(x,y) //function for subtraction of binaries
+ c=0;m=0;
+ for i=1:5
+ x1(1,i)=0
+ end
+ for i=5:-1:1
+ if c==1 then
+ if x(i)==0 & y(i)==1 then
+ x1(1,i)=0;c=1;
+ elseif x(i)==0 & y(i)==0
+ x1(1,i)=1;c=0;
+ elseif x(i)==1 & y(i)==1
+ x1(1,i)=1;c=1;
+ elseif x(i)==1 & y(i)==0
+ x1(1,i)=0;c=0;
+ end
+ else
+ if x(i)==1 & y(i)==1 then
+ x1(1,i)=0;c=0;
+ elseif x(i)==0 & y(i)==0
+ x1(1,i)=0;c=0;
+ elseif x(i)==1 & y(i)==0
+ x1(1,i)=1;c=0;
+ elseif x(i)==0 & y(i)==1
+ x1(1,i)=1;c=1;
+ end
+ end
+ end
+ disp(x1,'Remainder = ')
+endfunction
+d1=11011001;d2=01011;d22=[0,0,0,0,0]
+for i=8:-1:1
+ d3=d1/10;
+ div(1,i)=int(10*(d3-int(d3)))
+ d1=d1/10
+end
+for i=5:-1:1
+ d3=d2/10;
+ d21(1,i)=int(10*(d3-int(d3))+0.5)
+ d2=d2/10
+end
+div1(1,1)=0
+for j=1:4
+ div1(1,j+1)=div(1,j)
+end
+for i1=1:5
+ printf('After Step %i : \n',i1)
+ if com(div1,d21)==1 then
+ dis(1,i1)=1
+ n=sub(div1,d21)
+ else
+ dis(1,i1)=0
+ n=sub(div1,d22)
+end
+disp(dis,'Divisor = ')
+if i1==5 then
+ break
+end
+ for j=1:5
+ if j<5 then
+ div1(1,j)=n(j+1)
+ else
+ div1(1,j)=div(1,i1+4)
+ end
+ end
+
+printf('\n\n\n\n')
+end
\ No newline at end of file diff --git a/1332/CH1/EX1.26/1_26.pdf b/1332/CH1/EX1.26/1_26.pdf Binary files differnew file mode 100755 index 000000000..ee82c9cdb --- /dev/null +++ b/1332/CH1/EX1.26/1_26.pdf diff --git a/1332/CH1/EX1.26/1_26.sce b/1332/CH1/EX1.26/1_26.sce new file mode 100755 index 000000000..9a30d17e6 --- /dev/null +++ b/1332/CH1/EX1.26/1_26.sce @@ -0,0 +1,43 @@ +//Example 1.26
+//Multiplication
+//Page no. 19
+clc;clear;close;
+
+
+function [x1]=mul(x,y)
+ for i=1:8
+ x1(1,i)=0
+ end
+ printf('Multiplication of %.4i and %.4i = ',x,y)
+ x=x*y;
+ c=0;
+ for i=10:-1:1
+ x=x/10;
+ xd=floor((x-fix(x))*10+0.1)
+ if c==1 then
+ if xd==0 then
+ x1(1,i)=1;c=0
+ elseif xd==1
+ x1(1,i)=0;
+ c=1;
+ elseif xd==2
+ x1(1,i)=1;c=1;
+ end
+ else
+ if xd==0 | xd==1 then
+ x1(1,i)=xd;c=0
+ elseif xd==2
+ x1(1,i)=0;
+ i=i-1;c=1;
+ end
+ end
+ end
+ for i=1:10
+ if x1(1,i)==1 then
+ x1(1,i-1)=1;
+ break
+ end
+ end
+ disp(x1)
+endfunction
+mul(1110,1011);
\ No newline at end of file diff --git a/1332/CH1/EX1.29/1_29.pdf b/1332/CH1/EX1.29/1_29.pdf Binary files differnew file mode 100755 index 000000000..0b66602b3 --- /dev/null +++ b/1332/CH1/EX1.29/1_29.pdf diff --git a/1332/CH1/EX1.29/1_29.sce b/1332/CH1/EX1.29/1_29.sce new file mode 100755 index 000000000..3322e6c4b --- /dev/null +++ b/1332/CH1/EX1.29/1_29.sce @@ -0,0 +1,32 @@ +//Example 1.29
+//Normalized Floating Point Representation
+//Page no. 23
+clc;clear;close;
+
+function []=fp(x)
+ x1=x;
+ if x>0 then
+ for i=1:10
+ x=x/10
+ if int(x)==0 then
+ break
+ end
+ end
+ printf('\n %i\nNormalized Floating Point Representation of %g = %.4f x 10',i,x1,x)
+ else
+ for i=1:10
+ x=x*10
+ if ceil(x)~=0 then
+ break
+ end
+ end
+ x=x/10;i=i-1;
+ printf('\n -%i\nNormalized Floating Point Representation of %g = %.4f x 10',i,x1,x)
+ end
+
+endfunction
+
+x=[25.12,-0.00287,87000];
+for i=1:3
+ fp(x(i))
+end
\ No newline at end of file diff --git a/1332/CH1/EX1.3/1_3.pdf b/1332/CH1/EX1.3/1_3.pdf Binary files differnew file mode 100755 index 000000000..d41bc4e5b --- /dev/null +++ b/1332/CH1/EX1.3/1_3.pdf diff --git a/1332/CH1/EX1.3/1_3.sce b/1332/CH1/EX1.3/1_3.sce new file mode 100755 index 000000000..b7773ce0a --- /dev/null +++ b/1332/CH1/EX1.3/1_3.sce @@ -0,0 +1,19 @@ +//Example 1.3
+//Conversion to Base B from Decimal System
+//Page no. 5
+clc;close;clear;
+//conversion from binary to octal
+disp(dec2oct(bin2dec('10101101110')),'Octal form of 10101101110 is ='); //inbuilt function
+
+//conversion from binary to hexadecimal
+disp(dec2hex(bin2dec('10101101110')),'Hexadecimal form of 10101101110 is ='); //inbuilt function
+
+//conversion from binary to octal
+s=dec2oct(bin2dec('1011'));
+s1=dec2oct(bin2dec('110011010100')); //inbuilt function
+printf('\n Octal form of 1011.1100110101 is = \n\n %s.%s',s,s1)
+
+//conversion from binary to hexadecimal
+s=dec2hex(bin2dec('1011'));
+s1=dec2hex(bin2dec('110011010100')); //inbuilt function
+printf('\n\n Hexadecimal form of 1011.1100110101 is = \n\n %s.%s',s,s1)
\ No newline at end of file diff --git a/1332/CH1/EX1.30/1_30.pdf b/1332/CH1/EX1.30/1_30.pdf Binary files differnew file mode 100755 index 000000000..92b3a50fd --- /dev/null +++ b/1332/CH1/EX1.30/1_30.pdf diff --git a/1332/CH1/EX1.30/1_30.sce b/1332/CH1/EX1.30/1_30.sce new file mode 100755 index 000000000..a5dfde631 --- /dev/null +++ b/1332/CH1/EX1.30/1_30.sce @@ -0,0 +1,7 @@ +//Example 1.30
+//Add
+//Page no. 26
+clc;clear;close;
+a=0.4532e7;b=0.5427e7;
+c=a+b
+printf('Addition of %.6g and %.6g = %.6g',a,b,c)
\ No newline at end of file diff --git a/1332/CH1/EX1.31/1_31.pdf b/1332/CH1/EX1.31/1_31.pdf Binary files differnew file mode 100755 index 000000000..559a3f24e --- /dev/null +++ b/1332/CH1/EX1.31/1_31.pdf diff --git a/1332/CH1/EX1.31/1_31.sce b/1332/CH1/EX1.31/1_31.sce new file mode 100755 index 000000000..bc6ac9c61 --- /dev/null +++ b/1332/CH1/EX1.31/1_31.sce @@ -0,0 +1,7 @@ +//Example 1.31
+//Add
+//Page no. 26
+clc;clear;close;
+a=0.4532e5;b=0.5427e7;
+c=a+b
+printf('Addition of %.4g and %.6g = %.6g',a,b,c)
\ No newline at end of file diff --git a/1332/CH1/EX1.32/1_32.pdf b/1332/CH1/EX1.32/1_32.pdf Binary files differnew file mode 100755 index 000000000..14e9783ab --- /dev/null +++ b/1332/CH1/EX1.32/1_32.pdf diff --git a/1332/CH1/EX1.32/1_32.sce b/1332/CH1/EX1.32/1_32.sce new file mode 100755 index 000000000..9e1aee114 --- /dev/null +++ b/1332/CH1/EX1.32/1_32.sce @@ -0,0 +1,7 @@ +//Example 1.32
+//Add
+//Page no. 26
+clc;clear;close;
+a=0.4532e3;b=0.5427e7;
+c=a+b
+printf('Addition of %.2g and %.6g = %.4g',a,b,c)
\ No newline at end of file diff --git a/1332/CH1/EX1.33/1_33.pdf b/1332/CH1/EX1.33/1_33.pdf Binary files differnew file mode 100755 index 000000000..1d47ed1ff --- /dev/null +++ b/1332/CH1/EX1.33/1_33.pdf diff --git a/1332/CH1/EX1.33/1_33.sce b/1332/CH1/EX1.33/1_33.sce new file mode 100755 index 000000000..22c681433 --- /dev/null +++ b/1332/CH1/EX1.33/1_33.sce @@ -0,0 +1,10 @@ +//Example 1.33
+//Add
+//Page no. 27
+clc;clear;close;
+a=[0.4632e3,0.4632e99];b=[0.5427e3,0.5427e99];
+
+for i=1:2
+ c(i)=a(i)+b(i)
+ printf('\nAddition of %.2g and %.2g = %.5g\n',a(i),b(i),c(i))
+end
diff --git a/1332/CH1/EX1.34/1_34.pdf b/1332/CH1/EX1.34/1_34.pdf Binary files differnew file mode 100755 index 000000000..5a404efc6 --- /dev/null +++ b/1332/CH1/EX1.34/1_34.pdf diff --git a/1332/CH1/EX1.34/1_34.sce b/1332/CH1/EX1.34/1_34.sce new file mode 100755 index 000000000..fb2028694 --- /dev/null +++ b/1332/CH1/EX1.34/1_34.sce @@ -0,0 +1,9 @@ +//Example 1.34
+//Subtraction
+//Page no. 27
+clc;clear;close;
+a=[0.5427e-3,0.9627e4,0.9627e-99];b=[0.9632e-4,0.9622e4,0.9622e-99];
+for i=1:3
+ c(i)=a(i)-b(i)
+ printf('\nSubtraction of %.2g from %.3g = %.6g\n',a(i),b(i),c(i))
+end
diff --git a/1332/CH1/EX1.35/1_35.pdf b/1332/CH1/EX1.35/1_35.pdf Binary files differnew file mode 100755 index 000000000..67a3c7709 --- /dev/null +++ b/1332/CH1/EX1.35/1_35.pdf diff --git a/1332/CH1/EX1.35/1_35.sce b/1332/CH1/EX1.35/1_35.sce new file mode 100755 index 000000000..0d03ac374 --- /dev/null +++ b/1332/CH1/EX1.35/1_35.sce @@ -0,0 +1,9 @@ +//Example 1.35
+//Multiplication
+//Page no. 28
+clc;clear;close;
+a=[0.9632e12,0.1132e12,0.1132e52,0.1132e-52];b=[0.5427e-15,0.1027e15,0.1027e50,0.1027e-50];
+for i=1:4
+ c(i)=a(i)*b(i)
+ printf('\nMultiplication of %.3g and %.2g = %.6g\n',a(i),b(i),c(i))
+end
diff --git a/1332/CH1/EX1.36/1_36.pdf b/1332/CH1/EX1.36/1_36.pdf Binary files differnew file mode 100755 index 000000000..980948a73 --- /dev/null +++ b/1332/CH1/EX1.36/1_36.pdf diff --git a/1332/CH1/EX1.36/1_36.sce b/1332/CH1/EX1.36/1_36.sce new file mode 100755 index 000000000..eb586d51b --- /dev/null +++ b/1332/CH1/EX1.36/1_36.sce @@ -0,0 +1,9 @@ +//Example 1.36
+//Division
+//Page no. 28
+clc;clear;close;
+a=[0.1132e1,0.1132e-6,0.1132e6];b=[0.1000e-99,0.1000e99,0.1000e3];
+for i=1:3
+ c(i)=a(i)/b(i)
+ printf('\nDivision of %.2g by %.3g= %.3g\n',a(i),b(i),c(i))
+end
diff --git a/1332/CH1/EX1.4/1_4.pdf b/1332/CH1/EX1.4/1_4.pdf Binary files differnew file mode 100755 index 000000000..7628a1a39 --- /dev/null +++ b/1332/CH1/EX1.4/1_4.pdf diff --git a/1332/CH1/EX1.4/1_4.sce b/1332/CH1/EX1.4/1_4.sce new file mode 100755 index 000000000..352eb8074 --- /dev/null +++ b/1332/CH1/EX1.4/1_4.sce @@ -0,0 +1,14 @@ +//Example 1.4
+//Conversion to Binary System
+//Page no. 6
+clc;close;clear;
+//conversion from octal to binary
+disp(dec2bin(oct2dec('1753')),'Binary form of 1753 is ='); //inbuilt function
+
+//conversion from octal to binary
+disp(dec2bin(hex2dec('A478')),'Binary form of A478 is ='); //inbuilt function
+
+//conversion from octal to binary
+s=dec2bin(oct2dec('3'));
+s1=dec2bin(oct2dec('154')); //inbuilt function
+printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)
\ No newline at end of file diff --git a/1332/CH1/EX1.5/1_5.pdf b/1332/CH1/EX1.5/1_5.pdf Binary files differnew file mode 100755 index 000000000..60430b1da --- /dev/null +++ b/1332/CH1/EX1.5/1_5.pdf diff --git a/1332/CH1/EX1.5/1_5.sce b/1332/CH1/EX1.5/1_5.sce new file mode 100755 index 000000000..e63eb71b7 --- /dev/null +++ b/1332/CH1/EX1.5/1_5.sce @@ -0,0 +1,21 @@ +//Example 1.5
+//Conversion to Binary System
+//Page no. 6
+clc;close;clear;
+//conversion from octal to binary
+b=dec2bin(oct2dec('1753'))
+disp(b,'Binary form of 1753 is ='); //inbuilt function
+b=dec2hex(oct2dec('1753'))
+disp(b,'Hexadecimal form of 1753 is ='); //inbuilt function
+//conversion from octal to binary
+b=dec2bin(hex2dec('A478'))
+disp(b,'Binary form of A478 is ='); //inbuilt function
+b=dec2oct(hex2dec('A478'))
+disp(b,'Octal form of A478 is ='); //inbuilt function
+//conversion from octal to binary
+s=dec2bin(oct2dec('3'));
+s1=dec2bin(oct2dec('154')); //inbuilt function
+printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)
+s=dec2hex(oct2dec('3'));
+s1=dec2hex(oct2dec('154')); //inbuilt function
+printf('\n\n Hexadecimal form of 3.154 is = \n\n %s.%s',s,s1)
\ No newline at end of file diff --git a/1332/CH1/EX1.6/1_6.pdf b/1332/CH1/EX1.6/1_6.pdf Binary files differnew file mode 100755 index 000000000..2a14babf5 --- /dev/null +++ b/1332/CH1/EX1.6/1_6.pdf diff --git a/1332/CH1/EX1.6/1_6.sce b/1332/CH1/EX1.6/1_6.sce new file mode 100755 index 000000000..e054c98ac --- /dev/null +++ b/1332/CH1/EX1.6/1_6.sce @@ -0,0 +1,6 @@ +//Example 1.6
+//Conversion to Decimal Number
+//Page no. 7
+clc;close;clear;
+
+disp(dec2bin(182),'Binary of 182=') //inbuilt function
\ No newline at end of file diff --git a/1332/CH1/EX1.7/1_7.pdf b/1332/CH1/EX1.7/1_7.pdf Binary files differnew file mode 100755 index 000000000..7ed89426c --- /dev/null +++ b/1332/CH1/EX1.7/1_7.pdf diff --git a/1332/CH1/EX1.7/1_7.sce b/1332/CH1/EX1.7/1_7.sce new file mode 100755 index 000000000..510166fac --- /dev/null +++ b/1332/CH1/EX1.7/1_7.sce @@ -0,0 +1,6 @@ +//Example 1.7
+//Conversion to Decimal Number
+//Page no. 7
+clc;close;clear;
+
+disp(dec2oct(467),'Octal of 467=') //inbuilt function
\ No newline at end of file diff --git a/1332/CH1/EX1.8/1_8.pdf b/1332/CH1/EX1.8/1_8.pdf Binary files differnew file mode 100755 index 000000000..cb06ca2a1 --- /dev/null +++ b/1332/CH1/EX1.8/1_8.pdf diff --git a/1332/CH1/EX1.8/1_8.sce b/1332/CH1/EX1.8/1_8.sce new file mode 100755 index 000000000..b9713fc8d --- /dev/null +++ b/1332/CH1/EX1.8/1_8.sce @@ -0,0 +1,19 @@ +//Example 1.8
+//Conversion to Base B from Binary System
+//Page no. 8
+clc;close;clear;
+//conversion from binary to octal
+disp(dec2oct(bin2dec('10101101110')),'Octal form of 10101101110 is ='); //inbuilt function
+
+//conversion from binary to hexadecimal
+disp(dec2hex(bin2dec('10101101110')),'Hexadecimal form of 10101101110 is ='); //inbuilt function
+
+//conversion from binary to octal
+s=dec2oct(bin2dec('1011'));
+s1=dec2oct(bin2dec('110011010100')); //inbuilt function
+printf('\n Octal form of 1011.1100110101 is = \n\n %s.%s',s,s1)
+
+//conversion from binary to hexadecimal
+s=dec2hex(bin2dec('1011'));
+s1=dec2hex(bin2dec('110011010100')); //inbuilt function
+printf('\n\n Hexadecimal form of 1011.1100110101 is = \n\n %s.%s',s,s1)
\ No newline at end of file diff --git a/1332/CH1/EX1.9/1_9.pdf b/1332/CH1/EX1.9/1_9.pdf Binary files differnew file mode 100755 index 000000000..d5dd1fde5 --- /dev/null +++ b/1332/CH1/EX1.9/1_9.pdf diff --git a/1332/CH1/EX1.9/1_9.sce b/1332/CH1/EX1.9/1_9.sce new file mode 100755 index 000000000..0f9a2482c --- /dev/null +++ b/1332/CH1/EX1.9/1_9.sce @@ -0,0 +1,14 @@ +//Example 1.9
+//Conversion to Binary System
+//Page no. 8
+clc;close;clear;
+//conversion from octal to binary
+disp(dec2bin(oct2dec('1753')),'Binary form of 1753 is ='); //inbuilt function
+
+//conversion from octal to binary
+disp(dec2bin(hex2dec('A478')),'Binary form of A478 is ='); //inbuilt function
+
+//conversion from octal to binary
+s=dec2bin(oct2dec('3'));
+s1=dec2bin(oct2dec('154')); //inbuilt function
+printf('\n Octal form of 3.154 is = \n\n %s.00%s',s,s1)
\ No newline at end of file diff --git a/1332/CH10/EX10.1/10_1.pdf b/1332/CH10/EX10.1/10_1.pdf Binary files differnew file mode 100755 index 000000000..dc137f7ca --- /dev/null +++ b/1332/CH10/EX10.1/10_1.pdf diff --git a/1332/CH10/EX10.1/10_1.sce b/1332/CH10/EX10.1/10_1.sce new file mode 100755 index 000000000..7e9579e80 --- /dev/null +++ b/1332/CH10/EX10.1/10_1.sce @@ -0,0 +1,17 @@ +//Example 10.1
+//System of Non Linear Equations
+//Page no. 311
+clc;clear;close;
+
+deff('y=f(x)','y=x^2-exp(2*x)-4')
+deff('y=f1(x)','y=2*x-2*exp(2*x)')
+x0=0;e=0.00001
+for i=1:10
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation after %i Iterations by newton raphshon method is %.10f',i,x1)
\ No newline at end of file diff --git a/1332/CH10/EX10.2/10_2.pdf b/1332/CH10/EX10.2/10_2.pdf Binary files differnew file mode 100755 index 000000000..5ef8122da --- /dev/null +++ b/1332/CH10/EX10.2/10_2.pdf diff --git a/1332/CH10/EX10.2/10_2.sce b/1332/CH10/EX10.2/10_2.sce new file mode 100755 index 000000000..4221dc877 --- /dev/null +++ b/1332/CH10/EX10.2/10_2.sce @@ -0,0 +1,17 @@ +//Example 10.2
+//Contraction Method and Seidel Method
+//Page no. 315
+clc;clear;close;
+x(1)=0;y(1)=0
+printf('(a) Contraction Mapping\n\nn\txn\t\tyn\n--------------------------------\n 0\t%f\t%f\n',x(1),y(1))
+for i=2:9
+ x(i)=sin(x(i-1)+y(i-1))
+ y(i)=cos(x(i-1)-y(i-1))
+ printf(' %i\t%f\t%f\n',i-1,x(i),y(i))
+end
+printf('\n\n\n(b) Seidel Method\n\nn\txn\t\tyn\n--------------------------------\n 0\t%f\t%f\n',x(1),y(1))
+for i=2:9
+ x(i)=sin(x(i-1)+y(i-1))
+ y(i)=cos(x(i)-y(i-1))
+ printf(' %i\t%f\t%f\n',i-1,x(i),y(i))
+end
\ No newline at end of file diff --git a/1332/CH10/EX10.3/10_3.pdf b/1332/CH10/EX10.3/10_3.pdf Binary files differnew file mode 100755 index 000000000..d929b209e --- /dev/null +++ b/1332/CH10/EX10.3/10_3.pdf diff --git a/1332/CH10/EX10.3/10_3.sce b/1332/CH10/EX10.3/10_3.sce new file mode 100755 index 000000000..e8eb4d50a --- /dev/null +++ b/1332/CH10/EX10.3/10_3.sce @@ -0,0 +1,24 @@ +//Example 10.3
+//Non Linear System of Equation
+//Page no. 315
+clc;clear;close;
+x(1,1)=1;x(1,2)=0;x(1,3)=0;
+y(1,1)=0;y(1,2)=2;y(1,3)=2;
+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))
+for i=2:9
+ printf(' %i\t',i-1)
+ for j=1:3
+ if j==1 | j==2 then
+ x(i,j)=(-y(i-1,j)^2-4*x(i-1,j)^2+8*x(i-1,j)+4)/8
+ y(i,j)=(2*y(i-1,j)^2-2*x(i-1,j)+1)/4
+ printf('\t%f\t%f',x(i,j),y(i,j))
+ end
+ if j==3 then
+ x(i,j)=(-y(i-1,j)^2-4*x(i-1,j)^2+11*x(i-1,j)+4)/11
+ y(i,j)=(-2*y(i-1,j)^2+8*y(i-1,j)-2*x(i-1,j)-1)/4
+ printf('\t%f\t%f',x(i,j),y(i,j))
+ end
+ end
+ printf('\n')
+end
+printf('\n\n\n\nNote : There are computational errors in this example given by the book')
\ No newline at end of file diff --git a/1332/CH10/EX10.4/10_4.pdf b/1332/CH10/EX10.4/10_4.pdf Binary files differnew file mode 100755 index 000000000..6d8309fb4 --- /dev/null +++ b/1332/CH10/EX10.4/10_4.pdf diff --git a/1332/CH10/EX10.4/10_4.sce b/1332/CH10/EX10.4/10_4.sce new file mode 100755 index 000000000..3d6f5ec66 --- /dev/null +++ b/1332/CH10/EX10.4/10_4.sce @@ -0,0 +1,25 @@ +//Example 10.4
+//Newton Method
+//Page no. 317
+clc;clear;close;
+
+deff('y=f1(x1,x2)','y=x1+3*log10(x1)-x2^2')
+deff('y=f2(x1,x2)','y=2*x1^2-x1*x2-5*x1+1')
+deff('y=f11(x1,x2)','y=1+3/(log(10)*x1)')
+deff('y=f12(x1,x2)','y=-2*x2')
+deff('y=f21(x1,x2)','y=4*x1-x2-5')
+deff('y=f22(x1,x2)','y=-x1')
+x=[3.4;2.2];
+disp(x,'x(0) = ')
+for i=1:3
+ fx=[f1(x(1),x(2));f2(x(1),x(2))]
+ printf('\n fx(%i) = \n',i)
+ disp(fx)
+ A=[f11(x(1),x(2)),f12(x(1),x(2));f21(x(1),x(2)),f22(x(1),x(2)),]
+ disp(A,'A = ')
+ A_1=inv(A)
+ disp(A_1,'Inverse of A = ')
+ x=x-A_1*fx
+ printf('\n x(%i) = \n',i)
+ disp(x)
+end
\ No newline at end of file diff --git a/1332/CH10/EX10.5/10_5.pdf b/1332/CH10/EX10.5/10_5.pdf Binary files differnew file mode 100755 index 000000000..b75e34b20 --- /dev/null +++ b/1332/CH10/EX10.5/10_5.pdf diff --git a/1332/CH10/EX10.5/10_5.sce b/1332/CH10/EX10.5/10_5.sce new file mode 100755 index 000000000..380c7a71c --- /dev/null +++ b/1332/CH10/EX10.5/10_5.sce @@ -0,0 +1,30 @@ +//Example 10.5
+//Newton Raphshon Method
+//Page no. 320
+clc;clear;close;
+
+deff('y=f1(x,y)','y=x^3-3*x*y^2+1')
+deff('y=f2(x,y)','y=3*x^2*y-y^3')
+deff('y=f11(x,y)','y=3*x^2-6*y^2')
+deff('y=f12(x,y)','y=-6*x*y')
+deff('y=f21(x,y)','y=6*x*y')
+deff('y=f22(x,y)','y=3*x^2-3*y^2')
+x=[0;1];
+printf('\nx(0) = %g\ny(0) = %g\n',x(1),x(2))
+for i=1:3
+ fx=[f1(x(1),x(2));f2(x(1),x(2))]
+ printf('\n fx(%i) = \n',i)
+ disp(fx)
+ J=[f11(x(1),x(2)),f12(x(1),x(2));f21(x(1),x(2)),f22(x(1),x(2)),]
+ disp(J,'J = ')
+ d=det(J);
+ if d==0 then
+ dx1=0;dx2=0;
+ else
+ dx1=(fx(1)*J(2,2)-fx(2)*J(1,2))/d;
+ dx2=(fx(2)*J(1,1)-fx(1)*J(2,1))/d;
+ end
+ x(1)=x(1)+dx1;
+ x(2)=x(2)+dx2;
+ printf('\nx(%i) = %g\ny(%i) = %g\n',i,x(1),i,x(2))
+end
\ No newline at end of file diff --git a/1332/CH10/EX10.6/10_6.pdf b/1332/CH10/EX10.6/10_6.pdf Binary files differnew file mode 100755 index 000000000..cc5557e4a --- /dev/null +++ b/1332/CH10/EX10.6/10_6.pdf diff --git a/1332/CH10/EX10.6/10_6.sce b/1332/CH10/EX10.6/10_6.sce new file mode 100755 index 000000000..7ebf587ab --- /dev/null +++ b/1332/CH10/EX10.6/10_6.sce @@ -0,0 +1,29 @@ +//Example 10.6
+//Newton Method
+//Page no. 322
+clc;clear;close;
+
+deff('y=f1(x,y,z)','y=x-0.1*y^2+0.05*z^2-0.7')
+deff('y=f2(x,y,z)','y=y+0.3*x^2-0.1*x*z-0.5')
+deff('y=f3(x,y,z)','y=z+0.4*y^2+0.1*x*y-1.2')
+deff('y=f11(x,y,z)','y=1')
+deff('y=f12(x,y,z)','y=-0.2*y')
+deff('y=f13(x,y,z)','y=0.1*z')
+deff('y=f21(x,y,z)','y=0.6*x-0.1*z')
+deff('y=f22(x,y,z)','y=1')
+deff('y=f23(x,y,z)','y=-0.1*x')
+deff('y=f31(x,y,z)','y=0.1*y')
+deff('y=f32(x,y,z)','y=0.8*y+0.1*x')
+deff('y=f33(x,y,z)','y=1')
+x=[0;0;0];
+printf('n\txn\t\tyn\t\tzn\n---------------------------------------------------------\n')
+for i=1:6
+ fx=[f1(x(1),x(2),x(3));f2(x(1),x(2),x(3));f3(x(1),x(2),x(3))]
+ 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))]
+ J_1=inv(J)
+ printf(' %i\t%f\t%f\t%f\n',i-1,x(1),x(2),x(3))
+ x=x-J_1*fx
+end
+printf('\n\nThe solution is x = %f, y = %f and z = %f',x(1),x(2),x(3))
+
+printf('\n\n\nNote : There are computation errors in calculation given by the book')
\ No newline at end of file diff --git a/1332/CH10/EX10.7/10_7.pdf b/1332/CH10/EX10.7/10_7.pdf Binary files differnew file mode 100755 index 000000000..926860b3c --- /dev/null +++ b/1332/CH10/EX10.7/10_7.pdf diff --git a/1332/CH10/EX10.7/10_7.sce b/1332/CH10/EX10.7/10_7.sce new file mode 100755 index 000000000..beea1ec15 --- /dev/null +++ b/1332/CH10/EX10.7/10_7.sce @@ -0,0 +1,14 @@ +//Example 10.7
+//Iterative Method
+//Page no. 326
+clc;clear;close;
+
+x=[0;0;0];
+printf('n\txn\t\tyn\t\tzn\n---------------------------------------------------------\n')
+for i=1:7
+ printf(' %i\t%.10f\t%.10f\t%.10f\n',i-1,x(1),x(2),x(3))
+ x(1)=0.7+0.1*x(2)^2-0.05*x(3)^2
+ x(2)=0.5-0.3*x(1)^2+0.1*x(1)*x(3)
+ x(3)=1.2-0.4*x(2)^2-0.1*x(1)*x(2)
+end
+printf('\n\nThe solution is x = %.10f, y = %.10f and z = %.10f',x(1),x(2),x(3))
\ No newline at end of file diff --git a/1332/CH10/EX10.8/10_8.pdf b/1332/CH10/EX10.8/10_8.pdf Binary files differnew file mode 100755 index 000000000..51172ad38 --- /dev/null +++ b/1332/CH10/EX10.8/10_8.pdf diff --git a/1332/CH10/EX10.8/10_8.sce b/1332/CH10/EX10.8/10_8.sce new file mode 100755 index 000000000..2ba534796 --- /dev/null +++ b/1332/CH10/EX10.8/10_8.sce @@ -0,0 +1,16 @@ +//Example 10.8
+//Steepest Descent
+//Page no. 328
+clc;clear;close;
+
+deff('y=f(x1,x2)','y=(x1-2)^4+3*(x2+3)^2')
+x=[1;-2];
+printf('n\t x1\t\t x2\t\t F(x1,x2)\n-----------------------------------------------------\n')
+for i=1:11
+ Fx=[f(x(1),x(2))];
+ J=[4*(x(1)-2)^3,6*(x(2)+3)];
+ u=(Fx*J*J'*Fx)/(J*J'*Fx*J*J'*Fx)
+ printf(' %i\t%.10f\t%.10f\t%.10f\n',i-1,x(1),x(2),Fx)
+ x=x-u*J'*Fx
+end
+printf('\n\nThis shows that the solution tends to x1 = %i and x2 = %i',ceil(x(1)),floor(x(2)))
\ No newline at end of file diff --git a/1332/CH11/EX11.1/11_1.pdf b/1332/CH11/EX11.1/11_1.pdf Binary files differnew file mode 100755 index 000000000..ed2819e08 --- /dev/null +++ b/1332/CH11/EX11.1/11_1.pdf diff --git a/1332/CH11/EX11.1/11_1.sce b/1332/CH11/EX11.1/11_1.sce new file mode 100755 index 000000000..8149a5d76 --- /dev/null +++ b/1332/CH11/EX11.1/11_1.sce @@ -0,0 +1,17 @@ +//Example 11.1
+//Eigenvalues and Eigenvectors
+//Page no. 333
+clc;clear;close;
+
+A1=[0.6;0.2];A2=[-0.2;0.6];A3=[-0.6;-0.2];A4=[0.2;-0.6];
+T=[1.1,-0.3;-0.3,1.9];
+B1=T*A1;B2=T*A2;B3=T*A3;B4=T*A4;
+disp(B4,B3,B2,B1,'The transformed vectors are :')
+disp('These points lie on the ellipse:')
+printf(' 2 2\n(x-3y)+(3x+y)\n------ ------\n 16 4\n\n')
+A5=[0;2/sqrt(10)];
+disp('The vector (0,2/10^(1/2)) lies on the circle:')
+printf(' 2 2\nx + y = 4\n -\n 10\n\n')
+B5=T*A5;
+disp('Also lies on the same ellipse',B5)
+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')
\ No newline at end of file diff --git a/1332/CH11/EX11.10/11_10.pdf b/1332/CH11/EX11.10/11_10.pdf Binary files differnew file mode 100755 index 000000000..f586d6d7a --- /dev/null +++ b/1332/CH11/EX11.10/11_10.pdf diff --git a/1332/CH11/EX11.10/11_10.sce b/1332/CH11/EX11.10/11_10.sce new file mode 100755 index 000000000..bb91d6b91 --- /dev/null +++ b/1332/CH11/EX11.10/11_10.sce @@ -0,0 +1,49 @@ +//Example 11.10
+//LU Method
+//Page no. 363
+clc;close;clear;
+
+A=[120,80,40,-16;80,120,16,-40;40,16,120,-80;-16,-40,-80,120];
+disp(A,"A =")
+L=eye(4,4);
+for l=1:20
+for j=1:4
+ for i=1:j
+ k=0
+ for p=1:i-1
+ k=k-A(i,p)*A(p,j)
+ end
+ A(i,j)=A(i,j)+k
+ end
+ for i=j+1:4
+ k=0;
+ for p=1:j-1
+ k=k-A(i,p)*A(p,j)
+ end
+ A(i,j)=(A(i,j)+k)/A(j,j)
+ end
+end
+disp(A,"Modified A = ")
+ for i=1:4
+ for j=1:4
+ if i>j then
+ L(i,j)=A(i,j)
+ else
+ U(i,j)=A(i,j)
+ end
+ end
+end
+disp(U,"U =",L,"L =")
+A=U*L;
+printf('\n\nAfter %i iterations, matrix A =\n\n',l)
+for i=1:4
+ for j=1:4
+ printf(' %.2f\t',A(i,j))
+ end
+ printf('\n')
+end
+end
+printf('\n\nTherefore the eigenvalues are the diagonal elements f the transformed triangular matrix are:\n\n')
+for i=1:4
+ printf(' %.2f,',A(i,i))
+end
\ No newline at end of file diff --git a/1332/CH11/EX11.11/11_11.pdf b/1332/CH11/EX11.11/11_11.pdf Binary files differnew file mode 100755 index 000000000..cc1ab5a87 --- /dev/null +++ b/1332/CH11/EX11.11/11_11.pdf diff --git a/1332/CH11/EX11.11/11_11.sce b/1332/CH11/EX11.11/11_11.sce new file mode 100755 index 000000000..745b06f80 --- /dev/null +++ b/1332/CH11/EX11.11/11_11.sce @@ -0,0 +1,119 @@ +//Example 11.11
+//Generalized Eigenvalue Problem
+//Page no. 365
+clc;close;clear;
+
+A=[1,1,0.5;1,1,0.25;0.5,0.25,2]
+B=[2,2,2;2,5,5;2,5,11]
+disp(B,"B =",A,"A =")
+for i=1:3
+ G(i,i)=sqrt(B(i,i))
+end
+G=[B;eye(3,3)];
+
+//transformation to frobenius matrix
+for k=3:-1:2
+ g(k)=0;
+ for j=1:k-1
+ if(g(k)<G(k,j))
+ g(k)=G(k,j)
+ p=j;
+ end
+ end
+ if(g(k)~=0)
+ for j=1:3
+ r(1,j)=G(k,j)
+ end
+ for i=1:6
+ G(i,k-1)=G(i,k-1)/g(k)
+ end
+ for j=1:3
+ if(j~=k-1)
+ l=G(k,j)
+ for i=1:6
+ G(i,j)=G(i,j)-l*G(i,k-1)
+ end
+ end
+ end
+ end
+ for j=1:3
+ for i=1:3
+ c(i,1)=G(i,j)
+ end
+ G(k-1,j)=0
+ for i=1:3
+ G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)
+ end
+ end
+end
+
+//partition g
+for i=4:6
+ for j=1:3
+ T(i-3,j)=G(i,j)
+ end
+end
+
+//eigenvalues computation
+p=poly(B,'x')
+a=roots(p)
+printf('\n\nDiagonalized Matrix B = \n\n')
+for i=1:3
+ for j=1:3
+ if i~=j then
+ B(i,j)=0
+ else
+ B(i,j)=a(i)
+ end
+ end
+end
+disp(B)
+//eigenvectors computation
+for k=1:3
+ m=2
+ for l=1:3
+ y(l,k)=a(k)^(m)
+ m=m-1;
+ end
+end
+printf('\n\n')
+
+
+for k=1:3
+ for l=1:3
+ y1(l,1)=y(l,1)
+ y2(l,1)=y(l,2)
+ y3(l,1)=y(l,3)
+ end
+ x1=T*y3;
+ x2=T*y2;
+ x3=T*y1;
+end
+printf('\n\nEigenvectors of B are :\n\n')
+for i=1:3
+ printf('|%.5f|\t\t|%.5f|\t\t|%.5f|',x3(i,1),x2(i,1),x1(i,1))
+ printf('\n')
+end
+x=[x3,x2,x1]
+
+
+
+
+
+B=[2,2,2;2,5,5;2,5,11]
+G=0
+for i=1:3
+ for j=1:3
+ if i==j then
+ G(i,j)=sqrt(B(i,j))
+ else
+ G(i,j)=0;
+ end
+ end
+end
+
+B=inv(G)*x'*A*x*inv(G)
+disp(B,"Eigenvectors of A =")
+
+printf('\n\n\nNote : Computation Error in book in caculation of eigenvector of B thus for A')
+
diff --git a/1332/CH11/EX11.2/11_2.pdf b/1332/CH11/EX11.2/11_2.pdf Binary files differnew file mode 100755 index 000000000..78f0fd729 --- /dev/null +++ b/1332/CH11/EX11.2/11_2.pdf diff --git a/1332/CH11/EX11.2/11_2.sce b/1332/CH11/EX11.2/11_2.sce new file mode 100755 index 000000000..4bb0413f5 --- /dev/null +++ b/1332/CH11/EX11.2/11_2.sce @@ -0,0 +1,43 @@ +//Example 11.2
+//Leverrier's Method
+//Page no. 337
+clc;close;clear;
+
+A=[2,2,2;2,5,5;2,5,1];
+A1=A;
+C(1)=0;
+ for j=1:3
+ for k=1:3
+ if(j==k)
+ C(1)=C(1)+A1(j,k)
+ end
+ end
+ end
+ disp(A,'A=')
+ disp(A1,'A1=')
+ printf('\nC1=')
+ disp(C(1));
+for i=2:3
+ A2=A*(A1-C(i-1)*eye(3,3));
+ printf('\n\n\nA%i=',i)
+ disp(A2);
+ C(i)=0;
+ for j=1:3
+ for k=1:3
+ if(j==k)
+ C(i)=C(i)+A2(j,k)/i
+ end
+ end
+ end
+ printf('\nC%i=',i)
+ disp(C(i))
+ A1=A2;
+end
+printf('\n\n\nTherefore the characteristic polynomial is:\n 3 2\nx - %ix - %ix %i = 0',C(1),C(2),C(3))
+
+//verification
+printf('\n\nVerification:')
+s=poly(0,"s");
+p=poly(A,'x');
+A=A-eye(3,3)*%s;
+disp(p,'=',A)
diff --git a/1332/CH11/EX11.3/11_3.pdf b/1332/CH11/EX11.3/11_3.pdf Binary files differnew file mode 100755 index 000000000..afc59990b --- /dev/null +++ b/1332/CH11/EX11.3/11_3.pdf diff --git a/1332/CH11/EX11.3/11_3.sce b/1332/CH11/EX11.3/11_3.sce new file mode 100755 index 000000000..f25a0d626 --- /dev/null +++ b/1332/CH11/EX11.3/11_3.sce @@ -0,0 +1,90 @@ +//Example 11.3
+//Danilevsky Method
+//Page no. 341
+clc;close;clear;
+
+A=[-1,0,0;1,-2,3;0,2,-3];
+G=[A;eye(3,3)];
+disp(G);
+//transformation to frobenius matrix
+for k=3:-1:2
+ g(k)=0;
+ for j=1:k-1
+ if(g(k)<G(k,j))
+ g(k)=G(k,j)
+ p=j;
+ end
+ end
+ if(g(k)~=0)
+ for j=1:3
+ r(1,j)=G(k,j)
+ end
+ for i=1:6
+ G(i,k-1)=G(i,k-1)/g(k)
+ end
+ disp(G)
+ for j=1:3
+ if(j~=k-1)
+ l=G(k,j)
+ for i=1:6
+ G(i,j)=G(i,j)-l*G(i,k-1)
+ end
+ end
+ end
+ disp(G)
+ end
+ for j=1:3
+ for i=1:3
+ c(i,1)=G(i,j)
+ end
+ G(k-1,j)=0
+ for i=1:3
+ G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)
+ end
+ end
+ disp(G)
+end
+
+//partition g
+for i=4:6
+ for j=1:3
+ T(i-3,j)=G(i,j)
+ end
+end
+disp(T,'T=')
+
+//eigenvalues computation
+printf('\n\n\nCharateristic polynomial:')
+p=poly(A,'x')
+disp(p)
+printf('\n\n\nEigenvalues:')
+a=roots(p)
+disp(a')
+//eigenvectors computation
+for k=1:3
+ m=2
+ for l=1:3
+ y(l,k)=a(k,1)^(m)
+ m=m-1;
+ end
+end
+printf('\n\n')
+disp(y,'y=')
+
+//eigenvector computation
+
+for k=1:3
+ for l=1:3
+ y1(l,1)=y(l,1)
+ y2(l,1)=y(l,2)
+ y3(l,1)=y(l,3)
+ end
+ x1=T*y3;
+ x2=T*y2;
+ x3=T*y1;
+end
+printf('\n\nEigenvectors :\n')
+for i=1:3
+ printf('|%.1f|\t\t|%.1f|\t\t|%.1f|',x1(i,1),x2(i,1),x3(i,1))
+ printf('\n')
+end
diff --git a/1332/CH11/EX11.4/11_4.pdf b/1332/CH11/EX11.4/11_4.pdf Binary files differnew file mode 100755 index 000000000..7afaedb01 --- /dev/null +++ b/1332/CH11/EX11.4/11_4.pdf diff --git a/1332/CH11/EX11.4/11_4.sce b/1332/CH11/EX11.4/11_4.sce new file mode 100755 index 000000000..6e787e59a --- /dev/null +++ b/1332/CH11/EX11.4/11_4.sce @@ -0,0 +1,19 @@ +//Example 11.4
+//Power Method
+//Page no. 345
+clc;close;clear;
+
+A=[1,2;3,4];
+e=0.001;
+q0=[1;1];
+for i=1:5
+ q1=A*q0;
+ a=max(q1)
+ for j=1:2
+ q2(j)=q1(j)/a;
+ end
+ 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))
+ q1=q2;
+ q0=q1;
+end
+printf('Hence the largest eigenvalue is %.4f with the corresponding eigenvector as %.4f\n %i',a,q0(1),q0(2))
\ No newline at end of file diff --git a/1332/CH11/EX11.5/11_5.pdf b/1332/CH11/EX11.5/11_5.pdf Binary files differnew file mode 100755 index 000000000..1db354995 --- /dev/null +++ b/1332/CH11/EX11.5/11_5.pdf diff --git a/1332/CH11/EX11.5/11_5.sce b/1332/CH11/EX11.5/11_5.sce new file mode 100755 index 000000000..8c4c7be78 --- /dev/null +++ b/1332/CH11/EX11.5/11_5.sce @@ -0,0 +1,41 @@ +//Example 11.5
+//Inverse Power Method
+//Page no. 347
+clc;close;clear;
+
+A=[7,6,-3;-12,-20,24;-6,-12,16];
+e=10^-6;
+X=[1;1;1];
+B=0;
+Y=[0;0;0]
+a=0;l=0;
+for i=1:2
+ printf('When a=%i\n',a);
+ C=A-a*eye();
+ disp(C,"C=")
+ C_1=inv(C);
+ disp(C_1,"Inverse of C=");
+ printf('\n\nItr lambda X')
+ printf('\n------------------------------------------------------------------\n')
+ for j=1:10
+ printf('\n%i %f %f %f %f',j-1,l,X(1),X(2),X(3));
+ Y=C_1*X;
+ B=max(Y);
+ e1=abs(l-B);
+ X=Y/B;
+ m=0;
+ for k=1:3
+ m=m+(Y(k)-X(k))^2;
+ end
+ e2=sqrt(m);
+ er=max(e1,e2);
+ if(er<e)
+ break
+ end
+ l=B;
+
+ end
+ a=-3;
+ printf('\n\n\n\n')
+end
+printf('\n\n\nNote : Computation of Y is wrong given in the book')
\ No newline at end of file diff --git a/1332/CH11/EX11.6/11_6.pdf b/1332/CH11/EX11.6/11_6.pdf Binary files differnew file mode 100755 index 000000000..614f45376 --- /dev/null +++ b/1332/CH11/EX11.6/11_6.pdf diff --git a/1332/CH11/EX11.6/11_6.sce b/1332/CH11/EX11.6/11_6.sce new file mode 100755 index 000000000..1ead55877 --- /dev/null +++ b/1332/CH11/EX11.6/11_6.sce @@ -0,0 +1,26 @@ +//Example 11.6
+//Rayleigh Quotient
+//Page no. 348
+clc;close;clear;
+
+A=[10,7,8,7;7,5,6,5;8,6,10,9;7,5,9,10];
+q0=[1;1;1;1];
+for i=0:4
+ X=(A^i)*q0;
+ l=(X'*A*X)/(X'*X)
+ printf('\nLambda(%i) = %f\n',i+1,l)
+end
+printf('\n\nDominant Eigenvalue = %f\n\n\n',l)
+
+e=0.001;
+for i=1:5
+ q1=A*q0;
+ a=max(q1)
+ for j=1:4
+ q2(j)=q1(j)/a;
+ end
+
+ q1=q2;
+ q0=q1;
+end
+disp(q2,'Corresponding Eigenvector = ')
\ No newline at end of file diff --git a/1332/CH11/EX11.7/11_7.pdf b/1332/CH11/EX11.7/11_7.pdf Binary files differnew file mode 100755 index 000000000..537aae140 --- /dev/null +++ b/1332/CH11/EX11.7/11_7.pdf diff --git a/1332/CH11/EX11.7/11_7.sce b/1332/CH11/EX11.7/11_7.sce new file mode 100755 index 000000000..4aba85754 --- /dev/null +++ b/1332/CH11/EX11.7/11_7.sce @@ -0,0 +1,49 @@ +//Example 11.7
+//Jacobi's Method
+//Page no. 355
+clc;close;clear;
+
+A=[1,1,1/2;1,1,1/4;1/2,1/4,2];
+C=A;
+V=[sqrt(2),0,1/2;sqrt(2),0,1/4;3/(4*sqrt(2)),-1/(4*sqrt(2)),2]
+S=eye(3,3)
+disp(A,"A =")
+VI=0;
+for i=1:3
+ for j=1:3
+ if(i~=j)
+ VI=VI+A(i,j)^2 //initial off diag norm
+ end
+ end
+end
+VI=sqrt(VI);
+VF=VI*10^-7; //final threshold
+V1=VI/3;
+o=poly(0,"o");
+for i=1:3
+for q=2:3
+ for p=q-1:-1:1
+ if(A(p,q)>V1)
+ a=-A(p,q);
+ b=(A(p,p)-A(q,q))/2
+ if(b~=0)
+ w=b*abs(1/b)*(a/sqrt(a^2+b^2));
+ else
+ w=(a/sqrt(a^2+b^2));
+ end
+ sin0=w/sqrt(2*(1+sqrt(1-w^2)));
+ cos0=sqrt(1-sin0^2)
+ end
+ B(p,p)=A(p,p)*cos0^2+A(q,q)*sin0^2-2*A(p,q)*sin0*cos0
+ B(q,q)=A(p,p)*sin0^2+A(q,q)*cos0^2+2*A(p,q)*sin0*cos0
+ B(p,q)=(A(p,p)-A(q,q))*sin0*cos0+A(p,q)*(cos0^2-sin0^2)
+ S(i,i)=S(i,i)
+ S(i,p)=S(i,p)*cos0-S(i,q)*sin0
+ S(i,q)=S(i,p)*sin0+S(i,q)*cos0
+
+ end
+end
+end
+disp(B,"B =")
+disp(S,"S =")
+printf('\n\n\nComputation error in the solution provided by book')
\ No newline at end of file diff --git a/1332/CH11/EX11.8/11_8.pdf b/1332/CH11/EX11.8/11_8.pdf Binary files differnew file mode 100755 index 000000000..03ccb3fcd --- /dev/null +++ b/1332/CH11/EX11.8/11_8.pdf diff --git a/1332/CH11/EX11.8/11_8.sce b/1332/CH11/EX11.8/11_8.sce new file mode 100755 index 000000000..d366036b9 --- /dev/null +++ b/1332/CH11/EX11.8/11_8.sce @@ -0,0 +1,16 @@ +//Example 11.8
+//Recursive Formula
+//Page no. 357
+clc;close;clear;
+
+A=[2,-1,0,0;-1,2,-1,0;0,-1,2,-1;0,0,-1,2];
+l=poly(0,"l");
+p0=1;
+p1=A(1,1)-l;
+for i=2:4
+ p2=(A(i,i)-l)*p1-A(i,i-1)^2*p0;
+ p0=p1;
+ p1=p2;
+ printf('\n\np%i(l) = ',i);
+ disp(p2)
+end
diff --git a/1332/CH11/EX11.9/11_9.pdf b/1332/CH11/EX11.9/11_9.pdf Binary files differnew file mode 100755 index 000000000..6cd99ab28 --- /dev/null +++ b/1332/CH11/EX11.9/11_9.pdf diff --git a/1332/CH11/EX11.9/11_9.sce b/1332/CH11/EX11.9/11_9.sce new file mode 100755 index 000000000..5c95364bb --- /dev/null +++ b/1332/CH11/EX11.9/11_9.sce @@ -0,0 +1,88 @@ +//Example 11.9
+//QR Method
+//Page no. 360
+clc;close;clear;
+
+A=[2,-1,0;-1,2,-1;0,-1,2];
+deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')
+deff('y=s2(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')
+disp(A,'A=')
+l0=0;f=1;m=0;s=0;w=0;
+for n=1:5
+ for j=1:2
+ for k=1:2
+ V(j,k)=A(j,k)
+ end
+ end
+ disp(V,'V=')
+ p=poly(V,'x');
+ disp('=0',p);
+ a=roots(p);
+ for j=1:2
+ printf('\na(%i) = %f',j,a(j))
+ end
+ if(abs(a(1)-V(1,1))<=abs(a(2)-V(1,1)))
+ a=a(1)
+ else
+ a=a(2)
+ end
+ printf('\na = %f\n',a)
+ s=s+a;
+ A=A-a*eye()
+ R=A;Q=eye(3,3);
+
+ for j=1:2
+ for i=j+1:3
+ for k=1:3 //C matrix evaluation
+ for l=1:3
+ if(k==l)
+ if(k==i | k==j)
+ C(k,l)=c(i,j)
+ else
+ C(k,l)=1
+ end
+ end
+ if(k>l)
+ if(k==i & l==j)
+ C(k,l)=-1*s2(i,j)
+ else
+ C(k,l)=0
+ end
+ end
+ if(k<l)
+ if(k==j & l==i)
+ C(k,l)=s2(i,j)
+ else
+ C(k,l)=0
+ end
+ end
+ end
+ end
+
+ R=C*R;
+ Q=Q*C';
+
+ end
+ end
+disp(Q,'Q=',R,'R=')
+disp(Q*R,'Q*R=')
+A=R*Q;
+disp(A,'A=')
+end
+l1=l0+s;
+for i=2:3
+ for j=2:3
+ V(i-1,j-1)=A(i,j)
+ end
+end
+disp(V,'V=')
+ p=poly(V,'x');
+ disp('=0',p);
+ a=roots(p);
+ for j=1:2
+ printf('\na(%i) = %f',j,a(j))
+ end
+ l2=l1+a(1)
+ l3=l1+a(2)
+ disp(l3,'l3=',l2,'l2=',l1,'l1=')
+printf('\n\n\nNote : Values of V varies in each step resulting in different results due to error in book calculation')
\ No newline at end of file diff --git a/1332/CH12/EX12.1/12_1.pdf b/1332/CH12/EX12.1/12_1.pdf Binary files differnew file mode 100755 index 000000000..fb31c296f --- /dev/null +++ b/1332/CH12/EX12.1/12_1.pdf diff --git a/1332/CH12/EX12.1/12_1.sce b/1332/CH12/EX12.1/12_1.sce new file mode 100755 index 000000000..d4fd65b8d --- /dev/null +++ b/1332/CH12/EX12.1/12_1.sce @@ -0,0 +1,30 @@ +//Example 12.1
+//Linear Interpolation Technique
+//Page no. 372
+clc;close;clear;
+
+printf('x: ')
+f=[1,4,9,16,25];
+for i=1:5
+ printf('%i\t',i)
+end
+printf('\nf(x): ')
+for i=1:5
+ printf('%i\t',f(i))
+end
+x=2.5;
+x1=2;x2=3;printf('\n\nfor (2,4) and (3,9)')
+f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)
+printf('\nf(2.5) = %.1f',f(2.5))
+
+x=2.5;
+x1=2;x2=4;printf('\n\nfor (2,4) and (4,16)')
+f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)
+printf('\nf(2.5) = %.1f',f(2.5))
+
+x=2.5;
+x1=1;x2=3;printf('\n\nfor (1,1) and (3,9)')
+f(2.5)=f(x1)+(f(x2)-f(x1))*(x-x1)/(x2-x1)
+printf('\nf(2.5) = %.1f',f(2.5))
+
+printf('\n\nExact value = %.2f',2.5^2)
\ No newline at end of file diff --git a/1332/CH12/EX12.2/12_2.pdf b/1332/CH12/EX12.2/12_2.pdf Binary files differnew file mode 100755 index 000000000..f4b941b25 --- /dev/null +++ b/1332/CH12/EX12.2/12_2.pdf diff --git a/1332/CH12/EX12.2/12_2.sce b/1332/CH12/EX12.2/12_2.sce new file mode 100755 index 000000000..0f30446c9 --- /dev/null +++ b/1332/CH12/EX12.2/12_2.sce @@ -0,0 +1,20 @@ +//Example 12.2
+//Lagarangian Method
+//Page no. 373
+clc;close;clear;
+
+xk=[-1,0,2,5];
+yk=[10,7,7,22];
+
+P=0;
+x=poly(0,"x");
+for k=0:3
+ p=yk(k+1)
+ for j=0:3
+ if(j~=k)
+ p=p*((x-xk(j+1))/(xk(k+1)-xk(j+1)))
+ end
+ end
+ P=P+p;
+end
+disp(P,'P=')
\ No newline at end of file diff --git a/1332/CH12/EX12.3/12_3.pdf b/1332/CH12/EX12.3/12_3.pdf Binary files differnew file mode 100755 index 000000000..0faac3a60 --- /dev/null +++ b/1332/CH12/EX12.3/12_3.pdf diff --git a/1332/CH12/EX12.3/12_3.sce b/1332/CH12/EX12.3/12_3.sce new file mode 100755 index 000000000..f92656654 --- /dev/null +++ b/1332/CH12/EX12.3/12_3.sce @@ -0,0 +1,37 @@ +//Example 12.3
+//Aitken-Neville's Method
+//Page no. 378
+clc;close;clear;
+
+function [x,y,z]=tran(a,b) // function for exchanging values
+ z=a;y=b;x=z;
+endfunction
+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
+xi=[0.8,1,1.2,1.4,1.6];
+yi=[2.2255,2.7183,3.3201,4.0552,4.9530];
+x=1.23
+[xi(5),xi(1),a]=tran(xi(1),xi(5))
+[xi(4),xi(1),a]=tran(xi(1),xi(4))
+[xi(3),xi(2),a]=tran(xi(2),xi(3))
+[xi(2),xi(1),a]=tran(xi(1),xi(2))
+[yi(5),yi(1),a]=tran(yi(1),yi(5))
+[yi(4),yi(1),a]=tran(yi(1),yi(4))
+[yi(3),yi(2),a]=tran(yi(2),yi(3))
+[yi(2),yi(1),a]=tran(yi(1),yi(2))
+for i=1:5
+ x_xi(i)=x-xi(i);
+end
+printf('xi x-xi yi\n')
+printf('------------------------\n')
+for i=1:5
+ printf('%.1f %.2f\t%f\n',xi(i),x_xi(i),yi(i))
+end
+printf('\n\nPolynomials\n')
+printf('-----------\n')
+for i=1:4
+ for j=1:5-i
+ printf('%f\n',P(xi,yi,x_xi,j,i))
+ yi(j)=P(xi,yi,x_xi,j,i)
+ end
+ printf('\n\n\n')
+end
\ No newline at end of file diff --git a/1332/CH12/EX12.4/12_4.pdf b/1332/CH12/EX12.4/12_4.pdf Binary files differnew file mode 100755 index 000000000..d2532215e --- /dev/null +++ b/1332/CH12/EX12.4/12_4.pdf diff --git a/1332/CH12/EX12.4/12_4.sce b/1332/CH12/EX12.4/12_4.sce new file mode 100755 index 000000000..817582c27 --- /dev/null +++ b/1332/CH12/EX12.4/12_4.sce @@ -0,0 +1,24 @@ +//Example 12.4
+//Newton's Divided Difference Interpolation
+//Page no. 381
+clc;close;clear;
+
+x=[0,1,2,3,4,5]
+y=[1,2,5,10,17,26];
+y1=y;
+deff('yi=P(a,b,d,e)','yi=(b(d+1)-b(d))/(a(d+e)-a(d))') //function for finding polynomials
+for i=1:3
+ for j=1:6-i
+ z(j,i)=P(x,y,j,i)
+ y(j)=z(j,i)
+ end
+end
+z(6,1)=0;
+printf('x y f(x0,x1) f(x0,x1,x3) f(x0,x1,x2,x3)\n')
+printf('---------------------------------------------------------\n')
+ for j=1:6
+ 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))
+ end
+x1=2.6;
+f=y1(4)+(x1-x(4))*(z(4,1))+(x1-x(4))*(x1-x(5))*z(4,2)
+printf('\n\nf(2.6)=%.2f',f)
\ No newline at end of file diff --git a/1332/CH12/EX12.5/12_5.pdf b/1332/CH12/EX12.5/12_5.pdf Binary files differnew file mode 100755 index 000000000..1cf78509a --- /dev/null +++ b/1332/CH12/EX12.5/12_5.pdf diff --git a/1332/CH12/EX12.5/12_5.sce b/1332/CH12/EX12.5/12_5.sce new file mode 100755 index 000000000..8d07e690a --- /dev/null +++ b/1332/CH12/EX12.5/12_5.sce @@ -0,0 +1,111 @@ +//Example 12.5
+//Interpolation Methods
+//Page no. 403
+clc;close;clear;
+
+x=[0,1,2,3,4];
+y=[0,1,8,27,64];
+
+//Inverse lagrange Method
+P=0;
+y1=20;
+for k=0:4
+ p=x(k+1)
+ for j=0:4
+ if(j~=k)
+ p=p*((y1-y(j+1))/(y(k+1)-y(j+1)))
+ end
+ end
+ P=P+p;
+end
+disp(P,'Inverse Lagrange interpolation x=')
+
+
+//Newton's divide difference interpolation
+x1=x;
+deff('xi=P(a,b,d,y)','xi=(b(d+1)-b(d))/(a(d+y)-a(d))') //function for finding polynomials
+for i=1:2
+ for j=1:5-i
+ z(j,i)=P(y,x,j,i)
+ x(j)=z(j,i)
+ end
+end
+z(5,1)=0;
+printf('\n\n y\tx f(y0,y1) f(y0,y1,y3)\n')
+printf('------------------------------------------\n')
+ for j=1:5
+ printf(' %i\t%i \t%i\t\t%i\t\n',y(1,j),x1(1,j),z(j,1),z(j,2))
+ end
+y1=20;
+f=x1(4)+(y1-y(4))*(z(4,1))+(y1-y(4))*(y1-y(5))*z(4,2)
+printf('\n\nNewton Divide Difference x(20)=%.2f',f)
+
+x=x1;
+//Iterated Linear Interpolation
+function [x,y,z]=tran(a,b) // function for exchanging values
+ z=a;y=b;x=z;
+endfunction
+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
+y1=20
+
+[y(4),y(1),a]=tran(y(1),y(4))
+[y(3),y(2),a]=tran(y(2),y(3))
+[x(4),x(1),a]=tran(x(1),x(4))
+[x(3),x(2),a]=tran(x(2),x(3))
+for i=1:5
+ y1_y(i)=y1-y(i);
+end
+printf('y\ty1-y\tx\n')
+printf('------------------\n')
+for i=1:5
+ printf('%.1f\t%i\t%i\n',y(i),y1_y(i),x(i))
+end
+printf('\n\nPolynomials\n')
+printf('-----------\n')
+for i=1:4
+ for j=1:5-i
+ printf('%f\n',P(y,x,y1_y,j,i))
+ x(j)=P(y,x,y1_y,j,i)
+ end
+ printf('\n\n')
+end
+printf('Iterated Linear Interpolation x(20) = %f',x(j))
+
+x=[0,1,2,3,4];
+y=[0,1,8,27,64];
+y1=y;
+//Suggested Interpolation
+
+for i=1:4
+ for j=1:5-i
+ z(j,i)=y(j+1)-y(j);
+ y(j)=z(j,i)
+ end
+end
+printf('\n\n\n x\ty\tdy\td2y\td3y\td4y\n')
+printf('--------------------------------------------\n')
+for i=1:5
+ 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))
+end
+s=poly(0,'s')
+p=y1(4);k=3;
+for i=1:3
+ r=1;
+ for j=1:i
+ r=r*(s+(j-1))
+ end
+ r=r*z(k,i)/factorial(j);
+ k=k-1;
+ p=p+r;
+ printf('\n\nStage %i :',i)
+ disp(p)
+end
+s0=-7/19;
+disp(s0,'s0=');
+s1=(-7-s0*(s0+1)*6)/19
+disp(s1,'s1=')
+disp(3+s1,'x1=')
+s2=(-7-s1*(s1+1)*6-s1*(s1+1)*(s1+2))/19
+disp(s2,'s2=')
+x2=3+s2;
+disp(x2,'Suggested Interpolation x(20)=');
\ No newline at end of file diff --git a/1332/CH12/EX12.6/12_6.pdf b/1332/CH12/EX12.6/12_6.pdf Binary files differnew file mode 100755 index 000000000..743c584fb --- /dev/null +++ b/1332/CH12/EX12.6/12_6.pdf diff --git a/1332/CH12/EX12.6/12_6.sce b/1332/CH12/EX12.6/12_6.sce new file mode 100755 index 000000000..644917648 --- /dev/null +++ b/1332/CH12/EX12.6/12_6.sce @@ -0,0 +1,36 @@ +//Example 12.6
+//Chebyshev Interpolating Polynomial
+//Page no. 407
+clc;close;clear;
+
+deff('y=f(x)','y=1/(1+exp(-x))');
+a=-2;b=2;n=3;
+D=%pi/(2*n+2)
+for k=0:n
+ t(k+1)=-cos(D*(2*k+1))
+ x(k+1)=((a+b)/2)+(b-a)*t(k+1)/2
+ y(k+1)=f(x(k+1))
+ C(k+1)=0
+end
+for j=0:n
+ for k=0:n
+ L=(2*k+1)*D
+ C(j+1)=C(j+1)+y(k+1)*cos(j*L)
+ end
+end
+C(1)=C(1)/(n+1);
+for j=1:n
+ C(j+1)=2*C(j+1)/(n+1)
+end
+
+x=poly(0,"x")
+T(1)=1;T(2)=x;
+for j=1:n-1
+ T(j+2)=2*x*T(j+1)-T(j)
+end
+P=C(1)*T(1)
+for j=1:n
+ P=P+C(j+1)*T(j+1)
+end
+disp(P,'P3(x)=')
+printf('\n\n\nNote : Book has Calculation errors in calculation of coefficients')
\ No newline at end of file diff --git a/1332/CH12/EX12.7/12_7.pdf b/1332/CH12/EX12.7/12_7.pdf Binary files differnew file mode 100755 index 000000000..4f5e2dc04 --- /dev/null +++ b/1332/CH12/EX12.7/12_7.pdf diff --git a/1332/CH12/EX12.7/12_7.sce b/1332/CH12/EX12.7/12_7.sce new file mode 100755 index 000000000..587443fa3 --- /dev/null +++ b/1332/CH12/EX12.7/12_7.sce @@ -0,0 +1,36 @@ +//Example 12.7
+//Double Interpolation
+//Page no. 409
+clc;close;clear;
+
+x=[0,1,2,3,4];
+y=[0,1,2,3,4];
+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];
+printf('y / x')
+for i=1:5
+ printf('\t%i',x(i))
+end
+for i=1:5
+ printf('\n %i',y(i))
+ for j=1:5
+ printf('\t%i',z(j,i))
+ end
+end
+printf('\n\n\n')
+for i=1:5
+ x=2.5;
+ x1=2;x2=3;
+ z1(1,i)=z(i,x1+1)+(z(i,x2+1)-z(i,x1+1))*(x-x1)/(x2-x1)
+end
+printf('Values of z at x=2.5:\n\n y')
+for i=1:5
+ printf('\t%i',y(i))
+end
+printf('\n z')
+for i=1:5
+ printf('\t%g',z1(i))
+end
+y=1.5;
+y1=1;y2=2;
+z2=z1(y1+1)+(z1(y2+1)-z1(y1+1))*(y-y1)/(y2-y1)
+printf('\n\nValue of z at x=2.5 and y=1.5 : %g',z2)
\ No newline at end of file diff --git a/1332/CH12/EX12.8/12_8.pdf b/1332/CH12/EX12.8/12_8.pdf Binary files differnew file mode 100755 index 000000000..7d644984a --- /dev/null +++ b/1332/CH12/EX12.8/12_8.pdf diff --git a/1332/CH12/EX12.8/12_8.sce b/1332/CH12/EX12.8/12_8.sce new file mode 100755 index 000000000..06f597812 --- /dev/null +++ b/1332/CH12/EX12.8/12_8.sce @@ -0,0 +1,32 @@ +//Example 12.8
+//Spline Interpolation
+//Page no. 414
+clc;close;clear;
+
+xi=[0.10,0.11,0.12,0.13,0.14,0.15,0.16,0.17];
+yi=[0.1110,0.1234,0.1361,0.1491,0.1623,0.1759,0.1897,0.2038];
+h=0.01;
+
+pi(1)=0;qi(1)=0;pi(8)=0;qi(8)=0;
+for i=2:7
+ pi(i)=-1/(4+pi(i-1))
+ qi(i)=((6/h^2)*(yi(i+1)-2*yi(i)+yi(i-1))-qi(i-1))/(4+pi(i-1))
+end
+si2(8)=0;
+si2(1)=0;si1(8)=0;
+si1(1)=0;
+for i=7:-1:2
+ si2(i)=pi(i)*si2(i+1)+qi(i)
+end
+for i=2:8
+ si1(i)=si1(i-1)+h*(si2(i)+si2(i-1))/2
+end
+printf('\n i\t xi\t fi\t pi\t\t qi\t\t si2\t\t si1')
+printf('\n---------------------------------------------------------------------------------')
+for i=1:8
+ 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))
+end
+x=0.1325;
+i=4;
+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
+printf('\n\nSpline Interpolated Value of s(0.1325) is : %f',s)
\ No newline at end of file diff --git a/1332/CH13/EX13.1/13_1.pdf b/1332/CH13/EX13.1/13_1.pdf Binary files differnew file mode 100755 index 000000000..c09c4f2d0 --- /dev/null +++ b/1332/CH13/EX13.1/13_1.pdf diff --git a/1332/CH13/EX13.1/13_1.sce b/1332/CH13/EX13.1/13_1.sce new file mode 100755 index 000000000..e7e8a0f1f --- /dev/null +++ b/1332/CH13/EX13.1/13_1.sce @@ -0,0 +1,12 @@ +//Example 13.1
+//Differentiation
+//Page no. 420
+clc;close;clear;
+
+deff('y=f(x)','y=x^2+5')
+deff('y=f1(x,h)','y=(f(x+h)-f(x))/h')
+h=0.01;x=2.4
+d=f1(x,h)
+d1=(f1(x+h,h)-f1(x))/h
+printf('dy\n -- = %g\n dx',d)
+printf('\n\n\n d2y\n --- = %g\n dx2',d1)
\ No newline at end of file diff --git a/1332/CH13/EX13.2/13_2.pdf b/1332/CH13/EX13.2/13_2.pdf Binary files differnew file mode 100755 index 000000000..536787c2b --- /dev/null +++ b/1332/CH13/EX13.2/13_2.pdf diff --git a/1332/CH13/EX13.2/13_2.sce b/1332/CH13/EX13.2/13_2.sce new file mode 100755 index 000000000..a7b49e452 --- /dev/null +++ b/1332/CH13/EX13.2/13_2.sce @@ -0,0 +1,47 @@ +//Example 13.2
+//Calculation of x-coordinate of Minimum Point
+//Page no. 422
+clc;close;clear;
+
+for i=1:7
+ for j=1:6
+ z(i,j)=0
+ end
+end
+h=0.2
+printf(' x y d d2 d3 d4\n')
+printf('--------------------------------------------------------------')
+for i=1:7
+ z(i,1)=i/5;
+end
+z(1,2)=2.10022
+z(2,2)=1.98730
+z(3,2)=1.90940
+z(4,2)=1.86672
+z(5,2)=1.85937
+z(6,2)=1.88755
+z(7,2)=1.95147
+for i=3:6
+ for j=1:9-i
+ z(j,i)=z(j+1,i-1)-z(j,i-1)
+ end
+end
+disp(z)
+
+s=poly(0,'s')
+p=z(5,2);k=4;
+for i=3:5
+ r=1;
+ for j=1:i-2
+ r=r*(s+(j-1))
+ end
+ r=r*z(k,i)/factorial(j);
+ k=k-1;
+ p=p+r;
+
+end
+disp(p)
+s=(-z(4,3)+z(3,4)/2)/z(3,4)
+disp(s,'s=')
+x=z(5,1)+s*h
+disp(x,'x=')
\ No newline at end of file diff --git a/1332/CH13/EX13.3/13_3.pdf b/1332/CH13/EX13.3/13_3.pdf Binary files differnew file mode 100755 index 000000000..4dc22e60f --- /dev/null +++ b/1332/CH13/EX13.3/13_3.pdf diff --git a/1332/CH13/EX13.3/13_3.sce b/1332/CH13/EX13.3/13_3.sce new file mode 100755 index 000000000..e25ea55b4 --- /dev/null +++ b/1332/CH13/EX13.3/13_3.sce @@ -0,0 +1,44 @@ +//Example 13.3
+//Newton's Forward Difference Formula
+//Page no. 423
+clc;close;clear;
+printf(' x\t\t y\t\t d\t\t d2\t\t d3\t\t d4\n')
+printf('------------------------------------------------------------------------------------------')
+h=0.05;
+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]
+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')
+deff('y=f2(x,s)','y=(z(x,4)+z(x,5)*(s-1))/h^2')
+deff('y=f3(x,s)','y=z(x,5)/h^3')
+for i=3:6
+ for j=1:9-i
+ z(j,i)=z(j+1,i-1)-z(j,i-1)
+ end
+end
+printf('\n')
+for i=1:7
+ for j=1:6
+ if z(i,j)==0 then
+ printf(' \t')
+ else
+ printf('%.7f\t',z(i,j))
+ end
+ end
+ printf('\n')
+end
+s=poly(0,'s')
+p=z(5,2);k=4;
+for i=3:5
+ r=1;
+ for j=1:i-2
+ r=r*(s+(j-1))
+ end
+ r=r*z(k,i)/factorial(j);
+ k=k-1;
+ p=p+r;
+
+end
+disp(p,'y(s) = ')
+printf('\n\ny1(1) = %g',f1(1,0))
+printf('\n\ny2(1) = %g',f2(1,0))
+printf('\n\ny3(1) = %g',f3(1,0))
+printf('\n\ny1(1.025) = %g',f1(1,0.5))
\ No newline at end of file diff --git a/1332/CH13/EX13.4/13_4.pdf b/1332/CH13/EX13.4/13_4.pdf Binary files differnew file mode 100755 index 000000000..18afad65e --- /dev/null +++ b/1332/CH13/EX13.4/13_4.pdf diff --git a/1332/CH13/EX13.4/13_4.sce b/1332/CH13/EX13.4/13_4.sce new file mode 100755 index 000000000..bd42bdd24 --- /dev/null +++ b/1332/CH13/EX13.4/13_4.sce @@ -0,0 +1,27 @@ +//Example 13.4
+//Newton's Backward Difference Formula
+//Page no. 425
+clc;close;clear;
+printf(' x\t\t y\t\t d\t\t d2\t\t d3\t\t d4\n')
+printf('------------------------------------------------------------------------------------------')
+h=0.02;
+z=[0.96,1.8025;0.98,1.7939;1.00,1.7851;1.02,1.7763;1.04,1.7673];
+deff('y=f1(x,s)','y=(z(x,3)+(s+1/2)*z(x,4))/h')
+for i=3:6
+ for j=1:7-i
+ z(j,i)=z(j+1,i-1)-z(j,i-1)
+ end
+end
+printf('\n')
+for i=1:5
+ for j=1:6
+ if z(i,j)==0 then
+ printf(' \t')
+ else
+ printf('%.7f\t',z(i,j))
+ end
+ end
+ printf('\n')
+end
+printf('\n\ny1(1) = %g',f1(2,0))
+printf('\n\ny1(1.03) = %g',f1(4,0.5))
\ No newline at end of file diff --git a/1332/CH13/EX13.5/13_5.pdf b/1332/CH13/EX13.5/13_5.pdf Binary files differnew file mode 100755 index 000000000..626c1c82d --- /dev/null +++ b/1332/CH13/EX13.5/13_5.pdf diff --git a/1332/CH13/EX13.5/13_5.sce b/1332/CH13/EX13.5/13_5.sce new file mode 100755 index 000000000..1b588f1a6 --- /dev/null +++ b/1332/CH13/EX13.5/13_5.sce @@ -0,0 +1,30 @@ +//Example 13.5
+//Stirlings Central Difference Derivatives
+//Page no. 426
+clc;close;clear;
+printf(' x\t\t y\t\t d\t\t d2\t\t d3\n')
+printf('---------------------------------------------------------------------------')
+h=0.01;s=0.5;
+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')
+deff('y=f2(x,s)','y=(z(x-1,4))/h^2')
+deff('y=f3(x,s)','y=(z(x-1,5)+z(x-2,5))/(2*h^3)')
+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];
+for i=3:5
+ for j=1:19-i
+ z(j,i)=z(j+1,i-1)-z(j,i-1)
+ end
+end
+printf('\n')
+for i=1:17
+ for j=1:5
+ if z(i,j)==0 then
+ printf(' \t')
+ else
+ printf('%.7f\t',z(i,j))
+ end
+ end
+ printf('\n')
+end
+printf('\n\ny1(1.125) = %g (exact value = 0.4771404)',f1(13,0.5))
+printf('\n\ny2(1.125) = %g (exact value = -0.20951)',f2(13,0.5))
+printf('\n\ny3(1.125) = %g (exact value = 0.27935)',f3(13,0.5))
\ No newline at end of file diff --git a/1332/CH13/EX13.6/13_6.pdf b/1332/CH13/EX13.6/13_6.pdf Binary files differnew file mode 100755 index 000000000..07b130004 --- /dev/null +++ b/1332/CH13/EX13.6/13_6.pdf diff --git a/1332/CH13/EX13.6/13_6.sce b/1332/CH13/EX13.6/13_6.sce new file mode 100755 index 000000000..1bcad51ee --- /dev/null +++ b/1332/CH13/EX13.6/13_6.sce @@ -0,0 +1,11 @@ +//Example 13.6
+//Extrapolation
+//Page no. 430
+clc;close;clear;
+x=[-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8];
+y=[0.2019,0.30119,0.44933,0.67032,1,1.49182,2.22554,3.32012,4.95303]
+for i=1:4
+ printf('\nh = %g\n',x(10-i))
+ y1=(y(10-i)-y(i))/(2*x(10-i))
+ printf('f1(0) = %g\n\n',y1)
+end
\ No newline at end of file diff --git a/1332/CH13/EX13.7/13_7.pdf b/1332/CH13/EX13.7/13_7.pdf Binary files differnew file mode 100755 index 000000000..39686800f --- /dev/null +++ b/1332/CH13/EX13.7/13_7.pdf diff --git a/1332/CH13/EX13.7/13_7.sce b/1332/CH13/EX13.7/13_7.sce new file mode 100755 index 000000000..88c1182b6 --- /dev/null +++ b/1332/CH13/EX13.7/13_7.sce @@ -0,0 +1,21 @@ +//Example 13.7
+//Richardson Extrapolation
+//Page no. 431
+clc;close;clear;
+
+deff('y=f(x)','y=exp(2*x)')
+e=10^-4;h=0.8;
+D1=0;
+for i=1:4
+ printf('\n')
+ for j=1:i
+ if j==1 then
+ D(i,j)=(f(h)-f(-h))/(2*h)
+ else
+ D(i,j)=D(i,j-1)+(D(i,j-1)-D(i-1,j-1))/(2^(2*(j-1))-1)
+ end
+ printf('%g\t\t',D(i,j))
+ end
+ h=h/2
+end
+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))
diff --git a/1332/CH13/EX13.8/13_8.pdf b/1332/CH13/EX13.8/13_8.pdf Binary files differnew file mode 100755 index 000000000..aff2c3b88 --- /dev/null +++ b/1332/CH13/EX13.8/13_8.pdf diff --git a/1332/CH13/EX13.8/13_8.sce b/1332/CH13/EX13.8/13_8.sce new file mode 100755 index 000000000..502a1f6d7 --- /dev/null +++ b/1332/CH13/EX13.8/13_8.sce @@ -0,0 +1,31 @@ +//Example 13.8
+//Application
+//Page no. 433
+clc;close;clear;
+
+deff('y=f(x)','y=2/x^2')
+a=1;b=2;a1=1;b1=0;
+N=4;
+h=(b-a)/(N+1);
+for j=1:N
+ s(j)=f(a+j*h)
+end
+for i=1:N
+ for j=1:N
+ if abs(i-j)==1 then
+ A(i,j)=-1
+ end
+ if i==j then
+ A(i,j)=2+s(i)*h^2
+ end
+ end
+ if i==1 then
+ k(i,1)=s(i)+a1/h^2
+ elseif i==N
+ k(i,1)=s(i)+b1/h^2
+ else
+ k(i,1)=s(i)
+ end
+end
+disp(A,'A = ')
+disp(k,'k = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.10/14_10.pdf b/1332/CH14/EX14.10/14_10.pdf Binary files differnew file mode 100755 index 000000000..49dd3b86e --- /dev/null +++ b/1332/CH14/EX14.10/14_10.pdf diff --git a/1332/CH14/EX14.10/14_10.sce b/1332/CH14/EX14.10/14_10.sce new file mode 100755 index 000000000..e8c41ccb8 --- /dev/null +++ b/1332/CH14/EX14.10/14_10.sce @@ -0,0 +1,10 @@ +//Example 14.10
+//Spline Integration Method
+//Page no. 478
+clc;close;clear;
+
+deff('y=f(x)','y=sind(%pi*x)')
+deff('y=f1(x,h)','y=(f(x+h)-f(x))/h')
+h=0.01;
+n=2;h=0.5;a=0;b=1;
+disp(integrate('f(x)','x',0,1),'I = ')
diff --git a/1332/CH14/EX14.11/14_1.pdf b/1332/CH14/EX14.11/14_1.pdf Binary files differnew file mode 100755 index 000000000..1d01e37f0 --- /dev/null +++ b/1332/CH14/EX14.11/14_1.pdf diff --git a/1332/CH14/EX14.11/14_1.sce b/1332/CH14/EX14.11/14_1.sce new file mode 100755 index 000000000..597841b4d --- /dev/null +++ b/1332/CH14/EX14.11/14_1.sce @@ -0,0 +1,22 @@ +//Example 14.1
+//Trapezoidal Rule
+//Page no 440
+clc;clear;close;
+x1=1.46
+for i=1:6
+ x(1,i)=x1+i/100
+end
+y=[3.86,3.90,3.96,4.02,4.06,4.12]
+
+//trapezoidal rule
+S=0;
+h=(x(6)-x1)/6
+for i=1:6
+ if(i==1 | i==6)
+ S=S+y(i)
+ else
+ S=S+2*y(i)
+ end
+end
+S=S*h/2
+printf('\n I = %g',S)
\ No newline at end of file diff --git a/1332/CH14/EX14.14/14_14.pdf b/1332/CH14/EX14.14/14_14.pdf Binary files differnew file mode 100755 index 000000000..be2ef3b8b --- /dev/null +++ b/1332/CH14/EX14.14/14_14.pdf diff --git a/1332/CH14/EX14.14/14_14.sce b/1332/CH14/EX14.14/14_14.sce new file mode 100755 index 000000000..3096cfddd --- /dev/null +++ b/1332/CH14/EX14.14/14_14.sce @@ -0,0 +1,52 @@ +//Example 14.14
+//Trapezoidal and Simpsons Rule
+//Page no. 486
+clc;close;clear;
+
+x(1)=0.5;y(1)=0.5;h=0.25
+for i=2:3
+ x(i)=x(i-1)+h
+ y(i)=y(i-1)+h
+end
+printf(' y/x\t|\t%g\t%g\t%g',x(1),x(2),x(3))
+printf('\n--------|---------------------------')
+for i=1:3
+ printf('\n%g\t|\t',y(i))
+ for j=1:3
+ z(i,j)=x(j)*y(i)
+ printf('%g\t',z(i,j))
+ end
+end
+
+//trapezoidal rule
+s=0;
+for i=1:3
+ for j=1:3
+ if i==1 & j==1 then
+ s=s+z(i,j)
+ elseif i==3 & j==3
+ s=s+z(i,j)
+ else
+ s=s+2*z(i,j)
+ end
+ end
+end
+s=(s*(h^2))/4
+printf('\n\n')
+disp(s,'Trapezoidal Rule Sum = ')
+printf('\n\n')
+//simpsons rule
+s=0;
+for i=1:3
+ for j=1:3
+ if i/2-int(i/2)==0 & j/2-int(j/2)==0 then
+ s=s+16*z(i,j)
+ elseif i/2-int(i/2)~=0 & j/2-int(j/2)~=0
+ s=s+z(i,j)
+ else
+ s=s+4*z(i,j)
+ end
+ end
+end
+s=(s*(h^2))/9
+disp(s,'Simpsons Rule Sum = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.15/14_15.pdf b/1332/CH14/EX14.15/14_15.pdf Binary files differnew file mode 100755 index 000000000..a7948df3e --- /dev/null +++ b/1332/CH14/EX14.15/14_15.pdf diff --git a/1332/CH14/EX14.15/14_15.sce b/1332/CH14/EX14.15/14_15.sce new file mode 100755 index 000000000..7ccf3ba3f --- /dev/null +++ b/1332/CH14/EX14.15/14_15.sce @@ -0,0 +1,58 @@ +//Example 14.15
+//Trapezoidal and Simpsons Rule
+//Page no. 487
+clc;close;clear;
+
+x(1)=0;y(1)=0;h=0.25
+for i=2:5
+ x(i)=x(i-1)+h
+ y(i)=y(i-1)+h
+end
+printf(' y/x\t|\t%g\t%g\t%g\t%g\t%g',x(1),x(2),x(3),x(4),x(5))
+printf('\n--------|-------------------------------------------')
+for i=1:5
+ printf('\n%g\t|\t',y(i))
+ for j=1:5
+ z(i,j)=x(j)*y(i)
+ printf('%g\t',z(i,j))
+ end
+end
+
+//trapezoidal rule
+s=0;
+for i=1:5
+ for j=1:5
+ if i==1 & j==1 then
+ s=s+z(i,j)
+ elseif i==5 & j==5
+ s=s+z(i,j)
+ else
+ s=s+2*z(i,j)
+ end
+ end
+end
+s=(s*(h^2))/4
+printf('\n\n')
+disp(s,'Trapezoidal Rule Sum = ')
+printf('\n\n')
+
+//simpsons rule
+s=0;
+for i=1:5
+ for j=1:5
+ if i/2-int(i/2)==0 & j/2-int(j/2)==0 then
+ if i==j then
+ s=s+16*z(i,j)
+ else
+ s=s+4*z(i,j)
+ end
+
+ elseif i/2-int(i/2)~=0 & j/2-int(j/2)~=0
+ s=s+z(i,j)
+ else
+ s=s+4*z(i,j)
+ end
+ end
+end
+s=(s*(h^2))/9
+disp(s,'Simpsons Rule Sum = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.16/14_16.pdf b/1332/CH14/EX14.16/14_16.pdf Binary files differnew file mode 100755 index 000000000..3278c7619 --- /dev/null +++ b/1332/CH14/EX14.16/14_16.pdf diff --git a/1332/CH14/EX14.16/14_16.sce b/1332/CH14/EX14.16/14_16.sce new file mode 100755 index 000000000..6faac5d7c --- /dev/null +++ b/1332/CH14/EX14.16/14_16.sce @@ -0,0 +1,11 @@ +//Example 14.16
+//Multiple Integration with Variable Limits
+//Page no. 491
+clc;close;clear;
+
+deff('z=f(x)','z=x+1')
+deff('z=f1(y)','z=(y+1)^3*(y+3)^2')
+s=5/9*f(-sqrt(3/5))+8/9*f(0)+5/9*f(sqrt(3/5))
+s=s*5/9*f1(-sqrt(3/5))+8/9*f1(0)+5/9*f1(sqrt(3/5))
+s=s/256;
+disp(s,'I = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.18/14_18.pdf b/1332/CH14/EX14.18/14_18.pdf Binary files differnew file mode 100755 index 000000000..32bc29007 --- /dev/null +++ b/1332/CH14/EX14.18/14_18.pdf diff --git a/1332/CH14/EX14.18/14_18.sce b/1332/CH14/EX14.18/14_18.sce new file mode 100755 index 000000000..d0d509a46 --- /dev/null +++ b/1332/CH14/EX14.18/14_18.sce @@ -0,0 +1,7 @@ +//Example 14.18
+//Integration
+//Page no. 494
+clc;close;clear;
+
+s=integrate('x^2*sin(x^2)','x',0,1)
+disp(s,'I = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.19/14_19.pdf b/1332/CH14/EX14.19/14_19.pdf Binary files differnew file mode 100755 index 000000000..505cb9b0f --- /dev/null +++ b/1332/CH14/EX14.19/14_19.pdf diff --git a/1332/CH14/EX14.19/14_19.sce b/1332/CH14/EX14.19/14_19.sce new file mode 100755 index 000000000..3d32f9d0b --- /dev/null +++ b/1332/CH14/EX14.19/14_19.sce @@ -0,0 +1,7 @@ +//Example 14.19
+//Integration
+//Page no. 494
+clc;close;clear;
+
+s=integrate('sin(t)/t','t',1,999)
+disp(s,'I = ')
\ No newline at end of file diff --git a/1332/CH14/EX14.2/14_2.pdf b/1332/CH14/EX14.2/14_2.pdf Binary files differnew file mode 100755 index 000000000..325ddacfc --- /dev/null +++ b/1332/CH14/EX14.2/14_2.pdf diff --git a/1332/CH14/EX14.2/14_2.sce b/1332/CH14/EX14.2/14_2.sce new file mode 100755 index 000000000..3dbd1c2f1 --- /dev/null +++ b/1332/CH14/EX14.2/14_2.sce @@ -0,0 +1,44 @@ +//Example 14.2
+//Simpsons 1/3rd Rule
+//Page no 442
+clc;clear;close;
+x(1,1)=0
+for i=2:9
+
+ x(1,i)=x(1,1)+(i-1)*10
+end
+y=[30,31.63,33.44,35.47,37.75,40.33,43.29,46.69,50.67]
+
+//trapezoidal rule
+S=0;
+h=(x(9)-x(1))/8
+for j=1:9
+ S=0;
+ for i=1:j
+ if(i==1 | i==j)
+ S=S+y(i)
+ else
+ S=S+2*y(i)
+ end
+ end
+ S=S*h/2
+ printf('\n Velocity at t (%i) = %.2f',x(j),S)
+ y1(j)=S
+end
+
+y1(1)=0;
+//Simpsons 1/3rd Rule
+S=0;
+h=(x(9)-x(1))/8
+for i=1:9
+ if(i==1 | i==9)
+ S=S+y1(i)
+ elseif(((i)/2)-fix((i)/2)==0)
+ S=S+4*y1(i)
+ else
+ S=S+2*y1(i)
+ end
+end
+S=S*h/3;
+S=S/1000
+printf('\n\nSimpsons 1/3rd Rule Sum = %g km',S)
\ No newline at end of file diff --git a/1332/CH14/EX14.3/14_3.pdf b/1332/CH14/EX14.3/14_3.pdf Binary files differnew file mode 100755 index 000000000..d7345ba1c --- /dev/null +++ b/1332/CH14/EX14.3/14_3.pdf diff --git a/1332/CH14/EX14.3/14_3.sce b/1332/CH14/EX14.3/14_3.sce new file mode 100755 index 000000000..c28dca1f4 --- /dev/null +++ b/1332/CH14/EX14.3/14_3.sce @@ -0,0 +1,45 @@ +//Example 14.3
+//Trapezoidal Rule and Simpsons Rule
+//Page no. 442
+clc;close;clear;
+n=2;a=0;b=1;
+h=(b-a)/n
+deff('y=f(x)','y=1/(1+x)')
+for i=0:2
+ x(i+1)=i/2;
+ y(i+1)=f(x(i+1))
+end
+printf('xi\t ')
+for i=1:3
+ printf('%g\t ',x(i))
+end
+printf('\n yi\t')
+for i=1:3
+ printf('1/%g\t',1+(i-1)/2)
+end
+
+//trapezoidal rule
+S=0;
+for i=1:3
+ if(i==1 | i==3)
+ S=S+y(i)
+ else
+ S=S+2*y(i)
+ end
+end
+S=S*h/2
+printf('\n\nTrapezoidal Rule Sum = %g',S)
+
+//Simpsons 1/3rd Rule
+S=0;
+for i=1:3
+ if(i==1 | i==3)
+ S=S+y(i)
+ elseif(((i)/2)-fix((i)/2)==0)
+ S=S+4*y(i)
+ else
+ S=S+2*y(i)
+ end
+end
+S=S*h/3
+printf('\n\nSimpsons 1/3rd Rule Sum = %g',S)
\ No newline at end of file diff --git a/1332/CH14/EX14.5/14_5.pdf b/1332/CH14/EX14.5/14_5.pdf Binary files differnew file mode 100755 index 000000000..261029857 --- /dev/null +++ b/1332/CH14/EX14.5/14_5.pdf diff --git a/1332/CH14/EX14.5/14_5.sce b/1332/CH14/EX14.5/14_5.sce new file mode 100755 index 000000000..eecf2d374 --- /dev/null +++ b/1332/CH14/EX14.5/14_5.sce @@ -0,0 +1,35 @@ +//Example 14.5
+//Romberg Method
+//Page no. 457
+clc;close;clear;
+
+deff('y=f(x)','y=1/(1+x)')
+
+h=[0.5,0.25,0.125]
+for k=1:3
+ for i=0:h(k):1
+ x(i/h(k)+1)=i;
+ y(i/h(k)+1)=f(x(i/h(k)+1))
+ end
+ n=1+(1/h(k))
+ //trapezoidal rule
+ S=0;
+ for i=1:n
+ if(i==1 | i==n)
+ S=S+y(i)
+ else
+ S=S+2*y(i)
+ end
+ end
+ S=S*h(k)/2
+ printf('\n\nI(%g) = %g',h(k),S)
+ z(2*k-1,1)=S
+end
+for i=2:3
+ for k=1:4-i
+ 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
+end
+end
+
+printf('\n\n')
+disp(z,'The Table of values:')
\ No newline at end of file diff --git a/1332/CH14/EX14.7/14_7.pdf b/1332/CH14/EX14.7/14_7.pdf Binary files differnew file mode 100755 index 000000000..d1d920522 --- /dev/null +++ b/1332/CH14/EX14.7/14_7.pdf diff --git a/1332/CH14/EX14.7/14_7.sce b/1332/CH14/EX14.7/14_7.sce new file mode 100755 index 000000000..8744c7634 --- /dev/null +++ b/1332/CH14/EX14.7/14_7.sce @@ -0,0 +1,11 @@ +//Example 14.7
+//Gaussian Quadrature Formula
+//Page no. 463
+clc;close;clear;
+
+deff('y=f(x)','y=cos(x)*log(x)')
+s=0;
+for i=0:2:2000
+ s=s+integrate('((-1)^(i/2))*(x^i)/factorial(i)*log(x)','x',0,1)
+end
+disp(s,'Till 1000 terms .... I =')
\ No newline at end of file diff --git a/1332/CH14/EX14.8/14_8.pdf b/1332/CH14/EX14.8/14_8.pdf Binary files differnew file mode 100755 index 000000000..cb43eacdf --- /dev/null +++ b/1332/CH14/EX14.8/14_8.pdf diff --git a/1332/CH14/EX14.8/14_8.sce b/1332/CH14/EX14.8/14_8.sce new file mode 100755 index 000000000..695003f27 --- /dev/null +++ b/1332/CH14/EX14.8/14_8.sce @@ -0,0 +1,10 @@ +//Example 14.8
+//Gauss Legendre Two Point Rule
+//Page no. 472
+clc;close;clear;
+
+deff('y=f(x)','y=1/(x+3)')
+s=integrate('f(x)','x',-1,1)
+printf('By Direct Method, I = %g',s)
+s=f(-1/sqrt(3))+f(1/sqrt(3))
+printf('\n\n By Gauss-Legendre 2 point rule, I = %g',s)
\ No newline at end of file diff --git a/1332/CH14/EX14.9/14_9.pdf b/1332/CH14/EX14.9/14_9.pdf Binary files differnew file mode 100755 index 000000000..b4e41f738 --- /dev/null +++ b/1332/CH14/EX14.9/14_9.pdf diff --git a/1332/CH14/EX14.9/14_9.sce b/1332/CH14/EX14.9/14_9.sce new file mode 100755 index 000000000..48b3a30b4 --- /dev/null +++ b/1332/CH14/EX14.9/14_9.sce @@ -0,0 +1,10 @@ +//Example 14.9
+//Gauss Legendre Three Point Rule
+//Page no. 473
+clc;close;clear;
+
+deff('y=f(x)','y=1/(x+3)')
+s=integrate('f(x)','x',-1,1)
+printf('By Direct Method, I = %g',s)
+s=5/9*f(-sqrt(3/5))+8/9*f(0)+5/9*f(sqrt(3/5))
+printf('\n\n By Gauss-Legendre 3 point rule, I = %g',s)
\ No newline at end of file diff --git a/1332/CH15/EX15.1/15_1.pdf b/1332/CH15/EX15.1/15_1.pdf Binary files differnew file mode 100755 index 000000000..70f6de2ed --- /dev/null +++ b/1332/CH15/EX15.1/15_1.pdf diff --git a/1332/CH15/EX15.1/15_1.sce b/1332/CH15/EX15.1/15_1.sce new file mode 100755 index 000000000..473596fdb --- /dev/null +++ b/1332/CH15/EX15.1/15_1.sce @@ -0,0 +1,6 @@ +//Example 15.1
+//Ordinary Differential Equation
+//Page no. 503
+clc;clear;close;
+s=log(2)/log(1.02)
+disp(s,'Time Taken = ')
\ No newline at end of file diff --git a/1332/CH15/EX15.10/15_10.pdf b/1332/CH15/EX15.10/15_10.pdf Binary files differnew file mode 100755 index 000000000..5a1b5a2c4 --- /dev/null +++ b/1332/CH15/EX15.10/15_10.pdf diff --git a/1332/CH15/EX15.10/15_10.sce b/1332/CH15/EX15.10/15_10.sce new file mode 100755 index 000000000..4065a0704 --- /dev/null +++ b/1332/CH15/EX15.10/15_10.sce @@ -0,0 +1,14 @@ +//Example 15.10
+//Heun Method
+//Page no. 517
+clc;clear;close;
+deff('y=f(x,y)','y=y*2/x')
+y=2;
+h=0.25;
+for i=1:4
+ x=1+(i-1)*h
+ x1=x+h
+ ye=y+h*f(x,y)
+ y=y+h*(f(x,y)+f(x1,ye))/2
+ printf('\n y(%g) = %g\n',x1,y)
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.11/15_11.pdf b/1332/CH15/EX15.11/15_11.pdf Binary files differnew file mode 100755 index 000000000..fc0ee8bba --- /dev/null +++ b/1332/CH15/EX15.11/15_11.pdf diff --git a/1332/CH15/EX15.11/15_11.sce b/1332/CH15/EX15.11/15_11.sce new file mode 100755 index 000000000..5951a0304 --- /dev/null +++ b/1332/CH15/EX15.11/15_11.sce @@ -0,0 +1,16 @@ +//Example 15.11
+//Midpoint Method
+//Page no. 518
+clc;clear;close;
+deff('y=f(x,y)','y=y+x')
+y=1;
+h=0.2;
+printf('i\txi\tyi\tslope1\tslope2\ty(i+1)\n-----------------------------------------------\n')
+for i=1:3
+ x=(i-1)*h
+ s1=f(x,y);
+ s2=f(x+h/2,y+s1*h/2);
+ printf(' %i\t%g\t%g\t%g\t%g',i-1,x,y,s1,s2)
+ y=y+s2*h;
+ printf('\t%g\n',y)
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.12/15_12.pdf b/1332/CH15/EX15.12/15_12.pdf Binary files differnew file mode 100755 index 000000000..d0e9aca2b --- /dev/null +++ b/1332/CH15/EX15.12/15_12.pdf diff --git a/1332/CH15/EX15.12/15_12.sce b/1332/CH15/EX15.12/15_12.sce new file mode 100755 index 000000000..4266c4f45 --- /dev/null +++ b/1332/CH15/EX15.12/15_12.sce @@ -0,0 +1,17 @@ +//Example 15.12
+//Modified Midpoint Method
+//Page no. 519
+clc;clear;close;
+deff('y=f(x,y)','y=y+x')
+y=1;
+h=0.2;
+Z(1)=y;
+Z(2)=Z(1)+h*f(0,Z(1))
+printf('Z(%i) = %g',1,Z(2))
+for i=2:5
+ x=(i-1)*h;
+ Y(i-1)=(Z(i)+Z(i-1)+h*f(x,Z(i)))/2
+ Z(i+1)=Z(i-1)+2*h*f(x,Z(i))
+ printf('\n Y(%i) = %g\n\n\n Z(%i) = %g',i-1,Y(i-1),i,Z(i+1))
+end
+printf('\n\n\n y4 = %g',(4*Y(4)-Y(2))/3)
\ No newline at end of file diff --git a/1332/CH15/EX15.13/15_13.pdf b/1332/CH15/EX15.13/15_13.pdf Binary files differnew file mode 100755 index 000000000..66f57a157 --- /dev/null +++ b/1332/CH15/EX15.13/15_13.pdf diff --git a/1332/CH15/EX15.13/15_13.sce b/1332/CH15/EX15.13/15_13.sce new file mode 100755 index 000000000..63e0220b8 --- /dev/null +++ b/1332/CH15/EX15.13/15_13.sce @@ -0,0 +1,18 @@ +//Example 15.13
+//Single Step Method
+//Page no. 521
+clc;clear;close;
+
+deff('y=f(x)','y=x^2')
+deff('y=f1(x)','y=1/(1-x)')
+y=1;h=0.2;
+printf('n\tXn\tYn (by single-step method)\tYn (computed)\n-----------------------------------------------------------------\n')
+for i=1:6
+ x=(i-1)*h
+ if i<6 then
+ printf(' %i\t%.2f\t%.5f\t\t\t\t%.5f\n',i-1,x,y,f1(x))
+ else
+ printf(' %i\t%.2f\t%.5f\t\t\t\t \n',i-1,x,y)
+ end
+ y=y+h*f(y);
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.14/15_14.pdf b/1332/CH15/EX15.14/15_14.pdf Binary files differnew file mode 100755 index 000000000..fc64132ff --- /dev/null +++ b/1332/CH15/EX15.14/15_14.pdf diff --git a/1332/CH15/EX15.14/15_14.sce b/1332/CH15/EX15.14/15_14.sce new file mode 100755 index 000000000..3fe55fa35 --- /dev/null +++ b/1332/CH15/EX15.14/15_14.sce @@ -0,0 +1,24 @@ +//Example 15.14
+//Second Order Runge Kutta Method
+//Page no. 525
+clc;clear;close;
+
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;
+//simple runge kutta method
+K1=h*f(x,y);
+K2=h*f(x+h,y+K1);
+y1=y+(K1+K2)/2
+printf('\ny(1.1) by simple runge kutta method = %g\n\n',y1)
+
+//euler cauchy method
+K1=h*f(x,y);
+K2=h*f(x+h/2,y+K1/2);
+y1=y+(K1+K2)
+printf('y(1.1) by euler cauchy method = %g\n\n',y1)
+
+//optimal method
+K1=h*f(x,y);
+K2=h*f(x+2*h/3,y+2*K1/3);
+y1=y+(K1+3*K2)/4
+printf('y(1.1) by optimal method = %g',y1)
\ No newline at end of file diff --git a/1332/CH15/EX15.15/15_15.pdf b/1332/CH15/EX15.15/15_15.pdf Binary files differnew file mode 100755 index 000000000..0c61340a3 --- /dev/null +++ b/1332/CH15/EX15.15/15_15.pdf diff --git a/1332/CH15/EX15.15/15_15.sce b/1332/CH15/EX15.15/15_15.sce new file mode 100755 index 000000000..eb0fec2dd --- /dev/null +++ b/1332/CH15/EX15.15/15_15.sce @@ -0,0 +1,19 @@ +//Example 15.15
+//Third Order Runge Kutta Method
+//Page no. 526
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;
+//scheme 1
+K1=h*f(x,y);
+K2=h*f(x+h/2,y+K1/2);
+K3=h*f(x+h/2,y-K1+2*K2);
+y1=y+(K1+4*K2+K3)/6
+printf('\ny(1.1) by scheme 1 = %g\n\n',y1)
+
+//scheme 2
+K1=h*f(x,y);
+K2=h*f(x+h/3,y+K1/3);
+K3=h*f(x+2*h/3,y+2*K2/3);
+y1=y+(K1+3*K3)/4
+printf('\ny(1.1) by scheme 2 = %.7f\n\n',y1)
\ No newline at end of file diff --git a/1332/CH15/EX15.16/15_16.pdf b/1332/CH15/EX15.16/15_16.pdf Binary files differnew file mode 100755 index 000000000..810c69752 --- /dev/null +++ b/1332/CH15/EX15.16/15_16.pdf diff --git a/1332/CH15/EX15.16/15_16.sce b/1332/CH15/EX15.16/15_16.sce new file mode 100755 index 000000000..af9a6e102 --- /dev/null +++ b/1332/CH15/EX15.16/15_16.sce @@ -0,0 +1,13 @@ +//Example 15.16
+//Fourth Order Runge Kutta Method
+//Page no. 528
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;
+K1=h*f(x,y);
+K2=h*f(x+h/2,y+K1/2);
+K3=h*f(x+h/2,y+K2/2);
+K4=h*f(x+h,y+K3);
+disp(K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')
+y1=y+(K1+2*K2+2*K3+K4)/6
+printf('\ny(1.1) = %.8f\n\n',y1)
\ No newline at end of file diff --git a/1332/CH15/EX15.17/15_17.pdf b/1332/CH15/EX15.17/15_17.pdf Binary files differnew file mode 100755 index 000000000..16284f405 --- /dev/null +++ b/1332/CH15/EX15.17/15_17.pdf diff --git a/1332/CH15/EX15.17/15_17.sce b/1332/CH15/EX15.17/15_17.sce new file mode 100755 index 000000000..47e44f680 --- /dev/null +++ b/1332/CH15/EX15.17/15_17.sce @@ -0,0 +1,14 @@ +//Example 15.17
+//New Variant of Runge Kutta Method
+//Page no. 530
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;
+K1=h*f(x,y);
+K2=h*f(x+h/2,y+K1/2);
+K3=h*f(x+h/2,y+K2/2);
+K4=h*f(x+h,y+K3);
+K5=h*f(x+3*h/4,y+(5*K1+7*K2+13*K3-K4)/32)
+disp(K5,'K5 =',K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')
+y1=y+(K1+2*K2+2*K3+K5)/6
+printf('\ny(1.1) = %.8f\n\n',y1)
\ No newline at end of file diff --git a/1332/CH15/EX15.18/15_18.pdf b/1332/CH15/EX15.18/15_18.pdf Binary files differnew file mode 100755 index 000000000..8871dd8ba --- /dev/null +++ b/1332/CH15/EX15.18/15_18.pdf diff --git a/1332/CH15/EX15.18/15_18.sce b/1332/CH15/EX15.18/15_18.sce new file mode 100755 index 000000000..8290bfa98 --- /dev/null +++ b/1332/CH15/EX15.18/15_18.sce @@ -0,0 +1,18 @@ +//Example 15.18
+//Runge Kutta Merson Method
+//Page no. 532
+clc;clear;close;
+deff('y=f(x,y)','y=x+y')
+y=1;x=0;h=0.1;
+printf('n\t Xn\t Yn\t K1\t K2\t K3\t K4\t K5\tY(n+1)\n----------------------------------------------------------------------')
+for i=0:14
+ K1=h*f(x,y);
+K2=h*f(x+h/3,y+K1/3);
+K3=h*f(x+h/3,y+(K1+K2)/6);
+K4=h*f(x+h/2,y+(K1+3*K3)/8);
+K5=h*f(x+h,y+(K1-3*K3+4*K4)/2)
+y1=y+(K1+4*K4+K5)/6
+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)
+y=y1;
+x=x+h;
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.19/15_19.pdf b/1332/CH15/EX15.19/15_19.pdf Binary files differnew file mode 100755 index 000000000..023b2204e --- /dev/null +++ b/1332/CH15/EX15.19/15_19.pdf diff --git a/1332/CH15/EX15.19/15_19.sce b/1332/CH15/EX15.19/15_19.sce new file mode 100755 index 000000000..92732a7f5 --- /dev/null +++ b/1332/CH15/EX15.19/15_19.sce @@ -0,0 +1,17 @@ +//Example 15.19
+//Runge Kutta Fehlberg Method
+//Page no. 535
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;
+K1=h*f(x,y);
+K2=h*f(x+h/4,y+K1/4);
+K3=h*f(x+3*h/8,y+3*(K1+3*K2)/32);
+K4=h*f(x+12*h/13,y+1932*K1/2197-7200*K2/2197+7296*K3/2197);
+K5=h*f(x+h,y+439*K1/216-8*K2+3680*K3/513-845*K4/4104)
+K6=h*f(x+h/2,y-8*K1/27+2*K2-3544*K3/2565+1859*K4/4104-11*K5/40)
+disp(K6,'K6 =',K5,'K5 =',K4,'K4 =',K3,'K3 =',K2,'K2 =',K1,'K1 =')
+y1=y+(25*K1/216+1408*K3/2565+2197*K4/4104-K5/5)
+y11=y+(16*K1/135+6656*K3/12825+28561*K4/56430-9*K5/50+2*K6/55)
+printf('\ny(1.1) = %.9f\n\n',y1)
+printf('\ny~(1.1) = %.9f\n\n',y11)
\ No newline at end of file diff --git a/1332/CH15/EX15.20/15_20.pdf b/1332/CH15/EX15.20/15_20.pdf Binary files differnew file mode 100755 index 000000000..befbac3bf --- /dev/null +++ b/1332/CH15/EX15.20/15_20.pdf diff --git a/1332/CH15/EX15.20/15_20.sce b/1332/CH15/EX15.20/15_20.sce new file mode 100755 index 000000000..f767e52bd --- /dev/null +++ b/1332/CH15/EX15.20/15_20.sce @@ -0,0 +1,37 @@ +//Example 15.20
+//Carp Karp Runge Kutta Method
+//Page no. 537
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;printf('\n')
+U=[0,1/5,3/10,3/5,1,7/8];
+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];
+a=[37/378,0,250/621,125/594,0,512/1771];
+a1=[2825/27648,0,18575/48384,13525/55296,277/14336,1/4];
+for l=1:5
+ K(1)=h*f(x,y);
+for i=2:6
+ k=0;
+ for j=1:i-1
+ k=k+v(i,j)*K(j)
+ end
+ K(i)=h*f(x+U(i)*h,y+k)
+end
+k=0;
+for i=1:6
+ k=k+a(i)*K(i)
+end
+y1=y+k;
+k=0;
+for i=1:6
+ k=k+a1(i)*K(i)
+end
+y11=y+k;
+for i=1:6
+ printf('K%i = %.9f\n',i,K(i))
+end
+printf('\ny(1.1) = Y%i = %.9f\n',l,y1)
+printf('y~(1.1) = Y%i~ = %.9f\n',l,y11)
+y=y1;
+printf('\n\n\n')
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.21/15_21.pdf b/1332/CH15/EX15.21/15_21.pdf Binary files differnew file mode 100755 index 000000000..f56ff8f4b --- /dev/null +++ b/1332/CH15/EX15.21/15_21.pdf diff --git a/1332/CH15/EX15.21/15_21.sce b/1332/CH15/EX15.21/15_21.sce new file mode 100755 index 000000000..224cb22e9 --- /dev/null +++ b/1332/CH15/EX15.21/15_21.sce @@ -0,0 +1,13 @@ +//Example 15.21
+//Implicit Runge Kutta Method
+//Page no. 539
+clc;clear;close;
+deff('y=f(x,y)','y=x-y')
+y=1;x=1;h=0.1;printf('\n')
+U=[0,1/5];
+v=[0,0;1/2,1/2];
+a2=1;
+K(1)=h*f(x,y);
+K(2)=(x+h/2-y-K(1)/2)/(1/h-1/2)
+y1=y+(K(1)+a2*K(2))
+printf('\ny(1.1) = %.9f\n\n',y1)
\ No newline at end of file diff --git a/1332/CH15/EX15.22/15_22.pdf b/1332/CH15/EX15.22/15_22.pdf Binary files differnew file mode 100755 index 000000000..6da41498a --- /dev/null +++ b/1332/CH15/EX15.22/15_22.pdf diff --git a/1332/CH15/EX15.22/15_22.sce b/1332/CH15/EX15.22/15_22.sce new file mode 100755 index 000000000..720adda39 --- /dev/null +++ b/1332/CH15/EX15.22/15_22.sce @@ -0,0 +1,12 @@ +//Example 15.22
+//Linear Multi Step Method
+//Page no. 540
+clc;clear;close;
+deff('y=f(x,y)','y=x+y')
+y(1)=1;y(2)=1;x(1)=0;h=0.1;
+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)));
+for i=2:11
+ x(i)=(i-1)*h;
+ y(i+1)=(-y(i)-y(i-1)+h*(f(x(i),y(i))+f(x(i-1),y(i-1))))/2;
+ printf(' %i\t%.3f\t\t%.3f\t\t%.3f\n',i-1,x(i),y(i),f(x(i),y(i)))
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.23/15_23.pdf b/1332/CH15/EX15.23/15_23.pdf Binary files differnew file mode 100755 index 000000000..090680e52 --- /dev/null +++ b/1332/CH15/EX15.23/15_23.pdf diff --git a/1332/CH15/EX15.23/15_23.sce b/1332/CH15/EX15.23/15_23.sce new file mode 100755 index 000000000..3d3ed7f61 --- /dev/null +++ b/1332/CH15/EX15.23/15_23.sce @@ -0,0 +1,18 @@ +//Example 15.23
+//Milne Simpson Predictor Corrector Method
+//Page no. 544
+clc;clear;close;
+deff('y=f(x,y)','y=y+exp(x)')
+h=0.5;
+y=[1,1.824,3.718,7.722]
+for i=1:4
+ x=(i-1)*h;
+ f1(i)=f(x,y(i));
+ printf('\nf%i = %g',i-1,f1(i))
+end
+y41=y(1)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3
+f4=f(x+h,y41);
+y4=y(3)+h*(f4+4*f1(4)+f1(3))/3
+printf('\n\n\nPredictor = %.9f\n\n',y41)
+printf('Evaluator = %.9f\n\n',f4)
+printf('Corrector = %.9f',y4)
\ No newline at end of file diff --git a/1332/CH15/EX15.24/15_24.pdf b/1332/CH15/EX15.24/15_24.pdf Binary files differnew file mode 100755 index 000000000..ae2d85af4 --- /dev/null +++ b/1332/CH15/EX15.24/15_24.pdf diff --git a/1332/CH15/EX15.24/15_24.sce b/1332/CH15/EX15.24/15_24.sce new file mode 100755 index 000000000..79894698a --- /dev/null +++ b/1332/CH15/EX15.24/15_24.sce @@ -0,0 +1,31 @@ +//Example 15.24
+//Improved Milne Simpson Predictor Corrector Method
+//Page no. 546
+clc;clear;close;
+
+deff('y=f(x,y)','y=y-x^2')
+y(1)=1;h=0.25;x=0;
+printf('n\tXn\tYn\tfn\tY`n\tYn\tY`n+1\tm(n+1)\tv(n+1)\n------------------------------------------------------------------------\n')
+f1(1)=f(x,y(1));
+for i=1:3
+ K1=h*f(x,y(i));
+ K2=h*f(x+2*h/3,y(i)+2*K1/3);
+ y(i+1)=y(i)+(K1+3*K2)/4
+ printf(' %i\t%.3f\t%.3f\t%.3f\n',i-1,x,y(i),f1(i))
+ x=x+h
+ f1(i+1)=f(x,y(i+1))
+end
+Y31=0
+for i=3:10
+ Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3 //predictor
+ m4=Y41+28*(y(i+1)-Y31)/29 //modifier
+ v4=f(x+h,m4) //evaluator
+ Y4=y(i)+h*(v4+4*f1(4)+f1(3))/3 //corrector
+ 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)
+ y(i+2)=Y4
+ Y31=Y41;
+ f1(2)=f1(3);
+ f1(3)=f1(4);
+ f1(4)=f(x+h,y(i+2))
+ x=x+h
+end
diff --git a/1332/CH15/EX15.25/15_25.pdf b/1332/CH15/EX15.25/15_25.pdf Binary files differnew file mode 100755 index 000000000..7a132440e --- /dev/null +++ b/1332/CH15/EX15.25/15_25.pdf diff --git a/1332/CH15/EX15.25/15_25.sce b/1332/CH15/EX15.25/15_25.sce new file mode 100755 index 000000000..4225001f0 --- /dev/null +++ b/1332/CH15/EX15.25/15_25.sce @@ -0,0 +1,33 @@ +//Example 15.25
+//Hamming Predictor Corrector Method
+//Page no. 548
+clc;clear;close;
+
+deff('y=f(x,y)','y=y-x^2')
+y(1)=1;h=0.25;x=0;
+printf('n\tXn\tYn\tfn\tY`n\tYc(n)\tY`n+1\tm(n+1)\tv(n+1)\tYc(n+1)\n-----------------------------------------------------------------------------------------\n')
+f1(1)=f(x,y(1));
+for i=1:3
+ K1=h*f(x,y(i));
+ K2=h*f(x+2*h/3,y(i)+2*K1/3);
+ y(i+1)=y(i)+(K1+3*K2)/4
+ printf(' %i\t%.3f\t%.3f\t%.3f\n',i-1,x,y(i),f1(i))
+ x=x+h
+ f1(i+1)=f(x,y(i+1))
+end
+Y31=y(4);Yc=0
+for i=3:10
+ Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3 //predictor
+ m4=Y41+112*(Y31-Yc)/121 //modifier
+ v4=f(x+h,m4) //evaluator
+ Y4c=(9*y(i+1)-y(i-1))/8+3*h*(v4+2*f1(4)-f1(3))/8 //corrector
+ Y4=Y4c+9*(Y41-Y4c)/121 //final value
+ 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)
+ y(i+2)=Y4
+ Y31=Y41;
+ f1(2)=f1(3);
+ f1(3)=f1(4);
+ f1(4)=f(x+h,y(i+2))
+ Yc=Y4c
+ x=x+h
+end
diff --git a/1332/CH15/EX15.26/15_26.pdf b/1332/CH15/EX15.26/15_26.pdf Binary files differnew file mode 100755 index 000000000..afd84bfeb --- /dev/null +++ b/1332/CH15/EX15.26/15_26.pdf diff --git a/1332/CH15/EX15.26/15_26.sce b/1332/CH15/EX15.26/15_26.sce new file mode 100755 index 000000000..d2c699293 --- /dev/null +++ b/1332/CH15/EX15.26/15_26.sce @@ -0,0 +1,51 @@ +//Example 15.26
+//Multi Valued Method
+//Page no. 553
+clc;clear;close;
+
+deff('y=f1(x,y)','y=2*x^2-y')
+h=0.1;x=0;y=-1;
+deff('y=f2(x,y)','y=4*x-f1(x,y)')
+deff('y=f3(x,y)','y=4-f2(x,y)')
+B=[1,1,1,1;0,1,2,3;0,0,1,3;0,0,0,1];
+y0=[y;h*f1(x,y);h^2*f2(x,y)/2;h^3*f3(x,y)/6]
+y01=y0;
+r=[0;1;3/4;1/6]
+
+disp(r,'If r = ')
+printf('\n\n-------------------------------------------------------------------------\nx = 0\t\t\tx = 0.1\t\t\t\tx = 0.2\n\t')
+for i=1:2
+ y11=B*y01
+ s(i)=h*(f1(x+h,y11(1)))-y11(2)
+ y1=y11+s(i)*r
+ if i==2 then
+ break
+ end
+ y2=y1;
+ y22=y11;
+ y01=y1
+end
+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))
+for i=1:4
+ printf('%.5f \t%.5f \t%.5f \t%.5f \t%.5f\n',y0(i),y22(i),y2(i),y11(i),y1(i))
+end
+y0=[y;h*f1(x,y);h^2*f2(x,y)/2;h^3*f3(x,y)/6]
+y01=y0;
+r=[5/12;1;3/4;1/6]
+disp(r,'If r = ')
+printf('\n\n-------------------------------------------------------------------------\nx = 0\t\t\tx = 0.1\t\t\t\tx = 0.2\n\t')
+for i=1:2
+ y11=B*y01
+ s(i)=h*(f1(x+h,y11(1)))-y11(2)
+ y1=y11+s(i)*r
+ if i==2 then
+ break
+ end
+ y2=y1;
+ y22=y11;
+ y01=y1
+end
+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))
+for i=1:4
+ printf('%.5f \t%.5f \t%.5f \t%.5f \t%.5f\n',y0(i),y22(i),y2(i),y11(i),y1(i))
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.27/15_27.pdf b/1332/CH15/EX15.27/15_27.pdf Binary files differnew file mode 100755 index 000000000..74acfcccb --- /dev/null +++ b/1332/CH15/EX15.27/15_27.pdf diff --git a/1332/CH15/EX15.27/15_27.sce b/1332/CH15/EX15.27/15_27.sce new file mode 100755 index 000000000..594ef9812 --- /dev/null +++ b/1332/CH15/EX15.27/15_27.sce @@ -0,0 +1,35 @@ +//Example 15.27
+//First order ODE
+//Page no. 558
+clc;clear;close;
+
+deff('y=f1(x,y1,y2)','y=y1*y2+x')
+deff('y=f2(x,y1,y2)','y=y1-x')
+h=0.2;x=0;y1=0;y2=1;
+//heun method
+printf('Heun Method:\n\n x\ty1\ty2\n-------------------------\n')
+Y=[y1;y2]
+for i=1:8
+
+ F=[f1(x,Y(1),Y(2));f2(x,Y(1),Y(2))]
+ Y1=Y+h*F
+ x=x+h;
+ F1=[f1(x,Y1(1),Y1(2));f2(x,Y1(1),Y1(2))]
+ Y=Y+(h/2)*(F+F1)
+ printf(' %g\t%.3f\t%.3f\n',x-h,Y(1),Y(2))
+
+end
+
+//classical runge kutta method
+printf('\n\n\nClassical Runge Kutta Method:\n\n n\tx\tYn\tK1\tK2\tK3\tK4\tY(n+1)\n-----------------------------------------------------------------\n')
+Y=[y1;y2];x=0;
+for i=1:6
+ K1=h*[f1(x,Y(1),Y(2));f2(x,Y(1),Y(2))]
+ 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)]
+ 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)]
+ K4=h*[f1(x+h,Y(1)+K3(1),Y(2)+K3(2));f2(x+h,Y(1)+K3(1),Y(2)+K3(2))]
+ Y1=Y+(K1+2*K2+2*K3+K4)/6
+ 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))
+ Y=Y1;
+ x=x+h
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.28/15_28.pdf b/1332/CH15/EX15.28/15_28.pdf Binary files differnew file mode 100755 index 000000000..d0c347095 --- /dev/null +++ b/1332/CH15/EX15.28/15_28.pdf diff --git a/1332/CH15/EX15.28/15_28.sce b/1332/CH15/EX15.28/15_28.sce new file mode 100755 index 000000000..b5269493f --- /dev/null +++ b/1332/CH15/EX15.28/15_28.sce @@ -0,0 +1,11 @@ +//Example 15.28
+//Differential Equation
+//Page no. 562
+clc;clear;close;
+
+deff('y=f(x,y)','y=2*y^2/(1+x)')
+h=0.1;z(1)=-1;
+for i=1:11
+ printf('\nZ(%g) = %g\n',(i-1)/10,z(i))
+ z(i+1)=z(i)+h*f((i-1)/10,z(i))
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.6/15_6.pdf b/1332/CH15/EX15.6/15_6.pdf Binary files differnew file mode 100755 index 000000000..73991c137 --- /dev/null +++ b/1332/CH15/EX15.6/15_6.pdf diff --git a/1332/CH15/EX15.6/15_6.sce b/1332/CH15/EX15.6/15_6.sce new file mode 100755 index 000000000..48a656600 --- /dev/null +++ b/1332/CH15/EX15.6/15_6.sce @@ -0,0 +1,32 @@ +//Example 15.6
+//Taylor Method
+//Page no. 510
+clc;clear;close;
+
+deff('y=f1(x,y)','y=x^2+y^2')
+deff('y=f2(x,y)','y=2*x+2*y*f1(x,y)')
+deff('y=f3(x,y)','y=2+2*f1(x,y)^2+2*y*f2(x,y)')
+deff('y=f4(x,y)','y=6*f1(x,y)*f2(x,y)+2*y*f3(x,y)')
+h=0.2;
+for l=1:2
+ a=0;y=0;x=0;
+ printf('\n---------------\nh = %g\n---------------\n',h)
+ for i=1:4
+ x=a+(i-1)*h
+ k=0;
+ for j=1:4
+ if j==1 then
+ k=k+(h^j)*f1(x,y)/factorial(j)
+ elseif j==2
+ k=k+(h^j)*f2(x,y)/factorial(j)
+ elseif j==3
+ k=k+(h^j)*f3(x,y)/factorial(j)
+ else
+ k=k+(h^j)*f4(x,y)/factorial(j)
+ end
+end
+y=y+k;
+printf('\nx = %g\n\ny(%g) = %g\n\n',x,x+0.2,y)
+end
+h=h+0.2;
+end
diff --git a/1332/CH15/EX15.7/15_7.pdf b/1332/CH15/EX15.7/15_7.pdf Binary files differnew file mode 100755 index 000000000..5c6489776 --- /dev/null +++ b/1332/CH15/EX15.7/15_7.pdf diff --git a/1332/CH15/EX15.7/15_7.sce b/1332/CH15/EX15.7/15_7.sce new file mode 100755 index 000000000..62c4c7d60 --- /dev/null +++ b/1332/CH15/EX15.7/15_7.sce @@ -0,0 +1,10 @@ +//Example 15.7
+//Picard Method
+//Page no. 511
+clc;clear;close;
+deff('y=f(x,y)','y=x^2+y^2')
+y(1)=0;
+for i=1:2
+ y(i+1)=y(1)+integrate('f(x,y(i))','x',0,i/10)
+ printf('\n y(%g) = %g\n',i/10,y(i+1))
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.8/15_8.pdf b/1332/CH15/EX15.8/15_8.pdf Binary files differnew file mode 100755 index 000000000..a747463fe --- /dev/null +++ b/1332/CH15/EX15.8/15_8.pdf diff --git a/1332/CH15/EX15.8/15_8.sce b/1332/CH15/EX15.8/15_8.sce new file mode 100755 index 000000000..49c24e828 --- /dev/null +++ b/1332/CH15/EX15.8/15_8.sce @@ -0,0 +1,12 @@ +//Example 15.8
+//Euler Method
+//Page no. 513
+clc;clear;close;
+deff('y=f(x,y)','y=x+y')
+y(1)=1;
+h=0.1;
+for i=1:6
+ printf('\ny(%g) = %g\n',(i-1)/10,y(i))
+ y(i+1)=y(i)+h*f((i-1)/10,y(i))
+
+end
\ No newline at end of file diff --git a/1332/CH15/EX15.9/15_9.pdf b/1332/CH15/EX15.9/15_9.pdf Binary files differnew file mode 100755 index 000000000..61dede132 --- /dev/null +++ b/1332/CH15/EX15.9/15_9.pdf diff --git a/1332/CH15/EX15.9/15_9.sce b/1332/CH15/EX15.9/15_9.sce new file mode 100755 index 000000000..ec1387d75 --- /dev/null +++ b/1332/CH15/EX15.9/15_9.sce @@ -0,0 +1,14 @@ +//Example 15.9
+//Trapezium Method
+//Page no. 516
+clc;clear;close;
+deff('y=f(x,y)','y=x*y^2')
+y=1;
+h=0.2;
+y2=poly(0,'y2')
+for i=1:2
+ x=(i-1)*h;
+ x1=x+h
+ y1=roots(-y2+y+h*(f(x,y)+f(x1,y2))/2)
+ printf('\n Y(%i) = %g or %g\n',i,y1(1),y1(2))
+end
\ No newline at end of file diff --git a/1332/CH16/EX16.1/16_1.pdf b/1332/CH16/EX16.1/16_1.pdf Binary files differnew file mode 100755 index 000000000..22caad1e1 --- /dev/null +++ b/1332/CH16/EX16.1/16_1.pdf diff --git a/1332/CH16/EX16.1/16_1.sce b/1332/CH16/EX16.1/16_1.sce new file mode 100755 index 000000000..a4883eb81 --- /dev/null +++ b/1332/CH16/EX16.1/16_1.sce @@ -0,0 +1,33 @@ +//Example 16.1
+//Outline of Linear Shooting Method
+//Page no. 572
+clc;close;clear;
+
+deff('y=f(x)','y=x^2');
+h=0.5;X0=0;Y0=1;Z1=[-1,-1.5,-1.1771];i=1;Y1=Y0;
+for j=1:3
+ Z0=Z1(i);
+ i=i+1
+ Y0=1;
+ for n=1:2
+ printf('\nFor n = %i\n---------------------------\n',n-1)
+ K1(1)=h*Z0;
+ printf('\n K11 = %g',K1(1));
+ K1(2)=h*f(Y0);
+ printf('\n K12 = %g',K1(2));
+ K2=h*f(Y0+K1(2))
+ printf('\n K22 = %g',K2);
+ Z0=Z0+(K1(2)+K2)/2
+ printf('\n Z%i = %g',n,Z0);
+ K2=h*Z0;
+ printf('\n K21 = %g',K2);
+ Y0=Y0+(K1(1)+K2)/2
+ printf('\n Y%i = %g',n,Y0);
+ printf('\n\n\n')
+ if n==1 then
+ Y2=Y0
+ end
+ end
+ printf('\n\n\n')
+end
+printf('Hence the solution is y(%g) = %i, y(%g) = %.4f and y(%g) = %.1f',X0,Y1,X0+h,Y2,X0+2*h,Y0)
\ No newline at end of file diff --git a/1332/CH16/EX16.2/16_2.pdf b/1332/CH16/EX16.2/16_2.pdf Binary files differnew file mode 100755 index 000000000..07065af81 --- /dev/null +++ b/1332/CH16/EX16.2/16_2.pdf diff --git a/1332/CH16/EX16.2/16_2.sce b/1332/CH16/EX16.2/16_2.sce new file mode 100755 index 000000000..4bf89280f --- /dev/null +++ b/1332/CH16/EX16.2/16_2.sce @@ -0,0 +1,75 @@ +//Example 16.2
+//Linear Shooting Method
+//Page no. 576
+clc;close;clear;
+
+deff('y=f1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')
+deff('y=F1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')
+deff('y=F2(x,y,y1)','y=-x*y1+x^2*y')
+a=0;b=1;
+y0=1;y1=-1;n=5;
+h=(b-a)/n
+y=y0;y01=0;x=a;
+for i=0:5
+ yi1(1,i+1)=y
+ K1=h*y01;
+ R1=h*F1(x,y,y01);
+ K2=h*(y+R1/2);
+ R2=h*F1(x+h/2,y+K1/2,y01+R1/2)
+ K3=h*(y01+R2/2)
+ R3=h*F1(x+h/2,y+K2/2,y01+R2/2)
+ K4=h*(y+R3)
+ R4=h*F1(x+h,y+K3,y01+R3)
+ y=y+(K1+2*K2+2*K3+K4)/6
+ y01=y01+(R1+2*R2+2*R3+R4)/6
+ x=x+h
+end
+y=0;y01=1;x=a;
+for i=0:5
+ yi2(1,i+1)=y
+ K1=h*y01;
+ R1=h*F2(x,y,y01);
+ K2=h*(y+R1/2);
+ R2=h*F2(x+h/2,y+K1/2,y01+R1/2)
+ K3=h*(y01+R2/2)
+ R3=h*F2(x+h/2,y+K2/2,y01+R2/2)
+ K4=h*(y+R3)
+ R4=h*F2(x+h,y+K3,y01+R3)
+ y=y+(K1+2*K2+2*K3+K4)/6
+ y01=y01+(R1+2*R2+2*R3+R4)/6
+ x=x+h
+end
+for i=1:6
+ yi(i)=yi1(1,i)+((y1-yi1(6))/yi2(6))*yi2(i)
+end
+y=1;x=a;y01=y1
+for i=0:5
+ yir(1,i+1)=y;
+ K1=h*y01;
+ R1=h*f1(x,y,y01);
+ K2=h*(y+R1/2);
+ R2=h*f1(x+h/2,y+K1/2,y01+R1/2)
+ K3=h*(y01+R2/2)
+ R3=h*f1(x+h/2,y+K2/2,y01+R2/2)
+ K4=h*(y+R3)
+ R4=h*f1(x+h,y+K3,y01+R3)
+ y=y+(K1+2*K2+2*K3+K4)/6
+ y01=y01+(R1+2*R2+2*R3+R4)/6
+ x=x+h
+end
+x=a;
+printf('\n ------------------------------------------------------------------------------------------------------\n\tx')
+for i=1:6
+ printf('\t%.1f\t',x)
+ x=x+h
+end
+printf('\n\ty')
+for i=1:6
+ printf('\t%.4f\t',yi(i))
+end
+printf('\n by RK')
+for i=1:6
+ printf('\t%.4f\t',yir(i))
+end
+printf('\n ------------------------------------------------------------------------------------------------------')
+printf('\n\n\nNote: Computation error in calculation of values by RK method performed in book')
\ No newline at end of file diff --git a/1332/CH16/EX16.3/16_3.pdf b/1332/CH16/EX16.3/16_3.pdf Binary files differnew file mode 100755 index 000000000..5bb88e031 --- /dev/null +++ b/1332/CH16/EX16.3/16_3.pdf diff --git a/1332/CH16/EX16.3/16_3.sce b/1332/CH16/EX16.3/16_3.sce new file mode 100755 index 000000000..2d907fcd4 --- /dev/null +++ b/1332/CH16/EX16.3/16_3.sce @@ -0,0 +1,36 @@ +//Example 16.3
+//Multiple Shooting Method
+//Page no. 577
+clc;close;clear;
+
+h=0.25;x=0;y1=0;
+deff('y=f(x)','y=-(4*h^2)/(1+x)^2')
+deff('y=f1(x)','y=-2*(1+(h^2)/(1+x)^2)')
+
+for i=1:4
+ x=x+h
+ B(i)=f(x);
+ for j=1:4
+ if i==4 & i==j
+ A(i,j)=f1(x)+1/4
+ A(i,j-1)=2
+ elseif j==i then
+ A(i,j)=f1(x)
+ A(i,j+1)=1
+ if j-1~=0 then
+ A(i,j-1)=1
+ end
+ end
+ end
+end
+y=inv(A)*B
+disp(B,"B =",A,'A = ')
+printf('\n\n\n x :')
+for i=1:5
+ printf('\t%.2f',x)
+ x=x+h
+end
+x=0;printf('\n y :\t%.2f',y1);
+for i=1:4
+ printf('\t%.4f',y(i))
+end
diff --git a/1332/CH16/EX16.4/16_4.pdf b/1332/CH16/EX16.4/16_4.pdf Binary files differnew file mode 100755 index 000000000..1cfe37ab0 --- /dev/null +++ b/1332/CH16/EX16.4/16_4.pdf diff --git a/1332/CH16/EX16.4/16_4.sce b/1332/CH16/EX16.4/16_4.sce new file mode 100755 index 000000000..d880ae40c --- /dev/null +++ b/1332/CH16/EX16.4/16_4.sce @@ -0,0 +1,52 @@ +//Example 16.4
+//Finite Difference Method
+//Page no. 582
+clc;close;clear;
+
+x=0;h=0.25;q=-1;Y(1)=-2;Y(5)=1;
+printf('\n i\txi\tYi\tpi\tqi\tri\n-----------------------------------------------\n')
+for i=1:5
+ r(i)=-x^2
+ if i>1 & i<5 then
+ printf(' %i\t%g\t%s\t%g\t%i\t%g\n',i-1,x,"?",x,q,r(i))
+ else
+ printf(' %i\t%g\t%g\t%g\t%i\t%g\n',i-1,x,Y(i),x,q,r(i))
+ end
+ x=x+h
+end
+x=0;
+printf('-----------------------------------------------\n')
+for i=1:3
+ x=x+h
+ for j=1:3
+ if i==j then
+ A(i,j)=2+h^2*q
+ elseif i<j & abs(i-j)~=2
+ A(i,j)=-1+h*x/2
+ elseif i>j & abs(i-j)~=2
+ A(i,j)=-1-h*x/2
+ end
+ end
+ if i==3 then
+ B(i)=-h^2*r(i+1)+(-h*x/2+1)*Y(1+2*(i-1))
+ else
+ B(i)=-h^2*r(i+1)+(h*x/2+1)*Y(1+2*(i-1))
+ end
+ B(i)=(-1)^(i+1)*B(i)
+end
+disp(B,"B =",A,'A = ')
+y=inv(A)*B
+for i=1:3
+ Y(i+1)=y(i)
+end
+x=0;
+disp("The Solution is :",B,"B =",A,'A = ')
+printf(' x :')
+for i=1:5
+ printf('\t %.2f',x)
+ x=x+h
+end
+x=0;printf('\n y :');
+for i=1:5
+ printf('\t%.3f',Y(i))
+end
\ No newline at end of file diff --git a/1332/CH16/EX16.5/16_5.pdf b/1332/CH16/EX16.5/16_5.pdf Binary files differnew file mode 100755 index 000000000..eca8efd81 --- /dev/null +++ b/1332/CH16/EX16.5/16_5.pdf diff --git a/1332/CH16/EX16.5/16_5.sce b/1332/CH16/EX16.5/16_5.sce new file mode 100755 index 000000000..c3604344a --- /dev/null +++ b/1332/CH16/EX16.5/16_5.sce @@ -0,0 +1,29 @@ +//Example 16.5
+//Non Linear Problem
+//Page no. 584
+clc;close;clear;
+
+deff('y=f(x)','y=2/(1+x)')
+Y=[1,0.75,0.75,0.75,0.5];h=0.25
+A=[-2,1,0;1,-2,1;0,1,-2];A_1=inv(A)
+disp(A_1,"Inverse of A =",A,"A =")
+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----------------------------------------------------------------------------------------')
+for i=0:6
+ printf('\n %i',i)
+ for j=1:5
+ if j<4 & i~=0 then
+ Y(j+1)=y(j)
+ end
+ printf('\t\t%.4f',Y(j))
+ end
+ x=0;
+ for j=1:3
+ x=x+h
+ if j~=2 then
+ B(j)=h^2*f(x)*Y(j+1)^2-Y(1+2*(j-1))
+ else
+ B(j)=h^2*f(x)*Y(j+1)^2
+ end
+ end
+ y=A_1*B
+end
\ No newline at end of file diff --git a/1332/CH16/EX16.6/16_6.pdf b/1332/CH16/EX16.6/16_6.pdf Binary files differnew file mode 100755 index 000000000..cee0b88fa --- /dev/null +++ b/1332/CH16/EX16.6/16_6.pdf diff --git a/1332/CH16/EX16.6/16_6.sce b/1332/CH16/EX16.6/16_6.sce new file mode 100755 index 000000000..72049be59 --- /dev/null +++ b/1332/CH16/EX16.6/16_6.sce @@ -0,0 +1,33 @@ +//Example 16.6
+//Collocation Method
+//Page no. 589
+clc;close;clear;
+
+h1=0.000001;h=0.25;x=0;
+Y(1)=0;Y(5)=0;
+deff('y=p(x)','y=1')
+deff('y=q(x)','y=-2/(1+x)^2')
+deff('y=f(x)','y=(2*x-4)/(1+x)^4')
+deff('y=fi(x,j)','y=(1-x)*x^j')
+deff('y=f1(x,y)','y=(-x+y)/h1') //function for differentiation
+for i=1:4
+ x=x+h
+ for j=1:4
+ 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)
+ end
+end
+x=0;
+for i=1:4
+ x=x+h
+ B(i)=f(x)
+end
+disp(B,'B =',A,"A =")
+C=inv(A)*B
+x=0;
+for i=2:4
+ x=x+h;
+ for j=1:4
+ Y(i)=Y(i)+C(j)*fi(x,j)
+ end
+end
+disp(Y,"Solution Matrix Y = ")
\ No newline at end of file diff --git a/1332/CH18/EX18.4/18_4.pdf b/1332/CH18/EX18.4/18_4.pdf Binary files differnew file mode 100755 index 000000000..4cdbb77fc --- /dev/null +++ b/1332/CH18/EX18.4/18_4.pdf diff --git a/1332/CH18/EX18.4/18_4.sce b/1332/CH18/EX18.4/18_4.sce new file mode 100755 index 000000000..551df77d0 --- /dev/null +++ b/1332/CH18/EX18.4/18_4.sce @@ -0,0 +1,29 @@ +//Example 18.4
+//Forward Difference Method
+//Page no. 624
+clc;clear;close;
+
+h=0.2;k=0.02;
+r=k/h^2;
+printf('\n j\tt\t|\ti -->\t')
+for i=0:5
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tx -->\t')
+for i=0:5
+ printf('%.3f\t',(i)/5)
+end
+printf('\n-------------------------------------------------------------------------------')
+for j=1:6
+ printf('\n %i\t%.3f\t|\t\t',j-1,(j-1)/50)
+ for i=1:6
+ if i==1 | i==6 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=sin(%pi*(i-1)/5)
+ else
+ u(j,i)=(u(j-1,i-1)+u(j-1,i+1))/2
+ end
+ printf('%.3f\t',u(j,i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH18/EX18.5/18_5.pdf b/1332/CH18/EX18.5/18_5.pdf Binary files differnew file mode 100755 index 000000000..87e109bc2 --- /dev/null +++ b/1332/CH18/EX18.5/18_5.pdf diff --git a/1332/CH18/EX18.5/18_5.sce b/1332/CH18/EX18.5/18_5.sce new file mode 100755 index 000000000..d0c1aefe1 --- /dev/null +++ b/1332/CH18/EX18.5/18_5.sce @@ -0,0 +1,29 @@ +//Example 18.5
+//Bender Schmidt Method
+//Page no. 625
+clc;clear;close;
+
+h=0.1;k=0.005;
+r=k/h^2;
+printf('\n j |\ti -->\t')
+for i=0:10
+ printf(' %i\t',i)
+end
+printf('\n | |\tx -->\t')
+for i=0:10
+ printf('%.3f\t',(i)/10)
+end
+printf('\n------------------------------------------------------------------------------------------------------')
+for j=1:9
+ printf('\n %i |\t\t',j-1)
+ for i=1:11
+ if i==1 | i==11 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=sin(%pi*(i-1)/10)
+ else
+ u(j,i)=u(j-1,i)/2+(u(j-1,i-1)+u(j-1,i+1))/4
+ end
+ printf('%.3f\t',u(j,i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH18/EX18.6/18_6.pdf b/1332/CH18/EX18.6/18_6.pdf Binary files differnew file mode 100755 index 000000000..cde4fa2f1 --- /dev/null +++ b/1332/CH18/EX18.6/18_6.pdf diff --git a/1332/CH18/EX18.6/18_6.sce b/1332/CH18/EX18.6/18_6.sce new file mode 100755 index 000000000..fb0398d05 --- /dev/null +++ b/1332/CH18/EX18.6/18_6.sce @@ -0,0 +1,70 @@ +//Example 18.6
+//Crank Nicolson Method
+//Page no. 631
+clc;clear;close;
+h=1/2;k=1/8;
+r=k/h^2;
+for i=1:2:3
+ for j=1:9
+ if i==1 | j==1 then
+ u(i,j)=0;
+ end
+ if i==3 then
+ u(i,j)=(j-1)/8
+ end
+ end
+end
+a=[3,-1,0;-1,3,-1;0,-1,3];
+a=inv(a);
+for j=2:9
+ u(2,j)=(u(1,j-1)+2*u(2,j-1)+u(3,j-1)+u(1,j)+u(3,j))/6
+end
+u=u'
+printf('\nfor h = 1/2\n\n')
+printf('i\\j --> ')
+for i=1:3
+ printf('\t%i\t',i)
+end
+printf('\n---------------------------------------------------------------------------------------\n')
+for i=1:9
+ printf('\n %i',i)
+ for j=1:3
+ printf('\t %.9f',u(i,j))
+ end
+end
+
+
+
+
+h=1/4;k=1/8;
+r=k/h^2;
+for i=1:4:5
+ for j=1:9
+ if i==1 | j==1 then
+ u(i,j)=0;
+ end
+ if i==5 then
+ u(i,j)=(j-1)/8
+ end
+ end
+end
+a=[3,-1,0;-1,3,-1;0,-1,3];
+a=inv(a);
+for j=2:9
+ 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)]
+ x=a*b
+ u(2,j)=x(1);u(3,j)=x(2);u(4,j)=x(3);
+end
+u=u'
+printf('\n\n\n\n\nfor h = 1/4\n\n')
+printf('i\\j --> ')
+for i=1:5
+ printf('\t%i\t',i)
+end
+printf('\n---------------------------------------------------------------------------------------\n')
+for i=1:9
+ printf('\n %i',i)
+ for j=1:5
+ printf('\t %.9f',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH18/EX18.7/18_7.pdf b/1332/CH18/EX18.7/18_7.pdf Binary files differnew file mode 100755 index 000000000..832422a2e --- /dev/null +++ b/1332/CH18/EX18.7/18_7.pdf diff --git a/1332/CH18/EX18.7/18_7.sce b/1332/CH18/EX18.7/18_7.sce new file mode 100755 index 000000000..e4b7a9a90 --- /dev/null +++ b/1332/CH18/EX18.7/18_7.sce @@ -0,0 +1,29 @@ +//Example 18.7
+//Gauss Seidel Method
+//Page no. 637
+clc;clear;close;
+deff('y=f(x)','y=4*x-4*x^2')
+h=0.2;k=0.04;
+r=k/h^2;
+printf('\n k\t|\ti -->\t')
+for i=0:5
+ printf(' %i\t',i)
+end
+printf('\n |\t|\tx -->\t')
+for i=0:5
+ printf('%.2f\t',(i)/5)
+end
+printf('\n-------------------------------------------------------------------------------')
+for k=1:7
+ printf('\n %i\t|\t\t',k-1)
+ for i=1:6
+ if i==1 | i==6 then
+ u(k,i)=0;
+ elseif k==1 then
+ u(k,i)=f((i-1)/5)
+ else
+ u(k,i)=(u(k-1,i-1)+u(k-1,i+1))/2
+ end
+ printf('%.2f\t',u(k,i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH18/EX18.8/18_8.pdf b/1332/CH18/EX18.8/18_8.pdf Binary files differnew file mode 100755 index 000000000..24f33793a --- /dev/null +++ b/1332/CH18/EX18.8/18_8.pdf diff --git a/1332/CH18/EX18.8/18_8.sce b/1332/CH18/EX18.8/18_8.sce new file mode 100755 index 000000000..85f0b45ab --- /dev/null +++ b/1332/CH18/EX18.8/18_8.sce @@ -0,0 +1,121 @@ +//Example 18.8
+//ADI Method
+//Page no. 642
+clc;clear;close;
+
+for i=1:4
+ for j=1:5
+ P(i,j)=20
+ end
+end
+r=1;k=0;
+for i=1:6
+ v1(i)=20
+ u1(i)=20
+end
+P1=[25,30,35,50,60;35,0,0,0,70;45,0,0,0,80;60,70,80,100,90]
+for i=1:4
+ printf('\n')
+ for j=1:5
+ printf('%i\t',P(i,j))
+ end
+ if i==2 then
+ printf('-->')
+ end
+ printf('\t')
+ for j=1:5
+ printf('%i\t',P1(i,j))
+ if i>1 & i<4 & j>1 & j<5 then
+ P1(i,j)=P(i,j)
+ end
+ end
+end
+P1v=P1;P1h=P1;
+for i=1:6
+ for j=1:6
+ if i==j then
+ Av(i,j)=1+2*r
+ elseif abs(i-j)==1 & i+j~=5 & i+j~=9
+ Av(i,j)=-r
+ end
+ end
+end
+for i=1:6
+ for j=1:6
+ if i==j then
+ Ah(i,j)=1+2*r
+ elseif abs(i-j)==1 & i+j~=7
+ Ah(i,j)=-r
+ end
+ end
+end
+n=8
+for l=1:n
+ k=0;
+for j=0:2
+ for i=1:2
+ if i==1 then
+ 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)
+ else
+ 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)
+ end
+ end
+ k=k+1;
+end
+k=0;
+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)]
+ for i=1:6
+ v(i,l)=v1(i)
+ end
+ for i=1:6
+ u(i,l)=u1(i)
+ end
+ v1=inv(Av)*Bv
+ u1=inv(Ah)*Bh
+ k=1;
+ for i=2:3
+ for j=2:4
+ P1h(i,j)=u1(i+j+k-4)
+ end
+ k=k+2
+ end
+ k=0;
+ for j=2:4
+ for i=2:3
+ P1v(i,j)=v1(i+j+k-3)
+ end
+ k=k+1
+ end
+end
+printf('\n\n\n\nResults for Vertical Transverse in Celsius :\n')
+for i=1:7
+ printf('\n')
+ if i==1 then
+ printf('Itr -->')
+ for j=1:n
+ printf('\t %i',j-1)
+ end
+ printf('\n----------------------------------------------------------------------')
+ else
+ printf(' v%i',i-1)
+ for j=1:n
+ printf('\t%.2f',v(i-1,j))
+ end
+ end
+end
+printf('\n\n\n\nResults for Horizontal Transverse in Celsius :\n')
+for i=1:7
+ printf('\n')
+ if i==1 then
+ printf('Itr -->')
+ for j=1:n
+ printf('\t %i',j-1)
+ end
+ printf('\n----------------------------------------------------------------------')
+ else
+ printf(' u%i',i-1)
+ for j=1:n
+ printf('\t%.2f',u(i-1,j))
+ end
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.10/19_10.pdf b/1332/CH19/EX19.10/19_10.pdf Binary files differnew file mode 100755 index 000000000..cc36d21da --- /dev/null +++ b/1332/CH19/EX19.10/19_10.pdf diff --git a/1332/CH19/EX19.10/19_10.sce b/1332/CH19/EX19.10/19_10.sce new file mode 100755 index 000000000..2c8156737 --- /dev/null +++ b/1332/CH19/EX19.10/19_10.sce @@ -0,0 +1,39 @@ +//Example 19.10
+//Non Linear 1st Order Hyperboolic Differential Equation
+//Page no. 667
+clc;clear;close;
+
+c=-2;k=0.05;h=0.2;
+r=abs(c)*k/h;
+printf('\n i\t x\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t |\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*k)
+end
+i=1;
+x=0;
+printf('\n---------------------------------------------------------------------------------------')
+for j=1:7
+ for i=1:6
+ if j==1 then
+ u(i,j)=exp(-x);
+ u(i+1,j)=exp(-(x+h));
+ elseif i==1 then
+ u(i,j)=1
+ else
+ 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)
+ end
+ x=x+h
+ end
+end
+x=0;
+for i=1:6
+ printf('\n %i\t%.1f\t|\t\t',i-1,x)
+ for j=1:7
+ printf('%.3f\t',u(i,j))
+ end
+ x=x+h
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.11/19_11.pdf b/1332/CH19/EX19.11/19_11.pdf Binary files differnew file mode 100755 index 000000000..cdbbeaea5 --- /dev/null +++ b/1332/CH19/EX19.11/19_11.pdf diff --git a/1332/CH19/EX19.11/19_11.sce b/1332/CH19/EX19.11/19_11.sce new file mode 100755 index 000000000..f2a03cc1e --- /dev/null +++ b/1332/CH19/EX19.11/19_11.sce @@ -0,0 +1,48 @@ +//Example 19.11
+//Finite Difference Method
+//Page no. 670
+clc;clear;close;
+deff('y=f(x)','y=sin(%pi*x)')
+deff('y=g(x)','y=0')
+a=1;b=1;c=1;n=5;m=10;
+h=a/n;k=b/m;r=c*k/h;
+r1=r^2;r2=r1/2;s1=1-r1;s2=2*(1-r2)
+printf('\n i ')
+for i=1:n
+ printf('\t %i',i)
+end
+printf('\n-----------------------------------------------\nfi')
+for i=1:n
+ f1(i)=f(h*(i-1))
+ printf('\t%.3f',f1(i))
+end
+printf('\ngi')
+for i=1:n
+ g1(i)=g(h*(i-1))
+ printf('\t %g',g1(i))
+end
+printf('\n\n\n i / j --> ')
+for i=1:m
+ printf('\t %i',i)
+end
+printf('\n-------------------------------------------------------------------------------------------------')
+for j=1:m
+ for i=1:n
+ if i==1 | i==n then
+ u(i,j)=0;
+ elseif j==1
+ u(i,j)=f1(i)
+ elseif j==2
+ u(i,j)=s1*f1(i)+k*g1(i)+r2*(f1(i+1)+f1(i-1))
+ else
+ u(i,j)=s2*u(i,j-1)+r1*u(i-1,j-1)+u(i+1,j-1)-u(i,j-2)
+ end
+
+ end
+end
+for i=1:n
+ printf('\n %i\t',i)
+ for j=1:m
+ printf('\t%.3f',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.12/19_12.pdf b/1332/CH19/EX19.12/19_12.pdf Binary files differnew file mode 100755 index 000000000..911fb3604 --- /dev/null +++ b/1332/CH19/EX19.12/19_12.pdf diff --git a/1332/CH19/EX19.12/19_12.sce b/1332/CH19/EX19.12/19_12.sce new file mode 100755 index 000000000..7b5a4fc2d --- /dev/null +++ b/1332/CH19/EX19.12/19_12.sce @@ -0,0 +1,19 @@ +//Example 19.12
+//Hyperbolic Partial Differential Equations
+//Page no. 673
+clc;clear;close;
+deff('y=f(x)','y=12*x')
+Ua(1)=0.25;
+Ua(2)=0.75
+A=[1,-2;1,2];
+x1=inv(A)*Ua;
+printf('Xb = %g and Tb = %g',x1(1),x1(2))
+A=[2,-1;2,1];
+B=[-7.5;-8.5];
+x2=inv(A)*B;
+printf('\n\n Pb = %g and Qb = %g',x2(1),x2(2))
+x1(1)=x1(1)-Ua(1)
+du=x1'*x2
+printf('\n\n dU = %g',du)
+Ub=f(Ua(1))+du;
+printf('\n\n Modified Ub = %g',Ub)
\ No newline at end of file diff --git a/1332/CH19/EX19.13/19_13.pdf b/1332/CH19/EX19.13/19_13.pdf Binary files differnew file mode 100755 index 000000000..23d7a3a8e --- /dev/null +++ b/1332/CH19/EX19.13/19_13.pdf diff --git a/1332/CH19/EX19.13/19_13.sce b/1332/CH19/EX19.13/19_13.sce new file mode 100755 index 000000000..9cbb6a83e --- /dev/null +++ b/1332/CH19/EX19.13/19_13.sce @@ -0,0 +1,71 @@ +//Example 19.13
+//Hyperbolic Differential Equations in 2D or 3D
+//Page no. 675
+clc;clear;close;
+
+deff('y=f(x,y)','y=x*(2-x)*y*(2-y)')
+c2=3;k=0.4;h=0.4;c2=3;s2=0.5
+for l=0:11
+ if l==0 then
+ printf('\n t = %i\n\n i\t x\t|\tj -->\t',l)
+ for i=0:5
+ printf(' %i\t',i)
+ end
+ printf('\n |\t |\t|\ty -->\t')
+ for i=0:5
+ printf('%.3f\t',i*k)
+ end
+ x=0;
+ printf('\n---------------------------------------------------------------------------------------')
+ for i=1:6
+ y=0;
+ printf('\n %i\t%.3f\t|\t\t',i-1,x)
+ for j=1:6
+ if i==1 | i==6 then
+ u(i,j)=0;
+ elseif j==1 | j==6 then
+ u(i,j)=0
+ else
+ u(i,j)=f(x,y)
+ end
+ printf('%.3f\t',u(i,j))
+ y=y+k;
+ end
+ x=x+h
+end
+u2=u;
+else
+ printf('\n\n\n t = %i\n\n i\t x\t|\tj -->\t',l)
+ for i=0:5
+ printf(' %i\t',i)
+ end
+ printf('\n |\t |\t|\ty -->\t')
+ for i=0:5
+ printf('%.3f\t',i*k)
+ end
+ x=0;
+ printf('\n---------------------------------------------------------------------------------------')
+ for i=1:6
+ y=0;
+ printf('\n %i\t%.3f\t|\t\t',i-1,x)
+ for j=1:6
+ if i==1 | i==6 then
+ u(i,j)=0;
+ elseif j==1 | j==6 then
+ u(i,j)=0
+ elseif l==1
+ 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)
+ else
+ 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)
+ end
+ printf('%.4f\t',u(i,j))
+ y=y+k;
+ end
+ x=x+h
+ end
+end
+if l>1 then
+ u2=u1
+end
+u1=u;
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.3/19_3.pdf b/1332/CH19/EX19.3/19_3.pdf Binary files differnew file mode 100755 index 000000000..b307c53ee --- /dev/null +++ b/1332/CH19/EX19.3/19_3.pdf diff --git a/1332/CH19/EX19.3/19_3.sce b/1332/CH19/EX19.3/19_3.sce new file mode 100755 index 000000000..7d95b8dda --- /dev/null +++ b/1332/CH19/EX19.3/19_3.sce @@ -0,0 +1,29 @@ +//Example 19.3
+//Simple Explicit Method
+//Page no. 658
+clc;clear;close;
+
+c=-2;dt=0.07;dx=0.2;
+r=abs(c)*dt/dx;
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n---------------------------------------------------------------------------------------')
+for j=1:6
+ printf('\n %.1f\t%i\t|\t\t',(j-1)*dx,j-1)
+ for i=1:7
+ if i==1 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)
+ end
+ printf('%.3f\t',u(j,i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.4/19_4.pdf b/1332/CH19/EX19.4/19_4.pdf Binary files differnew file mode 100755 index 000000000..d304a5804 --- /dev/null +++ b/1332/CH19/EX19.4/19_4.pdf diff --git a/1332/CH19/EX19.4/19_4.sce b/1332/CH19/EX19.4/19_4.sce new file mode 100755 index 000000000..fccff750e --- /dev/null +++ b/1332/CH19/EX19.4/19_4.sce @@ -0,0 +1,29 @@ +//Example 19.4
+//Simple Implicit Method
+//Page no. 659
+clc;clear;close;
+
+c=-2;dt=0.07;dx=0.2;
+r=abs(c)*dt/dx;
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n---------------------------------------------------------------------------------------')
+for j=1:6
+ printf('\n %.1f\t%i\t|\t\t',(j-1)*dx,j-1)
+ for i=1:7
+ if i==1 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)
+ end
+ printf('%.3f\t',u(j,i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.5/19_5.pdf b/1332/CH19/EX19.5/19_5.pdf Binary files differnew file mode 100755 index 000000000..a311ceb7a --- /dev/null +++ b/1332/CH19/EX19.5/19_5.pdf diff --git a/1332/CH19/EX19.5/19_5.sce b/1332/CH19/EX19.5/19_5.sce new file mode 100755 index 000000000..3d17305b8 --- /dev/null +++ b/1332/CH19/EX19.5/19_5.sce @@ -0,0 +1,35 @@ +//Example 19.5
+//Lax Wendroff Method
+//Page no. 660
+clc;clear;close;
+
+c=-2;dt=0.07;dx=0.2;
+r=abs(c)*dt/dx;
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+i=1;
+printf('\n---------------------------------------------------------------------------------------')
+for j=1:7
+ for i=1:6
+ if j==1 then
+ u(i,j)=0;
+ u(i+1,j)=0;
+ elseif i==1 then
+ u(i,j)=1
+ else
+ 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
+ end
+ end
+end
+for i=1:6
+ printf('\n %.1f\t%i\t|\t\t',(i-1)*dx,i-1)
+ for j=1:7
+ printf('%.3f\t',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.6/19_6.pdf b/1332/CH19/EX19.6/19_6.pdf Binary files differnew file mode 100755 index 000000000..a7d3098e8 --- /dev/null +++ b/1332/CH19/EX19.6/19_6.pdf diff --git a/1332/CH19/EX19.6/19_6.sce b/1332/CH19/EX19.6/19_6.sce new file mode 100755 index 000000000..b38435524 --- /dev/null +++ b/1332/CH19/EX19.6/19_6.sce @@ -0,0 +1,29 @@ +//Example 19.6
+//Wendroff Method
+//Page no. 661
+clc;clear;close;
+
+c=2;k=0.07;h=0.2;
+a=(h+k*c)/(h-k*c)
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*k)
+end
+printf('\n---------------------------------------------------------------------------------------')
+for i=1:6
+ printf('\n %.1f\t%i\t|\t\t',(i-1)*h,i-1)
+ for j=1:7
+ if j==1 then
+ u(i,j)=0;
+ elseif i==1 then
+ u(i,j)=1
+ else
+ u(i,j)=u(i-1,j-1)+(u(i,j-1)-u(i-1,j))/a
+ end
+ printf('%.3f\t',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.7/19_7.pdf b/1332/CH19/EX19.7/19_7.pdf Binary files differnew file mode 100755 index 000000000..c8ccb435c --- /dev/null +++ b/1332/CH19/EX19.7/19_7.pdf diff --git a/1332/CH19/EX19.7/19_7.sce b/1332/CH19/EX19.7/19_7.sce new file mode 100755 index 000000000..bd422f2a3 --- /dev/null +++ b/1332/CH19/EX19.7/19_7.sce @@ -0,0 +1,35 @@ +//Example 19.7
+//Leapfrog Method
+//Page no. 662
+clc;clear;close;
+
+c=2;k=0.07;h=0.2;
+r=c*k/h
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*k)
+end
+printf('\n---------------------------------------------------------------------------------------')
+
+for j=1:7
+ for i=1:6
+ if j==1 | j==2 & i~=1 then
+ u(i,j)=0;
+ u(i+1,j)=0;
+ elseif i==1 then
+ u(i,j)=1
+ else
+ u(i,j)=u(i,j-2)-r*(u(i+1,j-1)-u(i-1,j-1))
+ end
+ end
+end
+for i=1:6
+ printf('\n %.1f\t%i\t|\t\t',(i-1)*h,i-1)
+ for j=1:7
+ printf('%.3f\t',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.8/19_8.pdf b/1332/CH19/EX19.8/19_8.pdf Binary files differnew file mode 100755 index 000000000..6979d51c1 --- /dev/null +++ b/1332/CH19/EX19.8/19_8.pdf diff --git a/1332/CH19/EX19.8/19_8.sce b/1332/CH19/EX19.8/19_8.sce new file mode 100755 index 000000000..6765fcef2 --- /dev/null +++ b/1332/CH19/EX19.8/19_8.sce @@ -0,0 +1,95 @@ +//Example 19.8
+//Variable Coefficients
+//Page no. 663
+clc;clear;close;
+
+//simple explicit method
+printf('\n\nBy Simple Explicit Method:\n\n')
+dt=0.05;dx=0.2;
+x=0;
+printf('\n i\t x\t r\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n \t\t\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n----------------------------------------------------------------------------------------------')
+for j=1:6
+ r=sqrt(1+2*x)*dt/dx;
+ printf('\n %i\t%.3f\t%.3f\t|\t\t',(j-1),x,r)
+ for i=1:7
+ if i==1 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)
+ end
+ printf('%.3f\t',u(j,i))
+
+ end
+ x=x+dx
+end
+
+
+//simple implicit method
+printf('\n\n\nBy Simple Implicit Method:\n')
+c=-2;dt=0.05;dx=0.2;x=0
+printf('\n i\t x\t r\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n \t\t\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n----------------------------------------------------------------------------------------------')
+for j=1:6
+ r=sqrt(1+2*x)*dt/dx;
+ printf('\n %i\t%.3f\t%.3f\t|\t\t',(j-1),x,r)
+ for i=1:7
+ if i==1 then
+ u(j,i)=0;
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)
+ end
+ printf('%.3f\t',u(j,i))
+ end
+ x=x+dx
+end
+
+
+//wendroff method
+printf('\n\n\nBy Wendroff Method:\n')
+k=0.05;h=0.2;
+x=0.1;
+printf('\n i\t x\t c\t a\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n \t\t\t\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*k)
+end
+printf('\n-------------------------------------------------------------------------------------------------------')
+for i=1:6
+ c=sqrt(1+2*x);
+ a=(h+k*c)/(h-k*c)
+ printf('\n %i\t%.3f\t%.3f\t%.3f\t|\t\t',(i-1),x-h/2,c,a)
+ for j=1:7
+ if j==1 then
+ u(i,j)=0;
+ u(i+1,j)=0;
+ elseif i==1 then
+ u(i,j)=1
+ else
+ u(i,j)=u(i-1,j-1)+(u(i,j-1)-u(i-1,j))/a
+ end
+ printf('%.3f\t',u(i,j))
+ end
+ x=x+h
+end
\ No newline at end of file diff --git a/1332/CH19/EX19.9/19_9.pdf b/1332/CH19/EX19.9/19_9.pdf Binary files differnew file mode 100755 index 000000000..3747bc489 --- /dev/null +++ b/1332/CH19/EX19.9/19_9.pdf diff --git a/1332/CH19/EX19.9/19_9.sce b/1332/CH19/EX19.9/19_9.sce new file mode 100755 index 000000000..8189d9600 --- /dev/null +++ b/1332/CH19/EX19.9/19_9.sce @@ -0,0 +1,93 @@ +//Example 19.9
+//Inhomogeneous 1st Order Hyperboolic Differential Equation
+//Page no. 665
+clc;clear;close;
+
+//simple explicit method
+printf('\n\nBy Simple Explicit Method:\n')
+c=-2;dt=0.07;dx=0.2;
+r=abs(c)*dt/dx;
+printf('\n i\tx\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n---------------------------------------------------------------------------------------')
+x=0;
+for j=1:6
+ printf('\n %i\t%.1f\t|\t\t',j-1,x)
+ for i=1:7
+ if i==1 then
+ u(j,i)=exp(-x);
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1-r)*u(j,i-1)+r*u(j-1,i-1)+dt*2*x
+ end
+ printf('%.3f\t',u(j,i))
+ end
+ x=x+dx
+end
+
+
+//simple implicit method
+printf('\n\n\nBy Simple Implicit Method:\n')
+c=-2;dt=0.07;dx=0.2;
+r=abs(c)*dt/dx;
+printf('\n i\tx\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*dt)
+end
+printf('\n---------------------------------------------------------------------------------------')
+x=0;
+for j=1:6
+ printf('\n %i\t%.1f\t|\t\t',j-1,x)
+ for i=1:7
+ if i==1 then
+ u(j,i)=exp(-x);
+ elseif j==1 then
+ u(j,i)=1
+ else
+ u(j,i)=(1/(1+r))*u(j,i-1)+r*u(j-1,i)/(1+r)+dt*2*x
+ end
+ printf('%.3f\t',u(j,i))
+ end
+ x=x+dx
+end
+
+
+//wendroff method
+printf('\n\n\nBy Wendroff Method:\n')
+c=2;k=0.07;h=0.2;
+a=(h+k*c)/(h-k*c)
+printf('\n x\ti\t|\tj -->\t')
+for i=0:6
+ printf(' %i\t',i)
+end
+printf('\n |\t|\t|\tt -->\t')
+for i=0:6
+ printf('%.3f\t',i*k)
+end
+printf('\n---------------------------------------------------------------------------------------')
+x=0;
+for i=1:6
+ printf('\n %.1f\t%i\t|\t\t',x,i-1)
+ for j=1:7
+ if j==1 then
+ u(i,j)=exp(-x);
+ elseif i==1 then
+ u(i,j)=1
+ else
+ 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))
+ end
+ printf('%.3f\t',u(i,j))
+ end
+ x=x+h
+end
\ No newline at end of file diff --git a/1332/CH2/EX2.4/2_4.pdf b/1332/CH2/EX2.4/2_4.pdf Binary files differnew file mode 100755 index 000000000..10033756a --- /dev/null +++ b/1332/CH2/EX2.4/2_4.pdf diff --git a/1332/CH2/EX2.4/2_4.sce b/1332/CH2/EX2.4/2_4.sce new file mode 100755 index 000000000..e2c8ba0fa --- /dev/null +++ b/1332/CH2/EX2.4/2_4.sce @@ -0,0 +1,12 @@ +//Example 2.4
+//Solving Simultaneous Linear Equation
+//Page 36
+clc;close;clear;
+//eq1= 5x-331y=3.5
+//eq2= 6x-397y=5.2
+
+A=[5,-331;6,-397];
+B=[3.5;5.2];
+C=inv(A)*B; //finding value by multiplying inverse with values
+disp(C(1,1),'Value of x=');
+disp(C(2,1),'Value of y=');
\ No newline at end of file diff --git a/1332/CH2/EX2.6/2_6.pdf b/1332/CH2/EX2.6/2_6.pdf Binary files differnew file mode 100755 index 000000000..594998e96 --- /dev/null +++ b/1332/CH2/EX2.6/2_6.pdf diff --git a/1332/CH2/EX2.6/2_6.sce b/1332/CH2/EX2.6/2_6.sce new file mode 100755 index 000000000..918b5281b --- /dev/null +++ b/1332/CH2/EX2.6/2_6.sce @@ -0,0 +1,5 @@ +//Example 2.6
+//Integration
+//Page no. 36
+clc;clear;close;
+disp(integrate('1/x','x',exp(-4),1),'Integration Value='); //performing integration with respect to dx
\ No newline at end of file diff --git a/1332/CH20/EX20.1/20_1.pdf b/1332/CH20/EX20.1/20_1.pdf Binary files differnew file mode 100755 index 000000000..e9c8204f9 --- /dev/null +++ b/1332/CH20/EX20.1/20_1.pdf diff --git a/1332/CH20/EX20.1/20_1.sce b/1332/CH20/EX20.1/20_1.sce new file mode 100755 index 000000000..ba5d7e975 --- /dev/null +++ b/1332/CH20/EX20.1/20_1.sce @@ -0,0 +1,19 @@ +//Example 20.1
+//Direct Method
+//Page no. 682
+clc;clear;close;
+h=1/3;
+A=[-4,1,1,0;1,-4,0,1;1,0,-4,1;0,1,1,-4]
+x=0;
+for i=1:4
+ x=x+h
+ if i==4 then
+ B(i,1)=0
+ else
+ B(i,1)=-1*sin(x*%pi)^2
+ end
+end
+disp(A,'A =')
+disp(B,'B =')
+U=inv(A)*B
+disp(U,'U =')
\ No newline at end of file diff --git a/1332/CH20/EX20.2/20_2.pdf b/1332/CH20/EX20.2/20_2.pdf Binary files differnew file mode 100755 index 000000000..d146384db --- /dev/null +++ b/1332/CH20/EX20.2/20_2.pdf diff --git a/1332/CH20/EX20.2/20_2.sce b/1332/CH20/EX20.2/20_2.sce new file mode 100755 index 000000000..e843444e6 --- /dev/null +++ b/1332/CH20/EX20.2/20_2.sce @@ -0,0 +1,34 @@ +//Example 20.2
+//Five Point Formula
+//Page no. 683
+clc;clear;close;
+
+A=[-4,1,1,0;1,0,-4,1;1,-4,0,1;0,1,1,-4];
+B=[-25;-150;-25;-150];
+u1=inv(A)*B;
+j=0;k=1
+for i=1:4
+ j=j+1;
+ printf('\nu%i%i = %g\n',k,j,u1(i))
+ if i==2 then
+ j=0;k=2
+ end
+end
+printf('\n\n U = \n')
+for i=1:4
+ printf('\n')
+ for j=1:4
+ if j==1 then
+ u(i,j)=0
+ elseif j==4
+ u(i,j)=100
+ elseif (i==1 | i==4) & j==2
+ u(i,j)=25
+ elseif i==1 | i==4
+ u(i,j)=u(i,j-1)*2
+ else
+ u(i,j)=u1((j-1)*2-i+2)
+ end
+ printf('\t%g\t',u(i,j))
+ end
+end
\ No newline at end of file diff --git a/1332/CH20/EX20.3/20_3.pdf b/1332/CH20/EX20.3/20_3.pdf Binary files differnew file mode 100755 index 000000000..c791134a1 --- /dev/null +++ b/1332/CH20/EX20.3/20_3.pdf diff --git a/1332/CH20/EX20.3/20_3.sce b/1332/CH20/EX20.3/20_3.sce new file mode 100755 index 000000000..5f5f2c893 --- /dev/null +++ b/1332/CH20/EX20.3/20_3.sce @@ -0,0 +1,35 @@ +//Example 20.3
+//Finite Difference Method
+//Page no. 685
+clc;clear;close;
+
+printf('Itr\t\t U11\t\t U21\t\t U12\t\t U22\n-----------------------------------------------------------------------\n')
+for i=1:4
+ for j=1:4
+ if j==1 then
+ u(i,j)=0
+ elseif j==4
+ u(i,j)=100
+ elseif (i==1 | i==4) & j==2
+ u(i,j)=25
+ elseif i==1 | i==4
+ u(i,j)=u(i,j-1)*2
+ else
+ u(i,j)=0
+ end
+ end
+end
+for k=0:17
+ 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))
+ for i=3:-1:2
+ for j=2:3
+ u1(i,j)=(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j))/4
+ end
+ end
+ for i=3:-1:2
+ for j=2:3
+ u(i,j)=u1(i,j)
+ end
+ end
+end
+disp(u,'U = ')
\ No newline at end of file diff --git a/1332/CH20/EX20.4/20_4.pdf b/1332/CH20/EX20.4/20_4.pdf Binary files differnew file mode 100755 index 000000000..eb3eeb564 --- /dev/null +++ b/1332/CH20/EX20.4/20_4.pdf diff --git a/1332/CH20/EX20.4/20_4.sce b/1332/CH20/EX20.4/20_4.sce new file mode 100755 index 000000000..d333541f9 --- /dev/null +++ b/1332/CH20/EX20.4/20_4.sce @@ -0,0 +1,36 @@ +//Example 20.4
+//Seven Point Formula
+//Page no. 686
+clc;clear;close;
+printf('Itr\t\t U111\t\t U211\t\t U121\t\t U221\n-----------------------------------------------------------------------\n')
+for i=1:4
+ for j=1:4
+ for k=3:-1:1
+ if k==3 then
+ u(i,j,k)=100
+ elseif (i==1 | i==4 | j==1 | j==4) & k==2
+ u(i,j,k)=300
+ elseif k==2
+ u(i,j,k)=0
+ elseif (i==1 | i==4 | j==1 | j==4) & k==1
+ u(i,j,k)=500
+ else
+ u(i,j,k)=700
+ end
+ end
+ end
+end
+k=2
+for l=0:14
+ 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))
+ for i=3:-1:2
+ for j=2:3
+ 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
+ end
+ end
+ for i=3:-1:2
+ for j=2:3
+ u(i,j,2)=u1(i,j)
+ end
+ end
+end
\ No newline at end of file diff --git a/1332/CH20/EX20.5/20_5.pdf b/1332/CH20/EX20.5/20_5.pdf Binary files differnew file mode 100755 index 000000000..74b004a29 --- /dev/null +++ b/1332/CH20/EX20.5/20_5.pdf diff --git a/1332/CH20/EX20.5/20_5.sce b/1332/CH20/EX20.5/20_5.sce new file mode 100755 index 000000000..bd9675796 --- /dev/null +++ b/1332/CH20/EX20.5/20_5.sce @@ -0,0 +1,35 @@ +//Example 20.5
+//Nine Point Formula
+//Page no. 688
+clc;clear;close;
+
+printf('Itr\t\t U11\t\t U12\t\t U21\t\t U22\n-----------------------------------------------------------------------\n')
+for i=1:4
+ for j=1:4
+ if j==1 then
+ u(i,j)=0
+ elseif j==4
+ u(i,j)=100
+ elseif (i==1 | i==4) & j==2
+ u(i,j)=25
+ elseif i==1 | i==4
+ u(i,j)=u(i,j-1)*2
+ else
+ u(i,j)=0
+ end
+ end
+end
+for k=0:17
+ 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))
+ for i=3:-1:2
+ for j=2:3
+ 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
+ end
+ end
+ for i=3:-1:2
+ for j=2:3
+ u(i,j)=u1(i,j)
+ end
+ end
+end
+disp(u,'The Solution of the System is = ')
\ No newline at end of file diff --git a/1332/CH20/EX20.6/20_6.pdf b/1332/CH20/EX20.6/20_6.pdf Binary files differnew file mode 100755 index 000000000..f49102b60 --- /dev/null +++ b/1332/CH20/EX20.6/20_6.pdf diff --git a/1332/CH20/EX20.6/20_6.sce b/1332/CH20/EX20.6/20_6.sce new file mode 100755 index 000000000..e3d56f63c --- /dev/null +++ b/1332/CH20/EX20.6/20_6.sce @@ -0,0 +1,47 @@ +//Example 20.6
+//Five Point Formula
+//Page no. 689
+clc;clear;close;
+
+h=0.25;k=0.25;y=1;x=0;
+deff('x=f(y)','x=y^3')
+
+for i=1:5
+ x=0;
+ printf('\n%g\t|',y)
+ for j=1:5
+ if (i==1 | i==5)
+ u(i,j)=f(x)
+ elseif j==5
+ u(i,j)=f(x)
+ else
+ u(i,j)=0
+ end
+ x=x+k;
+ printf('%f\t',u(i,j))
+ end
+ y=y-h
+end
+printf('\n\t-------------------------------------------------------------------------\n')
+x=0;
+ for j=1:5
+ printf('\t %g\t',x)
+ x=x+k
+ end
+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')
+
+for l=0:20
+ y=0;
+ 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))
+ for i=4:-1:2
+ y=y+k
+ for j=2:4
+ u1(i,j)=(u(i,j+1)+u(i,j-1)+u(i-1,j)+u(i+1,j)-h^2*y)/4
+ end
+ end
+ for i=4:-1:2
+ for j=2:4
+ u(i,j)=u1(i,j)
+ end
+ end
+end
\ No newline at end of file diff --git a/1332/CH20/EX20.7/20_7.pdf b/1332/CH20/EX20.7/20_7.pdf Binary files differnew file mode 100755 index 000000000..5fea7a9d4 --- /dev/null +++ b/1332/CH20/EX20.7/20_7.pdf diff --git a/1332/CH20/EX20.7/20_7.sce b/1332/CH20/EX20.7/20_7.sce new file mode 100755 index 000000000..7a68d0158 --- /dev/null +++ b/1332/CH20/EX20.7/20_7.sce @@ -0,0 +1,28 @@ +//Example 20.7
+//Laplace Distribution
+//Page no. 694
+clc;clear;close;
+
+dr=3;r0=4;dth=%pi/4;
+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
+for i=1:8
+ U(i)=0;
+end
+printf('Itr\t U1\t U2\t U3\t U4\t U5\t U6\t U7\t U8\n-----------------------------------------------------------------------')
+for l=0:15
+ printf('\n %i',l)
+ for i=1:8
+ if i==1 then
+ u1(i)=f(100,U(8),40,U(i+1))
+ elseif i==8
+ u1(i)=f(100,U(i-1),40,U(1))
+ else
+ u1(i)=f(100,U(i-1),40,U(i+1))
+ end
+
+ end
+ for i=1:8
+ U(i)=u1(i)
+ printf('\t%.3f',U(i))
+ end
+end
\ No newline at end of file diff --git a/1332/CH20/EX20.8/20_8.pdf b/1332/CH20/EX20.8/20_8.pdf Binary files differnew file mode 100755 index 000000000..73d74ff45 --- /dev/null +++ b/1332/CH20/EX20.8/20_8.pdf diff --git a/1332/CH20/EX20.8/20_8.sce b/1332/CH20/EX20.8/20_8.sce new file mode 100755 index 000000000..a4df9c2ea --- /dev/null +++ b/1332/CH20/EX20.8/20_8.sce @@ -0,0 +1,58 @@ +//Example 20.8
+//Spherical Coordinate System
+//Page no. 697
+clc;clear;close;
+deff('y=cot(x)','y=1/tan(x)')
+dr=5;r0=50;dth=%pi/4;dfi=%pi/4;N=-10;Z=60;Nb=0;Zt=70;
+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
+T1=40;T2=20;H1=35;H2=10;B1=5;B2=0;t1=240;t2=180;b1=100;b2=80;h1=210;h2=150
+printf('\n----------------------------------------------------------------------------\n')
+s=["T","H","B","t","h","b"];
+for i=1:8
+ if i<4 | i>6 then
+ T(1,i)=T1;
+ H(1,i)=H1;
+ B(1,i)=B1;
+ b(1,i)=b1;
+ t(1,i)=t1;
+ h(1,i)=h1;
+ else
+ T(1,i)=T2;
+ H(1,i)=H2;
+ b(1,i)=b2;
+ B(1,i)=B2;
+ t(1,i)=t2;
+ h(1,i)=h2;
+ end
+end
+h(1)=0;h(2)=0;
+Al=[T;H;B;t;h;b]
+for i=1:6
+ if i==1 then
+ printf('Temperature Distribution in Outer Sphere\n')
+ printf('----------------------------------------------------------------------------\n')
+ end
+ if i==4 then
+ printf('\nTemperature Distribution in Inner Sphere\n')
+ printf('----------------------------------------------------------------------------\n')
+ end
+ printf('\nPoint : ')
+ for j=1:8
+ printf('\t%s%i',s(i),j)
+ end
+ printf('\nTemperature : ')
+ for j=1:8
+ if (j==1 | j==2) & i==5 then
+ printf('\t%s',"?")
+ else
+ printf('\t%i',Al(i,j))
+ end
+ end
+ printf('\n----------------------------------------------------------------------------')
+end
+th0=10^-30
+Uh1=f(1000,Al(5,8),Al(2,1),Al(5,2),Al(6,1),Al(4,1),th0)
+disp(Uh1,'Uh1 = ')
+th0=%pi/4;
+Uh2=f(1000,Uh1,Al(2,2),Al(5,3),Al(6,2),Al(4,2),th0)
+disp(Uh2,'Uh2 = ')
\ No newline at end of file diff --git a/1332/CH21/EX21.1/21_1.PNG b/1332/CH21/EX21.1/21_1.PNG Binary files differnew file mode 100755 index 000000000..1484244a7 --- /dev/null +++ b/1332/CH21/EX21.1/21_1.PNG diff --git a/1332/CH21/EX21.1/21_1.sce b/1332/CH21/EX21.1/21_1.sce new file mode 100755 index 000000000..9afa7dadb --- /dev/null +++ b/1332/CH21/EX21.1/21_1.sce @@ -0,0 +1,34 @@ +//Example 21.1
+//Parallel Bisection Method
+//Page no. 721
+clc;close;clear;
+
+deff('y=f(x)','y=x^2-cos(x)')
+a=0;b=1;e=0.0001;i=1;
+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')
+printf('\n--------------------------------------------------------------------------------------------------------------------------------\n')
+while (abs(a-b)>=e)
+
+
+ h=(b-a)/5;
+ y(1)=f(a);
+ x(1)=a;
+ printf(' %i\t%g\t%g\t%f\t%f',i,a,b,h,x(1))
+ for j=2:6
+ x(j)=x(j-1)+h;
+ y(j)=f(x(j));
+ if (y(j-1)*y(j)<0)
+ a=x(j-1);
+ b=x(j);
+ end
+ printf('\t%f',x(j))
+ end
+ printf('\n\t\t\t\t\t')
+ for j=1:6
+ printf('%f\t',y(j))
+ end
+
+ printf('\n')
+ i=i+1;
+end
+
diff --git a/1332/CH21/EX21.2/21_2.pdf b/1332/CH21/EX21.2/21_2.pdf Binary files differnew file mode 100755 index 000000000..2a134234c --- /dev/null +++ b/1332/CH21/EX21.2/21_2.pdf diff --git a/1332/CH21/EX21.2/21_2.sce b/1332/CH21/EX21.2/21_2.sce new file mode 100755 index 000000000..d9ba4eb82 --- /dev/null +++ b/1332/CH21/EX21.2/21_2.sce @@ -0,0 +1,36 @@ +//Example 21.2
+//Lagrange Interpolation in Parallel Computing
+//Page no. 723
+clc;close;clear;
+
+xi=[-1,0,2,5];
+yi=[9,5,3,15];
+s=["x=1","n=4","Data:","(-1,9)","(0,5)","(2,3)","(5,15)"]
+for i=1:4
+ printf('\tProcessor\t')
+end
+printf('\n')
+for i=1:4
+ printf('\t N%i\t\t',i)
+end
+printf('\n')
+for i=1:7
+ for j=1:4
+ printf(' %s\t\t',s(i))
+ end
+ printf('\n')
+end
+
+x=1;T=0;
+for k=0:3
+ p=yi(k+1)
+ for j=0:3
+ if(j~=k)
+ p=p*((x-xi(j+1))/(xi(k+1)-xi(j+1)))
+ end
+ end
+ T=T+p;
+ printf('\nT(%i) = %g',k+1,p)
+end
+printf('\n\nT = %g',T)
+
diff --git a/1332/CH21/EX21.3/21_3.pdf b/1332/CH21/EX21.3/21_3.pdf Binary files differnew file mode 100755 index 000000000..b88937396 --- /dev/null +++ b/1332/CH21/EX21.3/21_3.pdf diff --git a/1332/CH21/EX21.3/21_3.sce b/1332/CH21/EX21.3/21_3.sce new file mode 100755 index 000000000..20bf478e0 --- /dev/null +++ b/1332/CH21/EX21.3/21_3.sce @@ -0,0 +1,45 @@ +//Example 21.3
+//Trapezoidal Rule and Simpsons Rule in Parallel Computing
+//Page no. 726
+clc;close;clear;
+n=8;a=0;b=8;
+h=(b-a)/n
+deff('y=f(x)','y=1/(1+x)')
+for i=0:8
+ x(i+1)=i;
+ y(i+1)=f(x(i+1))
+end
+printf('xi\t ')
+for i=1:9
+ printf('%i\t ',x(i))
+end
+printf('\n yi\t')
+for i=1:9
+ printf('1/%i\t',i)
+end
+
+//trapezoidal rule
+S=0;
+for i=1:9
+ if(i==1 | i==9)
+ S=S+y(i)
+ else
+ S=S+2*y(i)
+ end
+end
+S=S*h/2
+printf('\n\nTrapezoidal Rule Sum = %g',S)
+
+//Simpsons 1/3rd Rule
+S=0;
+for i=1:9
+ if(i==1 | i==9)
+ S=S+y(i)
+ elseif(((i)/2)-fix((i)/2)==0)
+ S=S+4*y(i)
+ else
+ S=S+2*y(i)
+ end
+end
+S=S*h/3
+printf('\n\nSimpsons 1/3rd Rule Sum = %g',S)
\ No newline at end of file diff --git a/1332/CH21/EX21.4/21_4.pdf b/1332/CH21/EX21.4/21_4.pdf Binary files differnew file mode 100755 index 000000000..39ba8646c --- /dev/null +++ b/1332/CH21/EX21.4/21_4.pdf diff --git a/1332/CH21/EX21.4/21_4.sce b/1332/CH21/EX21.4/21_4.sce new file mode 100755 index 000000000..77c6fdb28 --- /dev/null +++ b/1332/CH21/EX21.4/21_4.sce @@ -0,0 +1,34 @@ +//Example 21.4 +//Parallel Gauss-Seidel Method +//Page no. 730 +clc;close;clear; + +A=[3,2;6,2]; +B=[2;3]; +x(1)=1/4; +x(2)=1/5; +e=0.002; +old(1)=x(1); +old(2)=x(2); +new(1)=old(1); +new(2)=old(2); +printf('\t\tProcess 1\t\tProcess 2\n Itr\t\told\tnew1\t\told2\tnew2\n\n') +printf(' %i\t\t%g\t%g\t\t%g\t%g\n',0,old(1),new(1),old(2),new(2)) +for i=1:4 + printf(' %i',i) + for j=1:2 + k=0; + for l=1:j-1 + k=k-(A(j,l)*old(l)); + end + m=0; + for l=j+1:2 + m=m-(A(j,l)*old(l)); + end + new(j)=(B(j)+k+m)/A(j,j) + printf('\t\t%.5g\t%.5g',old(j),new(j)) + end + printf('\n') + old(1)=new(1) + old(2)=new(2) +end
\ No newline at end of file diff --git a/1332/CH21/EX21.5/21_5.pdf b/1332/CH21/EX21.5/21_5.pdf Binary files differnew file mode 100755 index 000000000..32d7aba78 --- /dev/null +++ b/1332/CH21/EX21.5/21_5.pdf diff --git a/1332/CH21/EX21.5/21_5.sce b/1332/CH21/EX21.5/21_5.sce new file mode 100755 index 000000000..e05b0443c --- /dev/null +++ b/1332/CH21/EX21.5/21_5.sce @@ -0,0 +1,75 @@ +//Example 21.5
+//Poissons Partial Differential Equation
+//Page no. 733
+clc;clear;close;
+
+s=["st","nd","rd"]
+for i=4:20
+ s(i)="th"
+end
+h=0.25;deff('y=f(x)','y=x^3');y=1;x=0;
+for i=1:6
+
+
+ if i~=6 then
+ printf('%g\t|',y)
+ y=y-h;
+ x=0;
+ for j=1:5
+ if i==1 | i==5 | j==5 then
+ P(i,j)=f(x)
+ else
+ P(i,j)=0
+ end
+ printf('%f\t',P(i,j))
+ x=x+h;
+ end
+ else
+ printf('---------------------------------------------------------------------------------\n\t')
+ x=0;
+ for j=1:5
+ printf(' %g\t\t',x)
+ x=x+h
+ end
+ end
+ printf('\n')
+end
+
+printf('\n\n\n')
+
+for l=0:17
+ y=1;
+ if l~=0 then
+ printf('After the %i%s Iteration : \n------------------------------------------------------\n %i',l,s(l),l)
+ for i=1:6
+ if i~=6 then
+ printf('\t%g',y)
+ y=y-h
+ for j=1:5
+ printf('\t%.3f',P(i,j))
+ end
+ else
+ x=0;
+ printf('\t')
+ for j=1:5
+ printf('\t%g',x)
+ x=x+h
+ end
+ end
+ printf('\n')
+ end
+ printf('------------------------------------------------------\n')
+end
+y=0;
+ for i=4:-1:2
+ y=y+h
+ for j=2:4
+ P1(i,j)=(P(i,j+1)+P(i,j-1)+P(i-1,j)+P(i+1,j)-h^2*y)/4
+ end
+ end
+ for i=4:-1:2
+ for j=2:4
+ P(i,j)=P1(i,j)
+ end
+ end
+end
\ No newline at end of file diff --git a/1332/CH22/EX22.1/22_1.pdf b/1332/CH22/EX22.1/22_1.pdf Binary files differnew file mode 100755 index 000000000..3be4d68b1 --- /dev/null +++ b/1332/CH22/EX22.1/22_1.pdf diff --git a/1332/CH22/EX22.1/22_1.sce b/1332/CH22/EX22.1/22_1.sce new file mode 100755 index 000000000..2b02b6483 --- /dev/null +++ b/1332/CH22/EX22.1/22_1.sce @@ -0,0 +1,35 @@ +//Example 22.1
+//MLP Algorithm
+//Page no. 748
+clc;clear;close;
+deff('y=f(x)','y=1/(1+exp(-x))')
+Wih=[0.1,-0.3;0.3,0.4];
+Who=[0.4;0.5]
+i=[0.2,0.6];
+t=0.7;
+a=10;
+for k=1:3
+ printf('\n\n\nAfter Iteration %i :\n\n',k)
+ disp(Wih,'Wih = ')
+ disp(Who,'Who = ')
+a1=i*Wih;
+disp(a1,'a = ')
+h=[f(a1(1)),f(a1(2))]
+disp(h,'h = ')
+b1=h*Who
+disp(b1,'b1 =')
+o=f(b1)
+disp(o,'o = ')
+d=o*(1-o)*(t-o)
+disp(d,'d =')
+for j=1:2
+ e(1,j)=h(j)*(1-h(j))*d*Who(j)
+end
+disp(e,'e =')
+dWho=a*h'*d;
+disp(dWho,'dWho =')
+Who=Who+dWho;
+dWih=a*i'*e;
+disp(dWih,'dWih =')
+Wih=Wih+dWih;
+end
\ No newline at end of file diff --git a/1332/CH22/EX22.2/22_2.pdf b/1332/CH22/EX22.2/22_2.pdf Binary files differnew file mode 100755 index 000000000..52d2c9aed --- /dev/null +++ b/1332/CH22/EX22.2/22_2.pdf diff --git a/1332/CH22/EX22.2/22_2.sce b/1332/CH22/EX22.2/22_2.sce new file mode 100755 index 000000000..a3bf487f5 --- /dev/null +++ b/1332/CH22/EX22.2/22_2.sce @@ -0,0 +1,12 @@ +//Example 22.2
+//MLP
+//Page no. 758
+clc;clear;close;
+
+deff('y=f(x)','y=x^3-x^2+x-1')
+printf('Input\t\tDesired\t\tNetwork\t\tError\n\t\t Output\t\t Output\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=[-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]
+for i=1:18
+ printf(' %.4f\t\t%.4f\t\t%.4f\t\t%.4f\n',in(i),f(in(i)),n(i),n(i)-f(in(i)))
+end
\ No newline at end of file diff --git a/1332/CH22/EX22.3/22_3.pdf b/1332/CH22/EX22.3/22_3.pdf Binary files differnew file mode 100755 index 000000000..8ac7a5424 --- /dev/null +++ b/1332/CH22/EX22.3/22_3.pdf diff --git a/1332/CH22/EX22.3/22_3.sce b/1332/CH22/EX22.3/22_3.sce new file mode 100755 index 000000000..9704cefdc --- /dev/null +++ b/1332/CH22/EX22.3/22_3.sce @@ -0,0 +1,29 @@ +//Example 22.3
+//Bisection Method
+//Page no. 764
+clc;clear;close;
+
+deff('y=f(x)','y=x^3-x^2+x-1')
+printf('N01\tN02\tN11\tN12\tN21\tNet31\tO31\tN41\tN42\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]
+N02(1)=2
+for i=2:13
+ N02(i)=1;
+end
+for i=1:13
+ net31(i)=f(N01(i+1))*f(N01(i))
+ if net31(i)>0 then
+ O31(i)=1;
+ else
+ O31(i)=0;
+ end
+ N41(i)=(1-O31(i))*(N01(i))+O31(i)*N01(i+1)
+ N42(i)=(1-O31(i))*N01(i+1)+O31(i)*N02(i)
+ if i==2 then
+ 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))
+ else
+ 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))
+end
+
+end
+printf('\n\nTherefore the solution is %.3f',N42(13))
\ No newline at end of file diff --git a/1332/CH22/EX22.4/22_4.pdf b/1332/CH22/EX22.4/22_4.pdf Binary files differnew file mode 100755 index 000000000..e545ac20c --- /dev/null +++ b/1332/CH22/EX22.4/22_4.pdf diff --git a/1332/CH22/EX22.4/22_4.sce b/1332/CH22/EX22.4/22_4.sce new file mode 100755 index 000000000..c740070fc --- /dev/null +++ b/1332/CH22/EX22.4/22_4.sce @@ -0,0 +1,17 @@ +//Example 22.4
+//Hopfield Neural Network
+//Page no. 766
+clc;clear;close;
+
+A=[1,2,1;-1,1,1;1,0,-1];
+disp(inv(A),'Inverse of A =',A,'A =')
+for i=1:3
+ for j=1:3
+ k=0;
+ for l=1:3
+ k=k+A(i,l)*A(j,l)
+ end
+ T(i,j)=k;
+ end
+end
+disp(T,'T =')
\ No newline at end of file diff --git a/1332/CH22/EX22.5/22_5.pdf b/1332/CH22/EX22.5/22_5.pdf Binary files differnew file mode 100755 index 000000000..df6c4c1e4 --- /dev/null +++ b/1332/CH22/EX22.5/22_5.pdf diff --git a/1332/CH22/EX22.5/22_5.sce b/1332/CH22/EX22.5/22_5.sce new file mode 100755 index 000000000..bfc474112 --- /dev/null +++ b/1332/CH22/EX22.5/22_5.sce @@ -0,0 +1,12 @@ +//Example 22.5
+//RBF Network
+//Page no. 773
+clc;clear;close;
+
+deff('y=f(x)','y=10*sin(x)')
+printf('Input\t\tDesired\t\tNetwork\t\tError\n\t\t Output\t\t Output\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=[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]
+for i=1:18
+ printf(' %.4f\t\t%.4f\t\t%.4f\t\t%.4f\n',in(i),f(in(i)),n(i),f(in(i))-n(i))
+end
\ No newline at end of file diff --git a/1332/CH22/EX22.7/22_7.pdf b/1332/CH22/EX22.7/22_7.pdf Binary files differnew file mode 100755 index 000000000..a38638a61 --- /dev/null +++ b/1332/CH22/EX22.7/22_7.pdf diff --git a/1332/CH22/EX22.7/22_7.sce b/1332/CH22/EX22.7/22_7.sce new file mode 100755 index 000000000..401181a64 --- /dev/null +++ b/1332/CH22/EX22.7/22_7.sce @@ -0,0 +1,13 @@ +//Example 22.7
+//First Order ODE
+//Page no. 783
+clc;clear;close;
+
+deff('y=f(x)','y=(exp(-x^2/2))/(1+x+x^3)')
+printf('Test Points\tActual Solution \tEstimated Solution\tError\n x\t\twa(x)\t\t\twt(x)\t\t\tdw(x)\n------------------------------------------------------------------------\n')
+x=[0.1054,0.1091,0.2693,0.2703,0.3067,0.3088,0.4268,0.4284,0.5098,0.5139];
+e=[0.1027,0.1063,0.2513,0.2522,0.2832,0.2849,0.3792,0.3805,0.4398,0.4427]
+for i=1:10
+ 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))))
+end
+printf('\n\n\nExperimental result varying from calculated result')
\ No newline at end of file diff --git a/1332/CH3/EX3.1/3_1.pdf b/1332/CH3/EX3.1/3_1.pdf Binary files differnew file mode 100755 index 000000000..5fb36e07b --- /dev/null +++ b/1332/CH3/EX3.1/3_1.pdf diff --git a/1332/CH3/EX3.1/3_1.sce b/1332/CH3/EX3.1/3_1.sce new file mode 100755 index 000000000..b93f90907 --- /dev/null +++ b/1332/CH3/EX3.1/3_1.sce @@ -0,0 +1,7 @@ +//Example 3.1
+//Limiting Error
+//Page no. 45
+clc;clear;close;
+R=1000;
+e=0.1*1000; //limiting error calculation
+printf('Magnitude of the Resistor resistence (R) =\n%i <= R <= %i',R-e,R+e)
\ No newline at end of file diff --git a/1332/CH3/EX3.2/3_2.pdf b/1332/CH3/EX3.2/3_2.pdf Binary files differnew file mode 100755 index 000000000..fdc37ff6c --- /dev/null +++ b/1332/CH3/EX3.2/3_2.pdf diff --git a/1332/CH3/EX3.2/3_2.sce b/1332/CH3/EX3.2/3_2.sce new file mode 100755 index 000000000..190e4c51a --- /dev/null +++ b/1332/CH3/EX3.2/3_2.sce @@ -0,0 +1,10 @@ +//Example 3.2
+//Known Error
+//Page no. 46
+clc;clear;close;
+l=28;d=5;
+v=%pi*l*(d/2)^2;
+printf('\nVolume of Cylinder= %f cu. cm',v);
+re_d=0.1;re_l=-0.5;
+re_v=2*re_d+re_l; //relative error computation
+printf('\n\nRelative error in volume= %f %%',re_v);
\ No newline at end of file diff --git a/1332/CH3/EX3.3/3_3.pdf b/1332/CH3/EX3.3/3_3.pdf Binary files differnew file mode 100755 index 000000000..7350232f1 --- /dev/null +++ b/1332/CH3/EX3.3/3_3.pdf diff --git a/1332/CH3/EX3.3/3_3.sce b/1332/CH3/EX3.3/3_3.sce new file mode 100755 index 000000000..d08d13685 --- /dev/null +++ b/1332/CH3/EX3.3/3_3.sce @@ -0,0 +1,9 @@ +//Example 3.3
+//Absolute, Relative and Percetage Errors
+//Page no. 48
+clc;clear;close;
+x=0.00006;x1=0.00005;
+ex=x-x1; //absolute error
+Ex=ex/x1; //relative error
+px=100*Ex; //percentage error
+printf('\nAbsolute Error= %f\nRelative Error= %f\nPercentage Error= %f %%',ex,Ex,px);
\ No newline at end of file diff --git a/1332/CH3/EX3.4/3_4.pdf b/1332/CH3/EX3.4/3_4.pdf Binary files differnew file mode 100755 index 000000000..52f4c0922 --- /dev/null +++ b/1332/CH3/EX3.4/3_4.pdf diff --git a/1332/CH3/EX3.4/3_4.sce b/1332/CH3/EX3.4/3_4.sce new file mode 100755 index 000000000..a5e93860e --- /dev/null +++ b/1332/CH3/EX3.4/3_4.sce @@ -0,0 +1,9 @@ +//Example 3.4
+//Absolute, Relative and Percetage Errors
+//Page no. 48
+clc;clear;close;
+x=100500;x1=100000;
+ex=x-x1; //absolute error
+Ex=ex/x1; //relative error
+px=100*Ex; //percentage error
+printf('\nAbsolute Error= %f\nRelative Error= %f\nPercentage Error= %f %%',ex,Ex,px);
\ No newline at end of file diff --git a/1332/CH3/EX3.5/3_5.pdf b/1332/CH3/EX3.5/3_5.pdf Binary files differnew file mode 100755 index 000000000..dd8a9b6ac --- /dev/null +++ b/1332/CH3/EX3.5/3_5.pdf diff --git a/1332/CH3/EX3.5/3_5.sce b/1332/CH3/EX3.5/3_5.sce new file mode 100755 index 000000000..2f06e53be --- /dev/null +++ b/1332/CH3/EX3.5/3_5.sce @@ -0,0 +1,22 @@ +//Example 3.5
+//Absolute, Relative and Percentage Errors
+//Page no. 52
+clc;clear;close;
+x=9.12345;y=7.654321;
+x1=9.1234;y1=7.6543; //on a 5 decimal computer
+ex=x-x1; //absolute error of x
+ey=y-y1; //absolute error of y
+z1=x1+y1;
+printf('\nAbsolute Error in x= %f',ex);
+printf('\nAbsolute Error in y= %f',ey);
+printf('\nAddition on a 5 decimal computer yields= %.5g',z1);
+z2=16.777;
+printf('\nAbsolute Total Error= %f',x+y-z2);
+printf('\nAbsolute Propagated Error= %f',x+y-z1);
+printf('\nAbsolute Round-off Error= %.4g',z1-z2);
+printf('\nRealtive Total Error= %.4g',(x+y-z2)/(x+y));
+printf('\nRelative Propagated Error= %.2g',(x+y-z1)/(x+y));
+printf('\nRelative Round-off Error= %.3g',(z1-z2)/(x+y));
+printf('\nBound on the propagated relative error= %f',2*10^-4);
+printf('\nBound on the total relative error= %f',3*10^-4);
+printf('\nAs we can see that both the propagated and total relative error are less than their bound values')
\ No newline at end of file diff --git a/1332/CH4/EX4.1/4_1.pdf b/1332/CH4/EX4.1/4_1.pdf Binary files differnew file mode 100755 index 000000000..51e12ff00 --- /dev/null +++ b/1332/CH4/EX4.1/4_1.pdf diff --git a/1332/CH4/EX4.1/4_1.sce b/1332/CH4/EX4.1/4_1.sce new file mode 100755 index 000000000..9c11c9e4c --- /dev/null +++ b/1332/CH4/EX4.1/4_1.sce @@ -0,0 +1,11 @@ +//Example 4.1
+//Quadratic Equation
+//Page no. 96
+clc;clear;close;
+a=input("Enter value of a= ");
+b=input("Enter vlaue of b= ");
+c=input("Enter value of c= ");
+x1=(-1*b+sqrt((b^2)-4*a*c))/(2*a); //1st root
+x2=(-1*b-sqrt((b^2)-4*a*c))/(2*a); //2nd root
+printf('\n1st Root= %f', x1);
+printf('\n2nd Root= %f', x2);
\ No newline at end of file diff --git a/1332/CH4/EX4.2/4_2.PNG b/1332/CH4/EX4.2/4_2.PNG Binary files differnew file mode 100755 index 000000000..65c176946 --- /dev/null +++ b/1332/CH4/EX4.2/4_2.PNG diff --git a/1332/CH4/EX4.2/4_2.sce b/1332/CH4/EX4.2/4_2.sce new file mode 100755 index 000000000..91f5454f1 --- /dev/null +++ b/1332/CH4/EX4.2/4_2.sce @@ -0,0 +1,65 @@ +//Example 4.2
+//Database Management
+//Page no. 112
+clc;clear;close;
+M=[12,25,21,35;25,7,23,29;10,27,7,36;26,26,26,35;29,0,23,30]; //marks
+
+//calculation of composite score
+for i=1:5,
+ j=1;k=0;
+ max1=M(i,j);
+ if(max1<M(i,j+1))
+ max1=M(i,j+1)
+ else
+ k=1;
+ end,
+
+ if(M(i,j+2)>M(i,j+k))
+ max2=M(i,j+2);
+ else
+ max2=M(i,j);
+ end,
+ CS(i,1)=max1+max2+M(i,4);
+end
+
+I=['Reg. No.','Name of Students','Test 1','Test 2','Test 3','Final';
+'CS/01','C.V.Rajan','12','25','21','35';
+'CS/02','B.X.Roy','25','07','23','29';
+'CS/03','P.C.Sasikumar','10','27','07','36';
+'CS/04','B.D.Box','26','26','26','35';
+'CS/05','K.K.Mukherjee','29','0','23','30';]
+printf('\n')
+for i=1:6
+ for j=1:6
+ if(j>2)
+ printf('\t')
+ end
+
+ printf('%s ',I(i,j));
+ if(i~=1)
+ if(j>2)
+ printf('\t')
+ end
+ printf(' ')
+
+ end
+ if(i==1 & j==6)
+ printf('Composite Score\n')
+ end
+
+ end
+
+ if(i~=1)
+ printf('%i\n',CS(i-1,1));
+end
+
+end
+//disp(CS,'Composite Score',I);
+max1=CS(1,1);j=1;
+for i=2:5
+ if(max1<CS(i,1))
+ max1=CS(i,1);j=i;
+ end,
+end
+printf('\n\nTopper is:\n%s\t%s\t%s',I(1,1),I(1,2),'Composite Score')
+printf('\nCS/0%i\t\t%s\t\t\t%i',j,I(j+1,2),CS(j,1))
diff --git a/1332/CH5/EX5.1/5_1.pdf b/1332/CH5/EX5.1/5_1.pdf Binary files differnew file mode 100755 index 000000000..3faf82a61 --- /dev/null +++ b/1332/CH5/EX5.1/5_1.pdf diff --git a/1332/CH5/EX5.1/5_1.sce b/1332/CH5/EX5.1/5_1.sce new file mode 100755 index 000000000..4c69a1459 --- /dev/null +++ b/1332/CH5/EX5.1/5_1.sce @@ -0,0 +1,19 @@ +//Example 5.1
+//Bisection Method
+//Page no. 145
+clc;clear;close;
+deff('y=f(x)','y=2^x-3*x')
+x1=0;x2=2;e=0.001;i=0;
+printf('Iteration\tx1\t\tx2\t\tz\t\tf(z)\n')
+printf('--------------------------------------------------------------------------\n')
+while abs(x1-x2)>e
+ z=(x1+x2)/2
+ printf(' %i\t\t%f\t%f\t%f\t%f\n',i,x1,x2,z,f(z))
+ if f(z)*f(x1)>0
+ x1=z
+ else
+ x2=z
+ end
+ i=i+1
+end
+printf('\n\nThe solution of this equation is %g after %i Iterations',z,i-1)
\ No newline at end of file diff --git a/1332/CH5/EX5.10/5_10.pdf b/1332/CH5/EX5.10/5_10.pdf Binary files differnew file mode 100755 index 000000000..4914623a6 --- /dev/null +++ b/1332/CH5/EX5.10/5_10.pdf diff --git a/1332/CH5/EX5.10/5_10.sce b/1332/CH5/EX5.10/5_10.sce new file mode 100755 index 000000000..7a07d4d3e --- /dev/null +++ b/1332/CH5/EX5.10/5_10.sce @@ -0,0 +1,19 @@ +//Example 5.10
+//Newton Raphson Method
+//Page no. 167
+clc;clear;close;
+deff('x=f(x)','x=x*exp(-x)')
+deff('x=f1(x)','x=exp(-x)-x*exp(-x)')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=2;e=0.00001
+for i=1:11
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, this is not convergent (i.e.) divergent')
\ No newline at end of file diff --git a/1332/CH5/EX5.11/5_11.pdf b/1332/CH5/EX5.11/5_11.pdf Binary files differnew file mode 100755 index 000000000..e9150c8fd --- /dev/null +++ b/1332/CH5/EX5.11/5_11.pdf diff --git a/1332/CH5/EX5.11/5_11.sce b/1332/CH5/EX5.11/5_11.sce new file mode 100755 index 000000000..a0a01d169 --- /dev/null +++ b/1332/CH5/EX5.11/5_11.sce @@ -0,0 +1,19 @@ +//Example 5.11
+//Newton Raphson Method
+//Page no. 167
+clc;clear;close;
+deff('x=f(x)','x=x^3-x-3')
+deff('x=f1(x)','x=3*x^2-1')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=0;e=0.00001
+for i=1:11
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, it is cyclic in nature')
\ No newline at end of file diff --git a/1332/CH5/EX5.12/5_12.pdf b/1332/CH5/EX5.12/5_12.pdf Binary files differnew file mode 100755 index 000000000..961961434 --- /dev/null +++ b/1332/CH5/EX5.12/5_12.pdf diff --git a/1332/CH5/EX5.12/5_12.sce b/1332/CH5/EX5.12/5_12.sce new file mode 100755 index 000000000..26cf430f3 --- /dev/null +++ b/1332/CH5/EX5.12/5_12.sce @@ -0,0 +1,19 @@ +//Example 5.12
+//Newton Raphson Method
+//Page no. 168
+clc;clear;close;
+deff('x=f(x)','x=atan(x)')
+deff('x=f1(x)','x=1/(1+x^2)')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=1.45;e=0.00001
+for i=1:12
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ 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)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, it is divergent')
\ No newline at end of file diff --git a/1332/CH5/EX5.13/5_13.pdf b/1332/CH5/EX5.13/5_13.pdf Binary files differnew file mode 100755 index 000000000..5e45e08a9 --- /dev/null +++ b/1332/CH5/EX5.13/5_13.pdf diff --git a/1332/CH5/EX5.13/5_13.sce b/1332/CH5/EX5.13/5_13.sce new file mode 100755 index 000000000..b6ff7e146 --- /dev/null +++ b/1332/CH5/EX5.13/5_13.sce @@ -0,0 +1,20 @@ +//Example 5.13
+//Secant Method
+//Page no. 170
+clc;clear;close;
+deff('x=f(x)','x=exp(x)-3*x-sin(x)')
+deff('x=f1(x)','x=exp(x)-3-cos(x)')
+printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')
+printf('----------------------------------------------------------------------------------------------------------\n')
+x0=0.567123008;x1=1;e=0.00001
+for i=1:9
+ x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))
+ e1=abs(x0-x2)
+ 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)
+ x0=x1;
+ x1=x2
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, the root is %.10f',x2)
\ No newline at end of file diff --git a/1332/CH5/EX5.14/5_14.pdf b/1332/CH5/EX5.14/5_14.pdf Binary files differnew file mode 100755 index 000000000..5a24b9cf7 --- /dev/null +++ b/1332/CH5/EX5.14/5_14.pdf diff --git a/1332/CH5/EX5.14/5_14.sce b/1332/CH5/EX5.14/5_14.sce new file mode 100755 index 000000000..2a813d4a1 --- /dev/null +++ b/1332/CH5/EX5.14/5_14.sce @@ -0,0 +1,27 @@ +//Example 5.14
+//Kizner Method
+//Page no. 172
+clc;clear;close;
+h2=0.00001
+deff('x=f(x)','x=2*x-3-cos(x)')
+deff('y=f1(x,y)','y=h2/(-x+y)') //function for differentiation
+printf('n\th\tc\txn\t\tf(xn)\t\tF(xn)\t\tk1\t\t v\t\tXn+1\n')
+printf('--------------------------------------------------------------------------------------------------------------------\n')
+x0=2;e=0.00001;h=0.5;c=0.5;
+for i=1:11
+ h1=-f(x0);
+ F=f1(f(x0),f(x0+h2))
+ k1=h1*F/2;
+ v=h*f(x0)/(c*(f(x0+c+h)-f(x0+c)))-k1/c;
+ a=0;
+ for j=0:3
+ a=a+(v^j)/factorial(j+1)
+ end
+ x1=x0+k1*a
+ 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)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, the solution is %.10f',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.15/5_15.pdf b/1332/CH5/EX5.15/5_15.pdf Binary files differnew file mode 100755 index 000000000..4f35809f0 --- /dev/null +++ b/1332/CH5/EX5.15/5_15.pdf diff --git a/1332/CH5/EX5.15/5_15.sce b/1332/CH5/EX5.15/5_15.sce new file mode 100755 index 000000000..ad499d353 --- /dev/null +++ b/1332/CH5/EX5.15/5_15.sce @@ -0,0 +1,10 @@ +//Example 5.15
+//Brent Method
+//Page no. 173
+clc;clear;close;
+deff('y=f(x)','y=x^2+x-2')
+x1=0;x2=0.5;x3=2;
+r=f(x2)/f(x3);s=f(x2)/f(x1);t=f(x1)/f(x3);
+q=(t-1)*(r-1)*(s-1);
+p=r*t*(s-1)*(x2-x3)-s*(1-r)*(x2-x1)+(t*s-r)*x2
+printf('Root is : %.10g',x2+(p/q))
\ No newline at end of file diff --git a/1332/CH5/EX5.19/5_19.pdf b/1332/CH5/EX5.19/5_19.pdf Binary files differnew file mode 100755 index 000000000..78c87073c --- /dev/null +++ b/1332/CH5/EX5.19/5_19.pdf diff --git a/1332/CH5/EX5.19/5_19.sce b/1332/CH5/EX5.19/5_19.sce new file mode 100755 index 000000000..60f796ac9 --- /dev/null +++ b/1332/CH5/EX5.19/5_19.sce @@ -0,0 +1,35 @@ +//Example 5.19
+//Horner Method
+//Page no. 177
+clc;clear;close;
+deff('y=f(x,a1,a2,a3,a4)','y=a1*x^3+a2*x^2+a3*x+a4')
+
+k=1;m=2;
+a=[4;-13;-31;-275];
+for i=1:10
+ s=1;
+ si=f(s,a(1),a(2),a(3),a(4))*abs(1/f(s,a(1),a(2),a(3),a(4)))
+ while 1
+ a1=f(s,a(1),a(2),a(3),a(4))*abs(1/f(s,a(1),a(2),a(3),a(4)))
+ if si~=a1 then
+ d(i)=s-1
+ break
+ end
+ si=a1;
+ s=s+1;
+ end
+ b(1)=a(1)
+ for j=1:3
+ for k=1:4-j
+ b(k+1)=a(k+1)+b(k)*d(i)
+ a(k+1)=b(k+1)
+ end
+ end
+ for j=1:3
+ a(j+1)=10^j*a(j+1)
+ end
+end
+printf('The positive root is %i.',d(1))
+for i=2:10
+ printf('%i',d(i))
+end
\ No newline at end of file diff --git a/1332/CH5/EX5.2/5_2.pdf b/1332/CH5/EX5.2/5_2.pdf Binary files differnew file mode 100755 index 000000000..79ffe1433 --- /dev/null +++ b/1332/CH5/EX5.2/5_2.pdf diff --git a/1332/CH5/EX5.2/5_2.sce b/1332/CH5/EX5.2/5_2.sce new file mode 100755 index 000000000..3010f55ef --- /dev/null +++ b/1332/CH5/EX5.2/5_2.sce @@ -0,0 +1,21 @@ +//Example 5.2
+//Bisection Method
+//Page no. 147
+clc;clear;close;
+deff('y=f(x)','y=x^x-2*x+2')
+x1=0;x2=2;e=0.001;i=0;
+printf('Iteration\tx1\t\tx2\t\tz\t\tf(z)\n')
+printf('--------------------------------------------------------------------------\n')
+while abs(x1-x2)>e
+ z=(x1+x2)/2
+ printf(' %i\t\t%f\t%f\t%f\t%f\n',i,x1,x2,z,f(z))
+ if f(z)*f(x1)>0
+ x1=z
+ else
+ x2=z
+ end
+ i=i+1
+end
+printf('\n\nThe solution of this equation is %g after %i Iterations',z,i-1)
+
+printf('\n\n\nNote : There are computational errors in the answer given by the book for this example')
\ No newline at end of file diff --git a/1332/CH5/EX5.20/5_20.pdf b/1332/CH5/EX5.20/5_20.pdf Binary files differnew file mode 100755 index 000000000..9a55e133d --- /dev/null +++ b/1332/CH5/EX5.20/5_20.pdf diff --git a/1332/CH5/EX5.20/5_20.sce b/1332/CH5/EX5.20/5_20.sce new file mode 100755 index 000000000..0f4205644 --- /dev/null +++ b/1332/CH5/EX5.20/5_20.sce @@ -0,0 +1,18 @@ +//Example 5.20
+//Laguerre Method
+//Page no. 180
+clc;clear;close;
+deff('y=f(x)','y=x^3+x^2+10*x-20')
+deff('y=f1(x)','y=3*x^2+2*x+10')
+deff('y=f2(x)','y=6*x+2')
+n=3;
+printf('i\tn\txi\t\tP(x)\t\tP1(x)\t\tP2(x)\t\tProot\t\tNroot\n')
+printf('---------------------------------------------------------------------------------------------------------\n')
+xi=1
+for i=0:9
+ Proot=xi-(n*f(xi))/(f1(xi)+sqrt((n-1)*f1(xi)^2-n*f(xi)*f2(xi)))
+ Nroot=xi-(n*f(xi))/(f1(xi)-sqrt((n-1)*f1(xi)^2-n*f(xi)*f2(xi)))
+ 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)
+ xi=Proot
+end
+printf('\n\nProot = %f\n\nNroot = %f',Proot,Nroot)
\ No newline at end of file diff --git a/1332/CH5/EX5.21/5_21.pdf b/1332/CH5/EX5.21/5_21.pdf Binary files differnew file mode 100755 index 000000000..d242b0bc8 --- /dev/null +++ b/1332/CH5/EX5.21/5_21.pdf diff --git a/1332/CH5/EX5.21/5_21.sce b/1332/CH5/EX5.21/5_21.sce new file mode 100755 index 000000000..7036e50fc --- /dev/null +++ b/1332/CH5/EX5.21/5_21.sce @@ -0,0 +1,74 @@ +//Example 5.21
+//Mullers Method
+//Page no. 182
+clc;clear;close;
+
+deff('y=f(x)','y=x^3-x-4')
+zi=[1;2;3];
+s=["i","z2","z0","z1","f2","f0","f1","a0","a1","a2","zr+","zr-"]
+li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))
+hi(1)=zi(3,1)-zi(2,1);
+for i=2:6
+ for j=1:3
+ fz(j,i-1)=f(zi(j,i-1))
+ end
+ di(i-1)=1+li(i-1)
+ 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))
+ 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)))
+ 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)))
+ if abs(D1(i-1))>abs(D2(i-1)) then
+ li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)
+ else
+ li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)
+ end
+ hi(i)=li(i)*hi(i-1);
+ z(i-1)=zi(3,i-1)+hi(i)
+ for j=1:2
+ zi(j,i)=zi(j+1,i-1)
+ end
+ zi(3,i)=z(i-1)
+end
+for i=1:12
+ if i==1 then
+ printf(s(i))
+ for j=1:5
+ printf('\t\t\t%i',j-1)
+ end
+ elseif i<=4
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',zi(i-1,j))
+ end
+ elseif i<=7
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',fz(i-4,j))
+ end
+ elseif i<=8
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',li(j))
+ end
+ elseif i<=9
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',di(j))
+ end
+ elseif i<=10
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',gi(j))
+ end
+ elseif i<=11
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',z(j))
+ end
+ elseif i<=12
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',zi(j))
+ end
+ end
+end
+printf('\n\nAt the end of the %i iteration, the root of the equation is %.10f',j-2,z(j))
\ No newline at end of file diff --git a/1332/CH5/EX5.22/5_22.pdf b/1332/CH5/EX5.22/5_22.pdf Binary files differnew file mode 100755 index 000000000..45e59fc6f --- /dev/null +++ b/1332/CH5/EX5.22/5_22.pdf diff --git a/1332/CH5/EX5.22/5_22.sce b/1332/CH5/EX5.22/5_22.sce new file mode 100755 index 000000000..a22b96f4c --- /dev/null +++ b/1332/CH5/EX5.22/5_22.sce @@ -0,0 +1,94 @@ +//Example 5.22
+//Mullers Method
+//Page no. 183
+clc;clear;close;
+
+deff('y=f(x)','y=x^3-x-4')
+zi=[1;2;3];
+s=["i","z0","z1","z2","f0","f1","f2","li","di","gi","li+1","hi","hi+1","zi+1","D+","D_"]
+li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))
+hi(1)=zi(3,1)-zi(2,1);
+for i=2:6
+ for j=1:3
+ fz(j,i-1)=f(zi(j,i-1))
+ end
+ di(i-1)=1+li(i-1)
+ 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))
+ 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)))
+ 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)))
+ if abs(D1(i-1))>abs(D2(i-1)) then
+ li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)
+ else
+ li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)
+ end
+ hi(i)=li(i)*hi(i-1);
+ z(i-1)=zi(3,i-1)+hi(i)
+ for j=1:2
+ zi(j,i)=zi(j+1,i-1)
+ end
+ zi(3,i)=z(i-1)
+end
+for i=1:16
+ if i==1 then
+ printf(s(i))
+ for j=1:5
+ printf('\t\t\t%i',j-1)
+ end
+ elseif i<=4
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',zi(i-1,j))
+ end
+ elseif i<=7
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',fz(i-4,j))
+ end
+ elseif i<=8
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',li(j))
+ end
+ elseif i<=9
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',di(j))
+ end
+ elseif i<=10
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',gi(j))
+ end
+ elseif i<=11
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',li(j+1))
+ end
+ elseif i<=12
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',hi(j))
+ end
+ elseif i<=13
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',hi(j+1))
+ end
+ elseif i<=14
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',z(j))
+ end
+ elseif i<=15
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',D1(j))
+ end
+ elseif i<=16
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',D2(j))
+ end
+ end
+end
+printf('\n\nAt the end of the %ith iteration, the root of the equation is %.10f',j-1,z(j))
\ No newline at end of file diff --git a/1332/CH5/EX5.23/5_23.pdf b/1332/CH5/EX5.23/5_23.pdf Binary files differnew file mode 100755 index 000000000..1d39ffef1 --- /dev/null +++ b/1332/CH5/EX5.23/5_23.pdf diff --git a/1332/CH5/EX5.23/5_23.sce b/1332/CH5/EX5.23/5_23.sce new file mode 100755 index 000000000..5c33f2821 --- /dev/null +++ b/1332/CH5/EX5.23/5_23.sce @@ -0,0 +1,68 @@ +//Example 5.23
+//Bairstow Hitchcock Method
+//Page no. 187
+clc;clear;close;
+deff('y=f(x,p,q)','y=x^2+p*z+q')
+a=[1,-1,1,-1,1]
+a=a';a=[a,a,a,a,a]
+printf('Iteration-->')
+for i=1:5
+ printf('\t%i\t',i)
+end
+printf('\n------------------------------------------------------------------------------------------')
+p(1,1)=-1.2;q(1,1)=0.95;
+s=["b1","b2","b3","b4","c1","c2","c3","c4","c","dp","dq","p","q"]
+//s1=[b1;b2;b3;b4;c1;c2;c3;c4;c;dp;dq;p;q]
+for i=1:5
+ b(1,i)=0;b(2,i)=a(1,i);c(1,i)=0;c(2,i)=a(1,i);
+ for k=1:4
+ b(k+2,i)=a(k+1,i)-p(1,i)*b(k+1,i)-q(1,i)*b(k,i)
+ c(k+2,i)=b(k+2,i)-p(1,i)*c(k+1,i)-q(1,i)*c(k,i)
+ end
+ cb(1,i)=c(6,i)-b(6,i);
+ 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))
+ 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))
+ p(1,i+1)=p(1,i)+dp(1,i);q(1,i+1)=q(1,i)+dq(1,i);
+end
+for j=1:13
+ printf('\n %s\t\t',s(j))
+ if j<5 then
+ for i=1:5
+ printf('%.9f\t',b(j+2,i))
+ end
+ elseif j<9 then
+ for i=1:5
+ printf('%.9f\t',c(j-2,i))
+ end
+ elseif j<10
+ for i=1:5
+ printf('%.9f\t',cb(1,i))
+ end
+ elseif j<11
+ for i=1:5
+ printf('%.9f\t',dp(1,i))
+ end
+ elseif j<12
+ for i=1:5
+ printf('%.9f\t',dq(1,i))
+ end
+ elseif j<13
+ for i=1:5
+ printf('%.9f\t',p(1,i+1))
+ end
+ else
+ for i=1:5
+ printf('%.9f\t',q(1,i+1))
+ end
+ end
+end
+z=poly(0,'z');
+a=f(z,p(1,i+1),q(1,i+1));
+printf('\n\nRoots for Quadratic Equation Q = ')
+disp(a)
+a=roots(a)
+printf('\n\tare\n')
+disp(a(1))
+disp(a(2))
+
+
diff --git a/1332/CH5/EX5.24/5_24.pdf b/1332/CH5/EX5.24/5_24.pdf Binary files differnew file mode 100755 index 000000000..47ef683ec --- /dev/null +++ b/1332/CH5/EX5.24/5_24.pdf diff --git a/1332/CH5/EX5.24/5_24.sce b/1332/CH5/EX5.24/5_24.sce new file mode 100755 index 000000000..751300084 --- /dev/null +++ b/1332/CH5/EX5.24/5_24.sce @@ -0,0 +1,17 @@ +//Example 5.24
+//Bernoulli Method
+//Page no. 189
+clc;clear;close;
+
+a=[1,-8,-15,10];
+for i=1:2
+ c(i)=0;
+end
+c(3)=1;
+for k=4:13
+ c(k)=-(a(2)*c(k-1)+a(3)*c(k-2)+a(4)*c(k-3))
+ r(k-3)=c(k)/c(k-1)
+end
+disp(c,'Ck Values')
+disp(r,'Rk Values')
+disp(r(k-3),'Therefore the exact root is = ')
\ No newline at end of file diff --git a/1332/CH5/EX5.25/5_25.pdf b/1332/CH5/EX5.25/5_25.pdf Binary files differnew file mode 100755 index 000000000..f450f12e4 --- /dev/null +++ b/1332/CH5/EX5.25/5_25.pdf diff --git a/1332/CH5/EX5.25/5_25.sce b/1332/CH5/EX5.25/5_25.sce new file mode 100755 index 000000000..743154e9c --- /dev/null +++ b/1332/CH5/EX5.25/5_25.sce @@ -0,0 +1,27 @@ +//Example 5.25
+//Graeffe Method
+//Page no. 191
+clc;clear;close;
+
+a=[1,-6,11,-6]
+k=0;
+for k=2:6
+ for i=1:4
+ a(k,i)=(-1)^(i-1)*(a(k-1,i))^2
+ j=1;
+ while i+j<5 & i+j>2
+ a(k,i)=a(k,i)+(-1)^(i-j-1)*2*(a(k-1,i-j))*a(k-1,i+j)
+ break
+ j=j+1;
+ end
+ end
+end
+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')
+printf('\n----------------------------------------------------------------------------------------------------\n')
+for i=1:4
+ 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))))
+end
+for i=5:6
+ 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))))
+end
+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))))
\ No newline at end of file diff --git a/1332/CH5/EX5.26/5_26.pdf b/1332/CH5/EX5.26/5_26.pdf Binary files differnew file mode 100755 index 000000000..a17b1ae3f --- /dev/null +++ b/1332/CH5/EX5.26/5_26.pdf diff --git a/1332/CH5/EX5.26/5_26.sce b/1332/CH5/EX5.26/5_26.sce new file mode 100755 index 000000000..fad297cc0 --- /dev/null +++ b/1332/CH5/EX5.26/5_26.sce @@ -0,0 +1,36 @@ +//Example 5.26
+//QD Method
+//Page no. 194
+clc;clear;close;
+
+a=[32,-48,18,-1]
+for i=1:5
+ e(i,1)=0;
+ e(i,4)=0;
+end
+q(1,1)=-a(2)/a(1);
+q(1,2)=0;q(1,3)=0;
+e(1,2)=a(3)/a(2);
+e(1,3)=a(4)/a(3);
+for i=2:16
+ for j=1:3
+ q(i,j)=e(i-1,j+1)+q(i-1,j)-e(i-1,j)
+ end
+ for j=1:2
+ e(i,j+1)=e(i-1,j+1)*q(i,j+1)/q(i,j)
+ end
+end
+printf('e0\t\tq1\t\te1\t\tq2\t\te2\t\tq3\t\te3\n')
+printf('------------------------------------------------------------------------------------------------------------\n')
+for i=1:14
+ for j=1:3
+ printf('\t\t%.10f\t',q(i,j))
+ end
+ printf('\n')
+ for j=1:4
+ printf('%.10f\t\t\t',e(i,j))
+ end
+ printf('\n')
+end
+printf('\t\t%.10f\t\t\t%.10f\t\t\t%.10f\n',q(15,1),q(15,2),q(15,3))
+printf('\nThe exact roots are \t%.10f and %.10f',q(15,1),q(15,3))
\ No newline at end of file diff --git a/1332/CH5/EX5.27/5_27.pdf b/1332/CH5/EX5.27/5_27.pdf Binary files differnew file mode 100755 index 000000000..a1f8662a6 --- /dev/null +++ b/1332/CH5/EX5.27/5_27.pdf diff --git a/1332/CH5/EX5.27/5_27.sce b/1332/CH5/EX5.27/5_27.sce new file mode 100755 index 000000000..5d44737f8 --- /dev/null +++ b/1332/CH5/EX5.27/5_27.sce @@ -0,0 +1,15 @@ +//Example 5.27
+//Linear Iteration Method
+//Page no. 198
+clc;clear;close;
+
+deff('x=f(x)','x=20/(x^2+2*x+10)')
+printf('n\tx\t\tf(x)\n')
+printf('-------------------------------------\n')
+x=1;
+for i=1:19
+ printf(' %i\t%.10f\t%.10f\n',i,x,f(x))
+ x1=x;
+ x=f(x);
+end
+printf('\n\nx = %.10f',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.28/5_28.pdf b/1332/CH5/EX5.28/5_28.pdf Binary files differnew file mode 100755 index 000000000..95f5f26c8 --- /dev/null +++ b/1332/CH5/EX5.28/5_28.pdf diff --git a/1332/CH5/EX5.28/5_28.sce b/1332/CH5/EX5.28/5_28.sce new file mode 100755 index 000000000..2fae0c40d --- /dev/null +++ b/1332/CH5/EX5.28/5_28.sce @@ -0,0 +1,21 @@ +//Example 5.28
+//Aitkens Method
+//Page no. 199
+clc;clear;close;
+
+deff('x=f(x)','x=20/(x^2+2*x+10)')
+printf('n\tx0\t\tx1\t\tx2\t\tx3\t\ty\t\tdx0\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=1;e=0.0001
+for i=1:3
+ x1=f(x0);x2=f(x1);x3=f(x2);
+ y=x3-((x3-x2)^2)/(x3-2*x2+x1)
+ dx0=y-x0;
+
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i,x0,x1,x2,x3,y,dx0)
+ x0=y;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,y)
\ No newline at end of file diff --git a/1332/CH5/EX5.29/5_29.pdf b/1332/CH5/EX5.29/5_29.pdf Binary files differnew file mode 100755 index 000000000..f8b274aa9 --- /dev/null +++ b/1332/CH5/EX5.29/5_29.pdf diff --git a/1332/CH5/EX5.29/5_29.sce b/1332/CH5/EX5.29/5_29.sce new file mode 100755 index 000000000..b3a773470 --- /dev/null +++ b/1332/CH5/EX5.29/5_29.sce @@ -0,0 +1,19 @@ +//Example 5.29
+//Newton Raphson Method
+//Page no. 199
+clc;clear;close;
+deff('x=f(x)','x=x^3+2*x^2+10*x-20')
+deff('x=f1(x)','x=3*x^2+4*x+10')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=01;e=0.00001
+for i=1:4
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.3/5_3.pdf b/1332/CH5/EX5.3/5_3.pdf Binary files differnew file mode 100755 index 000000000..110fcdc54 --- /dev/null +++ b/1332/CH5/EX5.3/5_3.pdf diff --git a/1332/CH5/EX5.3/5_3.sce b/1332/CH5/EX5.3/5_3.sce new file mode 100755 index 000000000..ab213bd25 --- /dev/null +++ b/1332/CH5/EX5.3/5_3.sce @@ -0,0 +1,21 @@ +//Example 5.3
+//Regula Falsi Method
+//Page no. 149
+clc;clear;close;
+deff('y=f(x)','y=x^3-3*x-5')
+x1=2;x2=3;e=0.00001
+printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)')
+printf('\n-------------------------------------------------------------------------------------------------\n')
+for i=0:19
+ x3=x2*f(x1)/(f(x1)-f(x2))+x1*f(x2)/(f(x2)-f(x1))
+ 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))
+ if f(x1)*f(x3)>0 then
+ x1=x3
+ else
+ x2=x3
+ end
+ if abs(f(x3))<e then
+ break
+ end
+end
+printf('\n\nTherefore the solution is %.10g',x3)
\ No newline at end of file diff --git a/1332/CH5/EX5.31/5_31.pdf b/1332/CH5/EX5.31/5_31.pdf Binary files differnew file mode 100755 index 000000000..58e49e4ad --- /dev/null +++ b/1332/CH5/EX5.31/5_31.pdf diff --git a/1332/CH5/EX5.31/5_31.sce b/1332/CH5/EX5.31/5_31.sce new file mode 100755 index 000000000..8d8862140 --- /dev/null +++ b/1332/CH5/EX5.31/5_31.sce @@ -0,0 +1,19 @@ +//Example 5.31
+//Secant Method
+//Page no. 200
+clc;clear;close;
+deff('x=f(x)','x=(x-0.6)*(x-1.3)^2*(x-2)^3+0.01234*log(x)')
+printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')
+printf('----------------------------------------------------------------------------------------------------------\n')
+x0=0.1;x1=1.2;e=0.00001
+for i=1:7
+ x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))
+ e1=abs(x0-x2)
+ 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)
+ x0=x1;
+ x1=x2
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, the root is %.10f',x2)
\ No newline at end of file diff --git a/1332/CH5/EX5.32/5_32.pdf b/1332/CH5/EX5.32/5_32.pdf Binary files differnew file mode 100755 index 000000000..3a5b58bb6 --- /dev/null +++ b/1332/CH5/EX5.32/5_32.pdf diff --git a/1332/CH5/EX5.32/5_32.sce b/1332/CH5/EX5.32/5_32.sce new file mode 100755 index 000000000..d026ad75b --- /dev/null +++ b/1332/CH5/EX5.32/5_32.sce @@ -0,0 +1,130 @@ +//Example 5.32
+//Regula Falsi, Newton Raphson and Mullers Method
+//Page no. 201
+clc;clear;close;
+deff('x=f(x)','x=x^5-3.7*x^4+7.4*x^3-10.8*x^2+10.8*x-6.8')
+deff('x=f1(x)','x=5*x^4-4*3.7*x^3+3*7.4*x^2-21.6*x+10.8')
+//newton raphson
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=1.5;e=0.00001
+for i=1:4
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation by newton raphshon after %i Iterations is %.10f\n\n\n',i,x1)
+
+//regula falsi
+x1=1;x2=2;e=0.00001
+printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)')
+printf('\n-------------------------------------------------------------------------------------------------\n')
+for i=0:7
+ x3=x2*f(x1)/(f(x1)-f(x2))+x1*f(x2)/(f(x2)-f(x1))
+ 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))
+ if f(x1)*f(x3)>0 then
+ x1=x3
+ else
+ x2=x3
+ end
+ if abs(f(x3))<e then
+ break
+ end
+end
+printf('\n\nTherefore the solution by regula falsi method after %i iterations is %.10g',i,x3)
+
+//mullers method
+zi=[1;2;3];
+s=["i","z0","z1","z2","f0","f1","f2","li","di","gi","li+1","hi","hi+1","zi+1","D+","D_"]
+li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))
+hi(1)=zi(3,1)-zi(2,1);
+for i=2:6
+ for j=1:3
+ fz(j,i-1)=f(zi(j,i-1))
+ end
+ di(i-1)=1+li(i-1)
+ 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))
+ 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)))
+ 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)))
+ if abs(D1(i-1))>abs(D2(i-1)) then
+ li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)
+ else
+ li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)
+ end
+ hi(i)=li(i)*hi(i-1);
+ z(i-1)=zi(3,i-1)+hi(i)
+ for j=1:2
+ zi(j,i)=zi(j+1,i-1)
+ end
+ zi(3,i)=z(i-1)
+end
+printf('\n\n ')
+for i=1:16
+ if i==1 then
+ printf(s(i))
+ for j=1:5
+ printf('\t\t\t %i',j-1)
+ end
+ printf('\n----------------------------------------------------------------------------------------------------------------------------------')
+ elseif i<=4
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',zi(i-1,j))
+ end
+ elseif i<=7
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',fz(i-4,j))
+ end
+ elseif i<=8
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',li(j))
+ end
+ elseif i<=9
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',di(j))
+ end
+ elseif i<=10
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',gi(j))
+ end
+ elseif i<=11
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',li(j+1))
+ end
+ elseif i<=12
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',hi(j))
+ end
+ elseif i<=13
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',hi(j+1))
+ end
+ elseif i<=14
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',z(j))
+ end
+ elseif i<=15
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',D1(j))
+ end
+ elseif i<=16
+ printf('\n %s',s(i))
+ for j=1:5
+ printf('\t\t%.10f',D2(j))
+ end
+ end
+end
+printf('\n\nAt the end of the %ith iteration by mullers method, the root of the equation is %.10f',j-1,z(j))
\ No newline at end of file diff --git a/1332/CH5/EX5.33/5_33.pdf b/1332/CH5/EX5.33/5_33.pdf Binary files differnew file mode 100755 index 000000000..b529f0b0d --- /dev/null +++ b/1332/CH5/EX5.33/5_33.pdf diff --git a/1332/CH5/EX5.33/5_33.sce b/1332/CH5/EX5.33/5_33.sce new file mode 100755 index 000000000..0c3c93eaf --- /dev/null +++ b/1332/CH5/EX5.33/5_33.sce @@ -0,0 +1,49 @@ +//Example 5.33
+//Newton Raphson and Mullers Method
+//Page no. 202
+clc;clear;close;
+deff('x=f(x)','x=x^4-8*x^3+18*x^2+0.12*x-24.24')
+deff('x=f1(x)','x=4*x^3-24*x^2+36*x+0.12')
+
+//newton raphson
+x9=[1.5,2.5,2.7,3.1;4,5,14,10]
+for h=1:4
+ x0=x9(1,h);e=0.00001
+for i=1:x9(2,h)
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\nThe solution of this equation by newton raphshon after %i Iterations is %.5f\n',i,x1)
+end
+
+//mullers method
+zx=[1,2,2.7,3.1;2,3,3.7,4.1;3,4,4.7,5.1]
+zi=[1;2;3];
+s=["i","z0","z1","z2","f0","f1","f2","li","di","gi","li+1","hi","hi+1","zi+1","D+","D_"]
+li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))
+hi(1)=zi(3,1)-zi(2,1);
+for i=2:4
+ for j=1:3
+ fz(j,i-1)=f(zi(j,i-1))
+ end
+ di(i-1)=1+li(i-1)
+ 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))
+ 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)))
+ 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)))
+ if abs(D1(i-1))>abs(D2(i-1)) then
+ li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)
+ else
+ li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)
+ end
+ hi(i)=li(i)*hi(i-1);
+ z(i-1)=zi(3,i-1)+hi(i)
+ for j=1:2
+ zi(j,i)=zi(j+1,i-1)
+ end
+ zi(3,i)=z(i-1)
+end
+printf('\n\nAt the end of the %ith iteration by mullers method, the root of the equation is %.10f',j+2,z(j))
\ No newline at end of file diff --git a/1332/CH5/EX5.34/5_34.pdf b/1332/CH5/EX5.34/5_34.pdf Binary files differnew file mode 100755 index 000000000..84d494e09 --- /dev/null +++ b/1332/CH5/EX5.34/5_34.pdf diff --git a/1332/CH5/EX5.34/5_34.sce b/1332/CH5/EX5.34/5_34.sce new file mode 100755 index 000000000..e1ca08e04 --- /dev/null +++ b/1332/CH5/EX5.34/5_34.sce @@ -0,0 +1,35 @@ +//Example 5.34
+//QD Method
+//Page no. 202
+clc;clear;close;
+a=[1,2,10,-20]
+for i=1:5
+ e(i,1)=0;
+ e(i,4)=0;
+end
+q(1,1)=-a(2)/a(1);
+q(1,2)=0;q(1,3)=0;
+e(1,2)=a(3)/a(2);
+e(1,3)=a(4)/a(3);
+for i=2:7
+ for j=1:3
+ q(i,j)=e(i-1,j+1)+q(i-1,j)-e(i-1,j)
+ end
+ for j=1:2
+ e(i,j+1)=e(i-1,j+1)*q(i,j+1)/q(i,j)
+ end
+end
+printf('e0\t\tq1\t\te1\t\tq2\t\te2\t\tq3\t\te3\n')
+printf('------------------------------------------------------------------------------------------------------------\n')
+for i=1:7
+ for j=1:3
+ printf('\t\t%.10f\t',q(i,j))
+ end
+ printf('\n')
+ for j=1:4
+ printf('%.10f\t\t\t',e(i,j))
+ end
+ printf('\n')
+end
+printf('\t\t%.10f\t\t\t%.10f\t\t\t%.10f\n',q(7,1),q(7,2),q(7,3))
+printf('\nThe exact roots are \t%.10f and %.10f',q(7,1),q(7,3))
\ No newline at end of file diff --git a/1332/CH5/EX5.35/5_35.pdf b/1332/CH5/EX5.35/5_35.pdf Binary files differnew file mode 100755 index 000000000..0aa782cf9 --- /dev/null +++ b/1332/CH5/EX5.35/5_35.pdf diff --git a/1332/CH5/EX5.35/5_35.sce b/1332/CH5/EX5.35/5_35.sce new file mode 100755 index 000000000..19086449b --- /dev/null +++ b/1332/CH5/EX5.35/5_35.sce @@ -0,0 +1,20 @@ +//Example 5.35
+//Newton Raphson Method
+//Page no. 203
+clc;clear;close;
+deff('x=f(x)','x=x^3-30*x^2+2552')
+deff('x=f1(x)','x=3*x^2-60*x')
+//newton raphson
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=10;e=0.00001
+for i=1:4
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThus the ball is submerged upto height of %.10f cm\n\n\n',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.36/5_36.pdf b/1332/CH5/EX5.36/5_36.pdf Binary files differnew file mode 100755 index 000000000..a19947337 --- /dev/null +++ b/1332/CH5/EX5.36/5_36.pdf diff --git a/1332/CH5/EX5.36/5_36.sce b/1332/CH5/EX5.36/5_36.sce new file mode 100755 index 000000000..0b5f55921 --- /dev/null +++ b/1332/CH5/EX5.36/5_36.sce @@ -0,0 +1,21 @@ +//Example 5.36
+//Secant Method
+//Page no. 204
+clc;clear;close;
+a=8670;c=10^-8;t2=1.4*10^-4;
+deff('x=f(x)','x=-t2+log((1-2*x/a)/(2-x/a))*(a*x*c)/(a+x)')
+
+printf('n\txn\t\tf(xn)\t\tXn+1\t\tf(Xn+1)\t\tXn+2\t\tError\n')
+printf('----------------------------------------------------------------------------------------------------------\n')
+x0=20000;x1=25000;e=0.00001
+for i=1:8
+ x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0))
+ e1=abs(x0-x2)
+ 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)
+ x0=x1;
+ x1=x2
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, Rb = %.10f ohm',x2)
\ No newline at end of file diff --git a/1332/CH5/EX5.37/5_37.pdf b/1332/CH5/EX5.37/5_37.pdf Binary files differnew file mode 100755 index 000000000..0cb884abe --- /dev/null +++ b/1332/CH5/EX5.37/5_37.pdf diff --git a/1332/CH5/EX5.37/5_37.sce b/1332/CH5/EX5.37/5_37.sce new file mode 100755 index 000000000..6a5dd99a3 --- /dev/null +++ b/1332/CH5/EX5.37/5_37.sce @@ -0,0 +1,20 @@ +//Example 5.37
+//Newton Raphson Method
+//Page no. 204
+clc;clear;close;
+p=1.1;T=250;R=0.082;a=3.6;b=0.043;
+deff('y=f(v)','y=p*v^3-(b*p+R*T)*v^2+a*v-a*b')
+deff('y=f1(v)','y=3*p*v^2-2*(b*p+R*T)*v')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=0.1;e=0.00001
+for i=1:10
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, Volume v = %.10f ltr',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.38/5_38.pdf b/1332/CH5/EX5.38/5_38.pdf Binary files differnew file mode 100755 index 000000000..812122e1e --- /dev/null +++ b/1332/CH5/EX5.38/5_38.pdf diff --git a/1332/CH5/EX5.38/5_38.sce b/1332/CH5/EX5.38/5_38.sce new file mode 100755 index 000000000..5706e0a48 --- /dev/null +++ b/1332/CH5/EX5.38/5_38.sce @@ -0,0 +1,19 @@ +//Example 5.38
+//Newton Raphson Method
+//Page no. 205
+clc;clear;close;
+deff('y=f(p)','y=p^3-9*p^2+33*p-65')
+deff('y=f1(p)','y=3*p^2-18*p+33')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=6;e=0.00001
+for i=1:10
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, Market Price at equilibrium = Rs. %.f',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.39/5_39.pdf b/1332/CH5/EX5.39/5_39.pdf Binary files differnew file mode 100755 index 000000000..58e872d80 --- /dev/null +++ b/1332/CH5/EX5.39/5_39.pdf diff --git a/1332/CH5/EX5.39/5_39.sce b/1332/CH5/EX5.39/5_39.sce new file mode 100755 index 000000000..c1f0fa6ef --- /dev/null +++ b/1332/CH5/EX5.39/5_39.sce @@ -0,0 +1,19 @@ +//Example 5.39
+//Newton Raphson Method
+//Page no. 205
+clc;clear;close;
+deff('y=f(v)','y=v^3-20*v+30')
+deff('y=f1(v)','y=3*v^2-20')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=10;e=0.00001
+for i=1:10
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, sides are = %.5f m x %.5f m x %.5f m',x1,x1,20/x1^2)
\ No newline at end of file diff --git a/1332/CH5/EX5.4/5_4.pdf b/1332/CH5/EX5.4/5_4.pdf Binary files differnew file mode 100755 index 000000000..994484bfe --- /dev/null +++ b/1332/CH5/EX5.4/5_4.pdf diff --git a/1332/CH5/EX5.4/5_4.sce b/1332/CH5/EX5.4/5_4.sce new file mode 100755 index 000000000..c4e4e4c5b --- /dev/null +++ b/1332/CH5/EX5.4/5_4.sce @@ -0,0 +1,25 @@ +//Example 5.4
+//Ridders Method
+//Page no. 153
+clc;clear;close;
+deff('y=f(x)','y=x^3-3*x-5')
+x1=2;x2=3;e=0.00001
+printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)\t sign\t x4')
+printf('\n----------------------------------------------------------------------------------------------------------\n')
+for i=0:8
+ x3=(x1+x2)/2
+ a=f(x1)-f(x2);
+ s=a*abs(1/a)
+ x4=x3+(x3-x2)*(s*f(x3))/sqrt(f(x3)-f(x1)*f(x2))
+ 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)
+ if f(x1)*f(x4)>0 then
+ x1=x4
+ else
+ x2=x4
+ end
+ if abs(f(x4))<e then
+ break
+ end
+end
+printf('\n\nThe solution of this equation is %g after %i Iterations',x4,i)
+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)')
\ No newline at end of file diff --git a/1332/CH5/EX5.40/5_40.pdf b/1332/CH5/EX5.40/5_40.pdf Binary files differnew file mode 100755 index 000000000..6c2359682 --- /dev/null +++ b/1332/CH5/EX5.40/5_40.pdf diff --git a/1332/CH5/EX5.40/5_40.sce b/1332/CH5/EX5.40/5_40.sce new file mode 100755 index 000000000..603a871ec --- /dev/null +++ b/1332/CH5/EX5.40/5_40.sce @@ -0,0 +1,19 @@ +//Example 5.40
+//Newton Raphson Method
+//Page no. 206
+clc;clear;close;
+deff('y=f(F)','y=-10*F^3-21*F+10')
+deff('y=f1(F)','y=-21-30*F^2')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=1;e=0.00001
+for i=1:10
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.6f\t%.5f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\t\t\t\t\t2\n Therefore, Magnetic Flux = %.5f Wb m',x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.5/5_5.pdf b/1332/CH5/EX5.5/5_5.pdf Binary files differnew file mode 100755 index 000000000..60408a895 --- /dev/null +++ b/1332/CH5/EX5.5/5_5.pdf diff --git a/1332/CH5/EX5.5/5_5.sce b/1332/CH5/EX5.5/5_5.sce new file mode 100755 index 000000000..a9426ea36 --- /dev/null +++ b/1332/CH5/EX5.5/5_5.sce @@ -0,0 +1,13 @@ +//Example 5.5
+//General Iterative Method
+//Page no. 154
+clc;clear;close;
+deff('x=f(x)','x=sqrt(3+5/x)')
+printf('n\tx\t\tf(x)\n')
+printf('------------------------------------\n')
+x=2;
+for i=1:8
+ printf(' %i\t%.10f\t%.10f\n',i,x,f(x))
+ x=f(x);
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x)
\ No newline at end of file diff --git a/1332/CH5/EX5.6/5_6.pdf b/1332/CH5/EX5.6/5_6.pdf Binary files differnew file mode 100755 index 000000000..bde612cfa --- /dev/null +++ b/1332/CH5/EX5.6/5_6.pdf diff --git a/1332/CH5/EX5.6/5_6.sce b/1332/CH5/EX5.6/5_6.sce new file mode 100755 index 000000000..c3488c540 --- /dev/null +++ b/1332/CH5/EX5.6/5_6.sce @@ -0,0 +1,13 @@ +//Example 5.6
+//Linear Iterative Method
+//Page no. 159
+clc;clear;close;
+deff('x=f(x)','x=1+sin(x)/10')
+printf('n\tx\t\tf(x)\n')
+printf('-------------------------------------\n')
+x=0;
+for i=1:7
+ printf(' %i\t%.10f\t%.10f\n',i,x,f(x))
+ x=f(x);
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x)
\ No newline at end of file diff --git a/1332/CH5/EX5.7/5_7.pdf b/1332/CH5/EX5.7/5_7.pdf Binary files differnew file mode 100755 index 000000000..f0152c41b --- /dev/null +++ b/1332/CH5/EX5.7/5_7.pdf diff --git a/1332/CH5/EX5.7/5_7.sce b/1332/CH5/EX5.7/5_7.sce new file mode 100755 index 000000000..94a830d62 --- /dev/null +++ b/1332/CH5/EX5.7/5_7.sce @@ -0,0 +1,20 @@ +//Example 5.7
+//Aitkens Method
+//Page no. 161
+clc;clear;close;
+deff('x=f(x)','x=exp(-x)')
+printf('n\tx0\t\tx1\t\tx2\t\tx3\t\ty\t\tdx0\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=0.5;e=0.0001
+for i=1:3
+ x1=f(x0);x2=f(x1);x3=f(x2);
+ y=x3-((x3-x2)^2)/(x3-2*x2+x1)
+ dx0=y-x0;
+
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i,x0,x1,x2,x3,y,dx0)
+ x0=y;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,y)
\ No newline at end of file diff --git a/1332/CH5/EX5.8/5_8.pdf b/1332/CH5/EX5.8/5_8.pdf Binary files differnew file mode 100755 index 000000000..e9f76d403 --- /dev/null +++ b/1332/CH5/EX5.8/5_8.pdf diff --git a/1332/CH5/EX5.8/5_8.sce b/1332/CH5/EX5.8/5_8.sce new file mode 100755 index 000000000..3274e687d --- /dev/null +++ b/1332/CH5/EX5.8/5_8.sce @@ -0,0 +1,19 @@ +//Example 5.8
+//Newton Raphson Method
+//Page no. 163
+clc;clear;close;
+deff('x=f(x)','x=x-exp(-x)')
+deff('x=f1(x)','x=1+exp(-x)')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=0.5;e=0.00001
+for i=1:4
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nThe solution of this equation after %i Iterations is %.10f',i,x1)
\ No newline at end of file diff --git a/1332/CH5/EX5.9/5_9.pdf b/1332/CH5/EX5.9/5_9.pdf Binary files differnew file mode 100755 index 000000000..ea228017a --- /dev/null +++ b/1332/CH5/EX5.9/5_9.pdf diff --git a/1332/CH5/EX5.9/5_9.sce b/1332/CH5/EX5.9/5_9.sce new file mode 100755 index 000000000..976a1d5af --- /dev/null +++ b/1332/CH5/EX5.9/5_9.sce @@ -0,0 +1,19 @@ +//Example 5.9
+//Modified Newton Raphson Method
+//Page no. 165
+clc;clear;close;
+deff('x=f(x)','x=exp(x)-3*x-sin(x)')
+deff('x=f1(x)','x=exp(x)-3-cos(x)')
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=0;e=0.00001
+for i=1:4
+ x1=x0-f(x0)/f1(x0)
+ e1=abs(x0-x1)
+ printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+ x0=x1;
+ if abs(x0)<e then
+ break;
+ end
+end
+printf('\n\nTherefore, the root is %.10f',x1)
\ No newline at end of file diff --git a/1332/CH6/EX6.1/6_1.pdf b/1332/CH6/EX6.1/6_1.pdf Binary files differnew file mode 100755 index 000000000..2553b87f9 --- /dev/null +++ b/1332/CH6/EX6.1/6_1.pdf diff --git a/1332/CH6/EX6.1/6_1.sce b/1332/CH6/EX6.1/6_1.sce new file mode 100755 index 000000000..a80a928f1 --- /dev/null +++ b/1332/CH6/EX6.1/6_1.sce @@ -0,0 +1,26 @@ +//Example 6.1
+//Gaussian Elimination Method
+//Page no. 220
+clc;clear;close;
+
+A=[5,10,1,28;1,1,1,6;4,8,3,29]; //augmented matrix
+
+//triangularization
+for i=1:4
+ B(1,i)=A(1,i)
+ B(2,i)=A(2,i)-(A(2,1)/A(1,1))*A(1,i)
+ B(3,i)=A(3,i)-(A(3,1)/A(1,1))*A(1,i)
+end
+disp(A,'Augmented Matrix=')
+disp(B,'Triangulated Matrix=')
+//back substitution
+x(3)=B(3,4)/B(3,3);
+printf('\nx(3)=%f\n',x(3))
+for i=2:-1:1
+ k=0
+ for j=i+1:3
+ k=k+B(i,j)*x(j)
+ end
+ x(i)=(1/B(i,i))*(B(i,4)-k)
+ printf('\nx(%i)=%f\n',i,x(i))
+end
diff --git a/1332/CH6/EX6.10/6_10.pdf b/1332/CH6/EX6.10/6_10.pdf Binary files differnew file mode 100755 index 000000000..e9a913dae --- /dev/null +++ b/1332/CH6/EX6.10/6_10.pdf diff --git a/1332/CH6/EX6.10/6_10.sce b/1332/CH6/EX6.10/6_10.sce new file mode 100755 index 000000000..91de51dfb --- /dev/null +++ b/1332/CH6/EX6.10/6_10.sce @@ -0,0 +1,15 @@ +//Example 6.10
+//Solving Matrices
+//Page no. 244
+clc;close;clear;
+warning('off')
+for i=1:7
+ s=0;
+ for j=1:7
+ A(i,j)=360360/(i+j)
+ end
+ B(i,1)=1;
+end
+X=inv(A)*B
+disp(360360*X,'The Solution by 360360*X= ')
+disp(X,'Final Solution = ')
\ No newline at end of file diff --git a/1332/CH6/EX6.2/6_2.pdf b/1332/CH6/EX6.2/6_2.pdf Binary files differnew file mode 100755 index 000000000..11f6ecb69 --- /dev/null +++ b/1332/CH6/EX6.2/6_2.pdf diff --git a/1332/CH6/EX6.2/6_2.sce b/1332/CH6/EX6.2/6_2.sce new file mode 100755 index 000000000..ee9f8db93 --- /dev/null +++ b/1332/CH6/EX6.2/6_2.sce @@ -0,0 +1,33 @@ +//Example 6.2
+//Gaussian Elimination Method for Tri-Diagonal System
+//Page no. 222
+clc;clear;close;
+
+//equation matrix
+A=[1,2,0,0;2,3,-1,0;0,4,2,3;0,0,2,-1];
+K=[5;5;11;10];i=1;
+
+//initialization
+w(1)=A(1,2)/A(1,1);
+g(1)=K(1)/A(1,1);
+printf('\nw(%i)=%f',i,w(i));printf('\ng(%i)=%f',i,g(i))
+
+//computation
+for i=2:3
+ w(i)=(A(i,i+1))/(A(i,i)-A(i,i-1)*w(i-1))
+ g(i)=(K(i)-A(i,i-1)*g(i-1))/(A(i,i)-A(i,i-1)*w(i-1))
+ printf('\nw(%i)=%f',i,w(i))
+ printf('\ng(%i)=%f',i,g(i))
+end
+i=4
+m=-2
+g(i)=m*(K(i)-A(i,i-1)*g(i-1))/(A(i,i)-A(i,i-1)*w(i-1))
+x(i)=g(i)
+printf('\ng(%i)=%f',i,g(i))
+printf('\n\nx(%i)=%f',i,x(i))
+
+//solution
+for i=3:-1:1
+ x(i)=g(i)-w(i)*x(i+1)
+ printf('\n\nx(%i)=%f',i,x(i))
+end
\ No newline at end of file diff --git a/1332/CH6/EX6.3/6_3.pdf b/1332/CH6/EX6.3/6_3.pdf Binary files differnew file mode 100755 index 000000000..32610d338 --- /dev/null +++ b/1332/CH6/EX6.3/6_3.pdf diff --git a/1332/CH6/EX6.3/6_3.sce b/1332/CH6/EX6.3/6_3.sce new file mode 100755 index 000000000..db2d658fe --- /dev/null +++ b/1332/CH6/EX6.3/6_3.sce @@ -0,0 +1,39 @@ +//Example 6.3
+//Gauss-Jordan Method
+//Page no. 224
+
+clc;clear;close;
+
+A=[5,10,1,28;4,8,3,29;1,1,1,6]; //augmented matrix
+
+for i=1:3
+ j=i
+ while (A(i,i)==0 & j<=3)
+ for k=1:4
+ B(1,k)=A(j+1,k)
+ A(j+1,k)=A(i,k)
+ A(i,k)=B(1,k)
+ end
+ disp(A)
+ j=j+1
+ end
+ disp(A)
+ for k=4:-1:i
+ A(i,k)=A(i,k)/A(i,i)
+ end
+ disp(A)
+ for k=1:3
+ if(k~=i) then
+ l=A(k,i)/A(i,i)
+ for m=i:4
+ A(k,m)=A(k,m)-l*A(i,m)
+ end
+ end
+
+ end
+ disp(A)
+end
+
+for i=1:3
+ printf('\nx(%i) = %g\n',i,A(i,4))
+end
\ No newline at end of file diff --git a/1332/CH6/EX6.4/6_4.pdf b/1332/CH6/EX6.4/6_4.pdf Binary files differnew file mode 100755 index 000000000..ba6bfc19b --- /dev/null +++ b/1332/CH6/EX6.4/6_4.pdf diff --git a/1332/CH6/EX6.4/6_4.sce b/1332/CH6/EX6.4/6_4.sce new file mode 100755 index 000000000..0371796a7 --- /dev/null +++ b/1332/CH6/EX6.4/6_4.sce @@ -0,0 +1,26 @@ +//Example 6.4
+//Gaussian Elimination Method without Pivoting
+//Page no. 227
+clc;clear;close;
+
+A=[0.3*10^-11,1,0.7;1,1,0.9]; //augmented matrix
+
+//triangularization
+for i=1:3
+ B(1,i)=A(1,i)
+ B(2,i)=A(2,i)-(A(2,1)/A(1,1))*A(1,i)
+end
+disp(A,'Augmented Matrix=')
+disp(B,'Triangulated Matrix=')
+
+//back substitution
+x(2)=B(2,3)/B(2,2);
+printf('\nx(2)=%f\n',x(2))
+for i=1:-1:1
+ k=0
+ for j=i+1:2
+ k=k+B(i,j)*x(j)
+ end
+ x(i)=(1/B(i,i))*(B(i,3)-k)
+ printf('\nx(%i)=%f\n',i,x(i))
+end
diff --git a/1332/CH6/EX6.5/6_5.pdf b/1332/CH6/EX6.5/6_5.pdf Binary files differnew file mode 100755 index 000000000..571664a3b --- /dev/null +++ b/1332/CH6/EX6.5/6_5.pdf diff --git a/1332/CH6/EX6.5/6_5.sce b/1332/CH6/EX6.5/6_5.sce new file mode 100755 index 000000000..c8db77c99 --- /dev/null +++ b/1332/CH6/EX6.5/6_5.sce @@ -0,0 +1,48 @@ +//Example 6.5
+//Dolittle Factorization Method
+//Page no. 233
+clc;clear;close;
+
+A=[2,1,1;1,3,1;1,1,4];
+printf('\tL\t\t *\t\tU\t\t =\t\tA')
+U(2,1)=0;U(3,1)=0;U(3,2)=0;
+L(1,2)=0;L(1,3)=0;L(2,3)=0;
+for i=1:3
+ L(i,i)=1
+end
+for i=1:3
+ U(1,i)=A(1,i)
+end
+L(2,1)=1/U(1,1);
+for i=2:3
+ U(2,i)=A(2,i)-U(1,i)*L(2,1);
+end
+L(3,1)=1/U(1,1);
+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);
+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);
+printf('\n')
+for i=1:3
+ for j=1:3
+ printf('%.2f\t',L(i,j))
+ end
+
+ if(i==2)
+ printf(' * ')
+ else
+ printf('\t')
+ end
+
+ for j=1:3
+ printf('%.2f\t',U(i,j))
+ end
+ if(i==2)
+ printf(' = ')
+ else
+ printf('\t')
+ end
+ for j=1:3
+ printf('%.2f\t',A(i,j))
+ end
+ printf('\n')
+end
+
diff --git a/1332/CH6/EX6.6/6_6.pdf b/1332/CH6/EX6.6/6_6.pdf Binary files differnew file mode 100755 index 000000000..3c26c2a45 --- /dev/null +++ b/1332/CH6/EX6.6/6_6.pdf diff --git a/1332/CH6/EX6.6/6_6.sce b/1332/CH6/EX6.6/6_6.sce new file mode 100755 index 000000000..7d5914fd3 --- /dev/null +++ b/1332/CH6/EX6.6/6_6.sce @@ -0,0 +1,56 @@ +//Example 6.6
+//Trangularization Method
+//Page no. 236
+clc;clear;close;
+
+A=[2,1,1;1,3,1;1,1,4];
+B=[7;10;15];
+printf('A can be factorizaed as follows:\n')
+printf('\tL\t\t *\t\tU\t\t =\t\tA')
+U(2,1)=0;U(3,1)=0;U(3,2)=0;
+L(1,2)=0;L(1,3)=0;L(2,3)=0;
+for i=1:3
+ L(i,i)=1
+end
+for i=1:3
+ U(1,i)=A(1,i)
+end
+L(2,1)=1/U(1,1);
+for i=2:3
+ U(2,i)=A(2,i)-U(1,i)*L(2,1);
+end
+L(3,1)=1/U(1,1);
+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);
+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);
+printf('\n')
+for i=1:3
+ for j=1:3
+ printf('%.2f\t',L(i,j))
+ end
+
+ if(i==2)
+ printf(' * ')
+ else
+ printf('\t')
+ end
+
+ for j=1:3
+ printf('%.2f\t',U(i,j))
+ end
+ if(i==2)
+ printf(' = ')
+ else
+ printf('\t')
+ end
+ for j=1:3
+ printf('%.2f\t',A(i,j))
+ end
+ printf('\n')
+end
+printf('\nY=U*X')
+ Y=inv(L)*B
+ X=inv(U)*Y
+printf('\n\nX=')
+for i=1:3
+ printf('\n %i',X(i,1))
+end
\ No newline at end of file diff --git a/1332/CH6/EX6.7/6_7.pdf b/1332/CH6/EX6.7/6_7.pdf Binary files differnew file mode 100755 index 000000000..eb7150c70 --- /dev/null +++ b/1332/CH6/EX6.7/6_7.pdf diff --git a/1332/CH6/EX6.7/6_7.sce b/1332/CH6/EX6.7/6_7.sce new file mode 100755 index 000000000..54da84f31 --- /dev/null +++ b/1332/CH6/EX6.7/6_7.sce @@ -0,0 +1,9 @@ +//Example 6.7
+//Wilkinson Method
+//Page no. 240
+clc;clear;close;
+
+A=[0.3*10^5,0.212,0.332;0.216,0.376,0.477;0.173,0.663,0.626];
+B=[0.235;0.128;0.285];
+X=inv(A)
+disp(X*B,'Final Solution = ')
\ No newline at end of file diff --git a/1332/CH6/EX6.8/6_8.pdf b/1332/CH6/EX6.8/6_8.pdf Binary files differnew file mode 100755 index 000000000..ea9170177 --- /dev/null +++ b/1332/CH6/EX6.8/6_8.pdf diff --git a/1332/CH6/EX6.8/6_8.sce b/1332/CH6/EX6.8/6_8.sce new file mode 100755 index 000000000..bec1d1835 --- /dev/null +++ b/1332/CH6/EX6.8/6_8.sce @@ -0,0 +1,26 @@ +//Example 6.8
+//Cholesky's Factorization
+//Page no. 243
+clc;clear;close;
+
+A=[1,2,3;2,5,8;3,8,22];
+U(2,1)=0;U(3,1)=0;U(3,2)=0;
+for i=1:3
+ for j=1:3
+ if(i==j)
+ k=0;
+ for m=1:i-1
+ k=k+U(m,i)^2;
+ end
+ U(i,j)=sqrt(A(i,j)-k)
+ end
+ if(j>i)
+ k=0;
+ for m=1:i-1
+ k=k+U(m,j)*U(m,i);
+ end
+ U(i,j)=(A(i,j)-k)/U(i,i)
+ end
+ end
+end
+disp(U,'Required Matrix (U)=')
\ No newline at end of file diff --git a/1332/CH6/EX6.9/6_9.pdf b/1332/CH6/EX6.9/6_9.pdf Binary files differnew file mode 100755 index 000000000..7873dc648 --- /dev/null +++ b/1332/CH6/EX6.9/6_9.pdf diff --git a/1332/CH6/EX6.9/6_9.sce b/1332/CH6/EX6.9/6_9.sce new file mode 100755 index 000000000..30679323f --- /dev/null +++ b/1332/CH6/EX6.9/6_9.sce @@ -0,0 +1,15 @@ +//Example 6.9
+//Complex System of Linear Equation
+//Page no. 244
+clc;clear;close;
+
+for i=1:7
+ s=0;
+ for j=1:7
+ A(i,j)=j^i
+ s=s+(-1)^(j+1)*A(i,j)
+ end
+ B(i,1)=s;
+end
+X=inv(A)*B
+disp(X,'The Solution = ')
diff --git a/1332/CH7/EX7.1/7_1.pdf b/1332/CH7/EX7.1/7_1.pdf Binary files differnew file mode 100755 index 000000000..5ced7521c --- /dev/null +++ b/1332/CH7/EX7.1/7_1.pdf diff --git a/1332/CH7/EX7.1/7_1.sce b/1332/CH7/EX7.1/7_1.sce new file mode 100755 index 000000000..007544335 --- /dev/null +++ b/1332/CH7/EX7.1/7_1.sce @@ -0,0 +1,152 @@ +//Example 7.1
+//Gauss-Jordan Two Array Method
+//Page no. 254
+clc;clear;close;
+
+A=[2,6,1;3,9,2;0,-1,3]; //matrix
+C=eye(3,3); //Unit Matrix
+for i=1:3 //interchange of row 1 and 2
+ B(1,i)=A(1,i);
+ A(1,i)=A(2,i);
+ A(2,i)=B(1,i);
+ B(2,i)=C(1,i);
+ C(1,i)=C(2,i);
+ C(2,i)=B(2,i);
+end
+printf('\n')
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+
+for i=1:3
+ A(1,i)=A(1,i)/3;
+ C(1,i)=C(1,i)/3;
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+for i=1:3
+ A(2,i)=A(2,i)-2*A(1,i);
+ C(2,i)=C(2,i)-2*C(1,i);
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+for i=1:3 //interchange of row 2 and 3
+ B(1,i)=A(2,i);
+ A(2,i)=A(3,i);
+ A(3,i)=B(1,i);
+ B(2,i)=C(2,i);
+ C(2,i)=C(3,i);
+ C(3,i)=B(2,i);
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+for i=1:3
+ A(2,i)=-1*A(2,i);
+ C(2,i)=-1*C(2,i);
+end
+for i=1:3
+ A(1,i)=A(1,i)-3*A(2,i);
+ C(1,i)=C(1,i)-3*C(2,i);
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+for i=1:3
+ A(3,i)=-3*A(3,i);
+ C(3,i)=-3*C(3,i);
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+for i=1:3
+ A(1,i)=A(1,i)-A(3,i)*(29/3);
+ C(1,i)=C(1,i)-29*C(3,i)/3;
+end
+for i=1:3
+ A(2,i)=A(2,i)+A(3,i)*3;
+ C(2,i)=C(2,i)+C(3,i)*3;
+end
+
+//printing of matrices A and C
+for i=1:3
+ for j=1:3
+ printf('%f\t',A(i,j))
+ end
+ printf('|\t');
+ for j=1:3
+ printf('%f\t',C(i,j))
+ end
+ printf('\n')
+end
+printf('\n\n');
+
+disp(C,'Inverse Matrix of A')
\ No newline at end of file diff --git a/1332/CH7/EX7.2/7_2.pdf b/1332/CH7/EX7.2/7_2.pdf Binary files differnew file mode 100755 index 000000000..678369974 --- /dev/null +++ b/1332/CH7/EX7.2/7_2.pdf diff --git a/1332/CH7/EX7.2/7_2.sce b/1332/CH7/EX7.2/7_2.sce new file mode 100755 index 000000000..419b94a98 --- /dev/null +++ b/1332/CH7/EX7.2/7_2.sce @@ -0,0 +1,35 @@ +//Example 7.2
+//Inverse in Place without Pivoting
+//Page no. 256
+clc;clear;close;
+
+A=[3,-6,7;9,0,-5;5,-8,6]; //matrix
+B=[3,-6,7;9,0,-5;5,-8,6]; //copied matrix
+for i=1:3
+ printf('\n\nStage %i',i);
+ for j=1:3
+ if(i==j)
+ B(i,j)=1/B(i,j);
+ else
+ B(i,j)=A(i,j)/A(i,i);
+ end,
+ end
+ disp(B)
+ for j=1:3
+ for k=1:3
+ if(i~=j)
+ B(j,k)=A(j,k)-A(j,i)*B(i,k);
+ end,
+ end
+ end
+ disp(B)
+ for j=1:3
+ if(i~=j)
+ B(j,i)=-1*A(j,i)*B(i,i);
+ end,
+
+ end
+ disp(B)
+ A=B;
+end
+disp(B,'Inverse of Matrix A=')
\ No newline at end of file diff --git a/1332/CH7/EX7.3/7_3.pdf b/1332/CH7/EX7.3/7_3.pdf Binary files differnew file mode 100755 index 000000000..27f11cc7f --- /dev/null +++ b/1332/CH7/EX7.3/7_3.pdf diff --git a/1332/CH7/EX7.3/7_3.sce b/1332/CH7/EX7.3/7_3.sce new file mode 100755 index 000000000..0b592ff5e --- /dev/null +++ b/1332/CH7/EX7.3/7_3.sce @@ -0,0 +1,55 @@ +//Example 7.3
+//Inverse in Place with Pivoting
+//Page no. 258
+clc;clear;close;
+
+A=[3,-6,7;9,0,-5;5,-8,6]; //matrix
+B=[3,-6,7;9,0,-5;5,-8,6]; //copied matrix
+
+for i=1:3
+ printf('\n\nStage %i',i)
+ if(i<3)
+ for j=1:3 //interchange of rows
+ C(i,j)=A(i,j);
+ A(i,j)=A(i+1,j);
+ A(i+1,j)=C(i,j);
+ C(i,j)=B(i,j);
+ B(i,j)=B(i+1,j);
+ B(i+1,j)=C(i,j);
+ end
+ end
+ disp(B)
+ for j=1:3
+ if(i==j)
+ B(i,j)=1/B(i,j);
+ else
+ B(i,j)=A(i,j)/A(i,i);
+ end,
+ end
+ for j=1:3
+ for k=1:3
+ if(i~=j)
+ B(j,k)=A(j,k)-A(j,i)*B(i,k);
+ end,
+ end
+ end
+ for j=1:3
+ if(i~=j)
+ B(j,i)=-1*A(j,i)*B(i,i);
+ end,
+
+ end
+ disp(B)
+ A=B;
+end
+for j=1:3 //interchange of column 2 and 3
+ C(j,1)=A(j,2);
+ A(j,2)=A(j,3);
+ A(j,3)=C(j,1);
+end
+for j=1:3 //interchange of column 2 and 1
+ C(j,1)=A(j,2);
+ A(j,2)=A(j,1);
+ A(j,1)=C(j,1);
+end
+disp(A,'Inverse of Matrix A=')
\ No newline at end of file diff --git a/1332/CH7/EX7.4/7_4.pdf b/1332/CH7/EX7.4/7_4.pdf Binary files differnew file mode 100755 index 000000000..9d3ee7627 --- /dev/null +++ b/1332/CH7/EX7.4/7_4.pdf diff --git a/1332/CH7/EX7.4/7_4.sce b/1332/CH7/EX7.4/7_4.sce new file mode 100755 index 000000000..3d99f2e53 --- /dev/null +++ b/1332/CH7/EX7.4/7_4.sce @@ -0,0 +1,24 @@ +//Example 7.4
+//Inverse of Triangular Matrices
+//Page no. 260
+clc;clear;close;
+
+R=[2,4,-4,0;0,3,-3,-3;0,0,4,2;0,0,0,3]; //matrix R
+for i=4:-1:1
+ for j=4:-1:1
+ if(i>j)
+ Y(i,j)=0;
+ end
+ if(i==j)
+ Y(i,j)=1/R(i,j);
+ end
+ if(i<j)
+ l=0;
+ for k=i+1:j
+ l=l-R(i,k)*Y(k,j);
+ end
+ Y(i,j)=l/R(i,i);
+ end
+ end
+end
+disp(Y,'Inverse of Matrix R=')
\ No newline at end of file diff --git a/1332/CH7/EX7.5/7_5.pdf b/1332/CH7/EX7.5/7_5.pdf Binary files differnew file mode 100755 index 000000000..6677720fc --- /dev/null +++ b/1332/CH7/EX7.5/7_5.pdf diff --git a/1332/CH7/EX7.5/7_5.sce b/1332/CH7/EX7.5/7_5.sce new file mode 100755 index 000000000..088b21263 --- /dev/null +++ b/1332/CH7/EX7.5/7_5.sce @@ -0,0 +1,19 @@ +//Example 7.5
+//Inverse of Complex Matrices
+//Page no. 262
+clc;clear;close;
+
+A=[1,-1,0;2,3,4;0,1,2];
+B=[1,1,3;1,3,-3;-2,-4,-4];
+P=A+%i*B;
+disp(P,'Matrix P=')
+disp(A,'Matrix A=');disp(B,'Matrix B=');
+A1=inv(A);B1=inv(B);
+disp(A1,'Inverse of Matrix A=');
+disp(B1,'Inverse of Matrix B=');
+B1A=B1*A;disp(B1A,'Inverse(B)*A=');
+AB1A_B=A*B1A+B;disp(AB1A_B,'A*Inverse(B)*A+B=');
+AB1A_B1=inv(AB1A_B);disp(AB1A_B1,'Inverse(A*Inverse(B)*A+B)=');
+X=B1A*AB1A_B1;disp(X,'X=');
+Y=-1*AB1A_B1;disp(Y,'Y=');
+Q=X+%i*Y;disp(Q,'Inverse of Matrix P=')
\ No newline at end of file diff --git a/1332/CH7/EX7.6/7_6.pdf b/1332/CH7/EX7.6/7_6.pdf Binary files differnew file mode 100755 index 000000000..bf43518c8 --- /dev/null +++ b/1332/CH7/EX7.6/7_6.pdf diff --git a/1332/CH7/EX7.6/7_6.sce b/1332/CH7/EX7.6/7_6.sce new file mode 100755 index 000000000..cba8ae798 --- /dev/null +++ b/1332/CH7/EX7.6/7_6.sce @@ -0,0 +1,27 @@ +//Example 7.6
+//Iterative Procedure
+//Page no. 265
+clc;clear;close;
+
+ A=[3,1,3/2;-5/4,-1/4,-3/4;-1/4,-1/4,-1/4];
+disp(A,'Matrix A=');
+B=[1,1,3.5;1,3,-3;-2,-3,-4];
+disp(B,'Assumed Matrix B=');
+e=0.1;
+
+//iterations
+E1=e;k=1;
+while(E1>=e)
+ printf('\n\n\nIteration %i\n',k)
+C=B*(2*eye(3,3)-A*B);disp(C,'Matrix C=');
+E=A*C-eye(3,3);disp(E,'Matrix E=');
+B=C;printf('\nInverse of Matrix A after %i iterations=',k);disp(B);
+E1=0;
+for i=1:3
+ for j=1:3
+ E1=E1+E(i,j)^2;
+ end
+end
+E1=sqrt(E1);
+k=k+1;
+end
diff --git a/1332/CH8/EX8.1/8_1.pdf b/1332/CH8/EX8.1/8_1.pdf Binary files differnew file mode 100755 index 000000000..f6bf6774f --- /dev/null +++ b/1332/CH8/EX8.1/8_1.pdf diff --git a/1332/CH8/EX8.1/8_1.sce b/1332/CH8/EX8.1/8_1.sce new file mode 100755 index 000000000..84097bab7 --- /dev/null +++ b/1332/CH8/EX8.1/8_1.sce @@ -0,0 +1,28 @@ +//Example 8.1
+//Jacobi Method
+//Page no. 273
+clc;clear;close;
+
+A=[8,-3,2;4,11,-1;6,3,12]; //equation matrix
+B=[20;33;36] //solution matrix
+for i=0:19
+ X(i+1,1)=i;
+end
+for i=2:4
+ X(1,i)=0;
+end
+for r=1:19
+ for i=1:3
+ k=0;
+ for j=1:3
+ if(i~=j)
+ k=k-A(i,j)*X(r,j+1);
+ end
+ end
+ X(r+1,i+1)=(k+B(i,1))/A(i,i);
+ end
+end
+printf(' r\t x(r)\t\ty(r)\t z(r)');
+printf('\n ------------------------------------')
+disp(X)
+printf('\n\nAfter 18 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(19,2),X(19,3),X(19,4))
\ No newline at end of file diff --git a/1332/CH8/EX8.2/8_2.pdf b/1332/CH8/EX8.2/8_2.pdf Binary files differnew file mode 100755 index 000000000..3e72b0e8b --- /dev/null +++ b/1332/CH8/EX8.2/8_2.pdf diff --git a/1332/CH8/EX8.2/8_2.sce b/1332/CH8/EX8.2/8_2.sce new file mode 100755 index 000000000..a78a9be4e --- /dev/null +++ b/1332/CH8/EX8.2/8_2.sce @@ -0,0 +1,34 @@ +//Example 8.2
+//Gauss-Seidel Method
+//Page no. 274
+clc;clear;close;
+
+A=[8,-3,2;4,11,-1;6,3,12]; //equation matrix
+B=[20;33;36] //solution matrix
+for i=0:10
+ X(i+1,1)=i;
+end
+for i=2:4
+ X(1,i)=0;
+end
+for r=1:10
+ for i=1:3
+ k1=0;
+ for j=1:i-1
+
+ k1=k1-A(i,j)*X(r+1,j+1);
+
+ end
+ k2=0;
+ for j=i+1:3
+
+ k2=k2-A(i,j)*X(r,j+1);
+
+ end
+ X(r+1,i+1)=(k1+k2+B(i,1))/A(i,i);
+ end
+end
+printf(' r\t x(r)\t\ty(r)\t z(r)');
+printf('\n ------------------------------------')
+disp(X)
+printf('\n\nAfter 9 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(10,2),X(10,3),X(10,4))
\ No newline at end of file diff --git a/1332/CH8/EX8.3/8_3.pdf b/1332/CH8/EX8.3/8_3.pdf Binary files differnew file mode 100755 index 000000000..41ce34421 --- /dev/null +++ b/1332/CH8/EX8.3/8_3.pdf diff --git a/1332/CH8/EX8.3/8_3.sce b/1332/CH8/EX8.3/8_3.sce new file mode 100755 index 000000000..ab311730a --- /dev/null +++ b/1332/CH8/EX8.3/8_3.sce @@ -0,0 +1,35 @@ +//Example 8.3
+//SOR Method
+//Page no. 275
+clc;clear;close;
+
+A=[5,2,1;-1,4,2;2,-3,10];
+B=[-12;20;3];
+w=0.9;
+for i=0:13
+ X(i+1,1)=i;
+end
+X(1,2)=-2.4;
+X(1,3)=5;
+X(1,4)=0.3;
+for r=1:13
+ for i=1:3
+ k1=0;
+ for j=1:i-1
+
+ k1=k1-A(i,j)*X(r+1,j+1);
+
+ end
+ k2=0;
+ for j=i+1:3
+
+ k2=k2-A(i,j)*X(r,j+1);
+
+ end
+ X(r+1,i+1)=(1-w)*X(r,i+1)+(w*k1+w*k2+w*B(i,1))/A(i,i);
+ end
+end
+printf(' r\t x(r)\t\ty(r)\t z(r)');
+printf('\n ------------------------------------');
+disp(X);
+printf('\n\nAfter 12 iterations exact solution is:\nx=%i\ty=%i\tz=%i',X(13,2),X(13,3),X(13,4));
\ No newline at end of file diff --git a/1332/CH8/EX8.4/8_4.PNG b/1332/CH8/EX8.4/8_4.PNG Binary files differnew file mode 100755 index 000000000..c038f0085 --- /dev/null +++ b/1332/CH8/EX8.4/8_4.PNG diff --git a/1332/CH8/EX8.4/8_4.sce b/1332/CH8/EX8.4/8_4.sce new file mode 100755 index 000000000..363580de9 --- /dev/null +++ b/1332/CH8/EX8.4/8_4.sce @@ -0,0 +1,52 @@ +//Example 8.4
+//Gauss-Seidel Point Iterative Method
+//Page no. 278
+clc;clear;close;
+
+
+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
+B=[5;10;10;0;0;5] //solution matrix
+for i=1:6
+ for j=1:6
+ if(A(j,j)==0)
+ for k=1:6
+ C(j,k)=A(j,k);
+ A(j,k)=A(j+1,k);
+ A(j+1,k)=C(j,k);
+ end
+ end
+ end
+end
+for i=0:7
+ X(i+1,1)=i;
+end
+for i=2:7
+ X(1,i)=0;
+end
+for r=1:7
+ for i=1:6
+ k1=0;
+ for j=1:i-1
+
+ k1=k1-A(i,j)*X(r+1,j+1);
+
+ end
+ k2=0;
+ for j=i+1:6
+
+ k2=k2-A(i,j)*X(r,j+1);
+
+ end
+ X(r+1,i+1)=(k1+k2+B(i,1))/A(i,i);
+ end
+end
+printf(' r ');
+for i=1:6
+ printf('x%i ',i);
+end
+printf('\n --------------------------------------------------------------------------------')
+disp(X)
+printf('\n\nAfter 6 iterations exact solution is:\n');
+for i=1:6
+ printf('x%i=%f ',i,X(7,i+1));
+end
diff --git a/1332/CH8/EX8.5/8_5.pdf b/1332/CH8/EX8.5/8_5.pdf Binary files differnew file mode 100755 index 000000000..430f95163 --- /dev/null +++ b/1332/CH8/EX8.5/8_5.pdf diff --git a/1332/CH8/EX8.5/8_5.sce b/1332/CH8/EX8.5/8_5.sce new file mode 100755 index 000000000..99c5dd81f --- /dev/null +++ b/1332/CH8/EX8.5/8_5.sce @@ -0,0 +1,82 @@ +//Example 8.5
+//Gauss-Seidel Point Iterative Method
+//Page no. 279
+clc;clear;close;
+
+A=[2,3,-4,1;1,-2,-5,1;5,-3,1,-4;10,2,-1,2]; //equation matrix
+B=[3;2;1;-4]; //solution matrix
+
+//transformation of the equations
+for i=1:4
+ A1(1,i)=A(4,i);
+ B1(1,1)=B(4,1);
+end
+for i=1:4
+ A1(3,i)=A(2,i);
+ B1(3,1)=B(2,1);
+end
+for i=1:4
+ A1(2,i)=A(1,i)-A(2,i);
+ B1(2,1)=B(1,1)-B(2,1);
+end
+for i=1:4
+ A1(4,i)=2*A(1,i)-A(2,i)+2*A(3,i)-A(4,i);
+ B1(4,1)=2*B(1,1)-B(2,1)+2*B(3,1)-B(4,1);
+end
+
+//printing of transformed equations
+printf('\nTransformed Equations are=\n\n')
+for i=1:4
+ for j=1:4
+ printf('(%ix(%i))',A1(i,j),j);
+ if(j<4)
+ printf(' + ')
+ end
+ end
+ printf('= %i\n',B1(i,1));
+end
+
+for i=1:4
+ for j=1:4
+ if(A(j,j)==0)
+ for k=1:4
+ C(j,k)=A(j,k);
+ A(j,k)=A(j+1,k);
+ A(j+1,k)=C(j,k);
+ end
+ end
+ end
+end
+for i=0:12
+ X(i+1,1)=i;
+end
+for i=2:5
+ X(1,i)=0;
+end
+for r=1:12
+ for i=1:4
+ k1=0;
+ for j=1:i-1
+
+ k1=k1-A1(i,j)*X(r+1,j+1);
+
+ end
+ k2=0;
+ for j=i+1:4
+
+ k2=k2-A1(i,j)*X(r,j+1);
+
+ end
+ X(r+1,i+1)=(k1+k2+B1(i,1))/A1(i,i);
+ end
+end
+printf('\n\n r ');
+for i=1:4
+ printf('x%i ',i);
+end
+printf('\n ------------------------------------------------------')
+disp(X)
+printf('\n\nAfter 11 iterations exact solution is:\n');
+for i=1:4
+ printf('x%i=%f ',i,X(12,i+1));
+end
diff --git a/1332/CH8/EX8.6/8_6.pdf b/1332/CH8/EX8.6/8_6.pdf Binary files differnew file mode 100755 index 000000000..37c49666f --- /dev/null +++ b/1332/CH8/EX8.6/8_6.pdf diff --git a/1332/CH8/EX8.6/8_6.sce b/1332/CH8/EX8.6/8_6.sce new file mode 100755 index 000000000..2fb06a7ee --- /dev/null +++ b/1332/CH8/EX8.6/8_6.sce @@ -0,0 +1,57 @@ +//Example 8.6
+//Block Jacobi Method
+//Page no. 281
+clc;clear;close;
+
+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
+B=[5;10;10;0;0;5] //solution matrix
+disp(B,'B=',A,'A=')
+for i=1:3
+ for j=1:3
+ A11(i,j)=A(i,j);
+ end
+ B1(i,1)=B(i,1);
+end
+for i=1:3
+ for j=1:3
+ A12(i,j)=A(i,j+3);
+ end
+end
+for i=1:3
+ for j=1:3
+ A21(i,j)=A(i+3,j);
+ end
+end
+for i=1:3
+ for j=1:3
+ A22(i,j)=A(i+3,j+3);
+ end
+ B2(i,1)=B(i+3,1);
+end
+disp(B2,'B2=',B1,'B1=',A22,'A22=',A21,'A21=',A12,'A12=',A11,'A11=');
+A11_1=inv(A11);A22_1=inv(A22);
+disp(A22_1,'Inverse of A22=',A11_1,'Inverse of A11=')
+for i=1:3
+ X1(i,1)=0;
+ X2(i,1)=0;
+end
+for r=1:2
+ X11=A11_1*(-1*A12*X2+B1);
+ X22=A22_1*(-1*A21*X1+B2);
+ X1=X11;
+ X2=X22;
+ disp(X1,'X1=')
+ disp(X2,'X2=')
+end
+for i=1:6
+ if(i<4)
+ X(i,1)=X1(i,1);
+ else
+ X(i,1)=X2(i-3,1);
+ end
+end
+disp(X,'X=')
+printf('\n\n\nNote : There is a computation error in calculation of X1(2)')
+
+
+
diff --git a/1332/CH8/EX8.7/8_7.pdf b/1332/CH8/EX8.7/8_7.pdf Binary files differnew file mode 100755 index 000000000..cc9a74dcf --- /dev/null +++ b/1332/CH8/EX8.7/8_7.pdf diff --git a/1332/CH8/EX8.7/8_7.sce b/1332/CH8/EX8.7/8_7.sce new file mode 100755 index 000000000..15f382a2a --- /dev/null +++ b/1332/CH8/EX8.7/8_7.sce @@ -0,0 +1,101 @@ +//Example 8.7
+//Block Gauss-Seidel Method
+//Page no. 283
+clc;clear;close;
+
+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
+B=[5;10;10;0;0;5] //solution matrix
+disp(B,'B=',A,'A=')
+
+for i=1:2
+ for j=1:2
+ A11(i,j)=A(i,j);
+ end
+ B1(i,1)=B(i,1);
+end
+for i=1:2
+ for j=1:2
+ A12(i,j)=A(i,j+2);
+ end
+ B2(i,1)=B(i+2,1);
+end
+for i=1:2
+ for j=1:2
+ A13(i,j)=A(i,j+4);
+ end
+ B3(i,1)=B(i+4,1);
+end
+for i=1:2
+ for j=1:2
+ A21(i,j)=A(i+2,j);
+ end
+end
+for i=1:2
+ for j=1:2
+ A22(i,j)=A(i+2,j+2);
+ end
+end
+for i=1:2
+ for j=1:2
+ A23(i,j)=A(i+2,j+4);
+ end
+end
+for i=1:2
+ for j=1:2
+ A31(i,j)=A(i+4,j);
+ end
+end
+for i=1:2
+ for j=1:2
+ A32(i,j)=A(i+4,j+2);
+ end
+end
+for i=1:2
+ for j=1:2
+ A33(i,j)=A(i+4,j+4);
+ end
+end
+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=');
+A11_1=inv(A11);A22_1=inv(A22);A33_1=inv(A33);
+disp(A33_1,'Inverse of Matrix A33=',A22_1,'Inverse of Matrix A22=',A11_1,'Inverse of Matrix A11=');
+for i=1:2
+ X1(i,1)=0;
+ X2(i,1)=0;
+ X3(i,1)=0;
+end
+for i=1:6
+ X(i,1)=i-1;
+end
+for i=2:7
+ X(1,i)=0;
+end
+for r=1:5
+ X11=A11_1*(-1*A12*X2+(-1)*A13*X3+B1);
+ X22=A22_1*(-1*A21*X11+(-1)*A23*X3+B2);
+ X33=A33_1*(-1*A31*X11+(-1)*A32*X22+B3);
+ X1=X11;
+ X2=X22;
+ X3=X33;
+ disp(X3,'X3=',X2,'X2=',X1,'X1=')
+ for i=2:7
+ if(i<4)
+ X(r+1,i)=X1(i-1,1);
+ end
+ if(i<6 & i>3)
+ X(r+1,i)=X2(i-3,1);
+ end
+ if(i<8 & i>5)
+ X(r+1,i)=X3(i-5,1);
+ end
+ end
+end
+printf('\n\nIteration');
+for i=1:6
+ printf(' x%i ',i);
+end
+printf('\n --------------------------------------------------------------------------------')
+disp(X)
+printf('\n\nAfter 4 iterations exact solution is:\n');
+for i=1:6
+ printf('x%i=%f ',i,X(5,i+1));
+end
\ No newline at end of file diff --git a/1332/CH8/EX8.8/8_8.pdf b/1332/CH8/EX8.8/8_8.pdf Binary files differnew file mode 100755 index 000000000..fa26f7083 --- /dev/null +++ b/1332/CH8/EX8.8/8_8.pdf diff --git a/1332/CH8/EX8.8/8_8.sce b/1332/CH8/EX8.8/8_8.sce new file mode 100755 index 000000000..d17143b28 --- /dev/null +++ b/1332/CH8/EX8.8/8_8.sce @@ -0,0 +1,102 @@ +//Example 8.8
+//Block SOR Method
+//Page no. 284
+clc;clear;close;
+
+
+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
+B=[5;10;10;0;0;5] //solution matrix
+disp(B,'B=',A,'A=')
+w=0.8
+for i=1:2
+ for j=1:2
+ A11(i,j)=A(i,j);
+ end
+ B1(i,1)=B(i,1);
+end
+for i=1:2
+ for j=1:2
+ A12(i,j)=A(i,j+2);
+ end
+ B2(i,1)=B(i+2,1);
+end
+for i=1:2
+ for j=1:2
+ A13(i,j)=A(i,j+4);
+ end
+ B3(i,1)=B(i+4,1);
+end
+for i=1:2
+ for j=1:2
+ A21(i,j)=A(i+2,j);
+ end
+end
+for i=1:2
+ for j=1:2
+ A22(i,j)=A(i+2,j+2);
+ end
+end
+for i=1:2
+ for j=1:2
+ A23(i,j)=A(i+2,j+4);
+ end
+end
+for i=1:2
+ for j=1:2
+ A31(i,j)=A(i+4,j);
+ end
+end
+for i=1:2
+ for j=1:2
+ A32(i,j)=A(i+4,j+2);
+ end
+end
+for i=1:2
+ for j=1:2
+ A33(i,j)=A(i+4,j+4);
+ end
+end
+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=');
+A11_1=inv(A11);A22_1=inv(A22);A33_1=inv(A33);
+disp(A33_1,'Inverse of Matrix A33=',A22_1,'Inverse of Matrix A22=',A11_1,'Inverse of Matrix A11=');
+for i=1:2
+ X1(i,1)=0;
+ X2(i,1)=0;
+ X3(i,1)=0;
+end
+for i=1:7
+ X(i,1)=i-1;
+end
+for i=2:7
+ X(1,i)=0;
+end
+for r=1:6
+ X11=A11_1*((1-w)*X1+(-1)*w*A12*X2+(-1)*w*A13*X3+w*B1);
+ X22=A22_1*((1-w)*X2+(-1)*w*A21*X11+(-1)*w*A23*X3+w*B2);
+ X33=A33_1*((1-w)*X3+(-1)*w*A31*X11+(-1)*w*A32*X22+w*B3);
+ X1=X11;
+ X2=X22;
+ X3=X33;
+ disp(X3,'X3=',X2,'X2=',X1,'X1=')
+ for i=2:7
+ if(i<4)
+ X(r+1,i)=X1(i-1,1);
+ end
+ if(i<6 & i>3)
+ X(r+1,i)=X2(i-3,1);
+ end
+ if(i<8 & i>5)
+ X(r+1,i)=X3(i-5,1);
+ end
+ end
+end
+printf('\n\nIteration');
+for i=1:6
+ printf(' x%i ',i);
+end
+printf('\n --------------------------------------------------------------------------------')
+disp(X)
+printf('\n\nAfter 5 iterations exact solution is:\n');
+for i=1:6
+ printf('x%i=%f ',i,X(6,i+1));
+end
\ No newline at end of file diff --git a/1332/CH9/EX9.1/9_1.pdf b/1332/CH9/EX9.1/9_1.pdf Binary files differnew file mode 100755 index 000000000..460aca796 --- /dev/null +++ b/1332/CH9/EX9.1/9_1.pdf diff --git a/1332/CH9/EX9.1/9_1.sce b/1332/CH9/EX9.1/9_1.sce new file mode 100755 index 000000000..06416f8c5 --- /dev/null +++ b/1332/CH9/EX9.1/9_1.sce @@ -0,0 +1,11 @@ +//Example 9.1
+//Moore-Penrose Generalized Inverse
+//Page no. 292
+clc;clear;close;
+
+AT=[3,0,3;0,3,3];
+A=AT'; //transpose
+I=inv(AT*A); //inverse
+disp(I,'Inverse of AT*A=',AT*A,'AT*A=',A,'A=',AT,'AT=');
+A#=I*AT;
+disp(A#,'Moore-Penrose Generalized Inverse of A=')
\ No newline at end of file diff --git a/1332/CH9/EX9.2/9_2.pdf b/1332/CH9/EX9.2/9_2.pdf Binary files differnew file mode 100755 index 000000000..81f76b7f6 --- /dev/null +++ b/1332/CH9/EX9.2/9_2.pdf diff --git a/1332/CH9/EX9.2/9_2.sce b/1332/CH9/EX9.2/9_2.sce new file mode 100755 index 000000000..3d0d4911a --- /dev/null +++ b/1332/CH9/EX9.2/9_2.sce @@ -0,0 +1,60 @@ +//Example 9.2
+//Curve Fitting
+//Page no. 293
+clc;clear;close;
+x(1)=0.25;
+for i=2:6
+ x(1,i)=x(1,i-1)+0.25;
+end //x values
+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
+
+//construction of normal equations
+for i=1:6
+ Y(1,i)=log10(y(1,i));
+end
+Ex=0;
+for i=1:6
+ Ex=Ex+x(1,i);
+end
+EY=0;
+for i=1:6
+ EY=EY+Y(1,i);
+end
+Ex2=0;
+for i=1:6
+ Ex2=Ex2+x(1,i)^2;
+end
+ExY=0;
+for i=1:6
+ ExY=ExY+x(1,i)*Y(1,i);
+end
+printf('E x(k)\t\t y(k)\t\tE Y(k)\t\tE x2(k)\t\tE x(k)*Y(k)')
+printf('\n----------------------------------------------------------------------------')
+for i=1:6
+ 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))
+end
+printf('\n----------------------------------------------------------------------------')
+printf('\n%f\t%f\t%f\t%f\t%f',Ex,0,EY,Ex2,ExY)
+printf('\n----------------------------------------------------------------------------\n\n')
+A=[6,Ex;Ex,Ex2]; //system of normal equations
+B=[EY;ExY];
+X=inv(A)*B;
+a=exp(X(1,1));
+b=-1*X(2,1);
+for i=1:2
+ for j=1:2
+ printf('%f ',A(i,j))
+ end
+ if(i==1)
+ printf(' *')
+ end
+
+ printf('\ta%i',i);
+ if(i==1)
+ printf(' =')
+ end
+
+ printf('\t%f\n',B(i,1))
+end
+printf('\n\na1=%f\na2=%f\n\na=%f\nb=%f\n\n',X(1,1),X(2,1),a,b)
+printf('The fitted curve is:\n %fx\ny=%f e',b,a)
\ No newline at end of file diff --git a/1332/CH9/EX9.3/9_3.pdf b/1332/CH9/EX9.3/9_3.pdf Binary files differnew file mode 100755 index 000000000..41156b47d --- /dev/null +++ b/1332/CH9/EX9.3/9_3.pdf diff --git a/1332/CH9/EX9.3/9_3.sce b/1332/CH9/EX9.3/9_3.sce new file mode 100755 index 000000000..9213721c0 --- /dev/null +++ b/1332/CH9/EX9.3/9_3.sce @@ -0,0 +1,61 @@ +//Example 9.3
+//Gram-Schmidt Orthogonalization/Orthonormalization Process
+//Page no. 294
+clc;clear;close;
+deff('y=f(x,a)','y=sqrt(x(1,a)^2+x(2,a)^2+x(3,a)^2+x(4,a)^2)');
+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)');
+
+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];
+for i=1:4
+ V(i,1)=U(i,1);
+end
+for i=1:4
+ if(f(V,1)~=0)
+ W(i,1)=V(i,1)/f(V,1);
+ else
+ W(i,1)=0;
+ end
+end
+for j=2:6
+ for i=1:4
+ for l=1:4
+ k(l,1)=0;
+ end
+ for l=1:j-1
+ for m=1:4
+ w(m,1)=W(m,l);
+ end
+ k=k-(f1(U,j,W,l))*w;
+ end
+ V(i,j)=U(i,j)+k(i,1);
+ end
+ for i=1:4
+ if(j~=4)
+ if(f(V,j)~=0)
+ W(i,j)=V(i,j)/f(V,j);
+ else
+ W(i,j)=0;
+ end
+ else
+ W(i,j)=0;
+ end
+ end
+
+end
+disp(U,'U=')
+disp('W=')
+printf('\n')
+for i=1:4
+ for j=1:6
+ printf('%.4f\t\t',W(i,j))
+ end
+ printf('\n')
+end
+disp('V=')
+printf('\n')
+for i=1:4
+ for j=1:6
+ printf('%.4f\t\t',V(i,j))
+ end
+ printf('\n')
+end
\ No newline at end of file diff --git a/1332/CH9/EX9.4/9_4.pdf b/1332/CH9/EX9.4/9_4.pdf Binary files differnew file mode 100755 index 000000000..6996647bf --- /dev/null +++ b/1332/CH9/EX9.4/9_4.pdf diff --git a/1332/CH9/EX9.4/9_4.sce b/1332/CH9/EX9.4/9_4.sce new file mode 100755 index 000000000..624b0e36e --- /dev/null +++ b/1332/CH9/EX9.4/9_4.sce @@ -0,0 +1,34 @@ +//Example 9.4
+//QR Decomposition
+//Page no. 296
+clc;clear;close;
+
+A=[2,1,1;1,3,1;1,1,4];
+B=A*A';
+disp(B,'AT*A=')
+//cholesky factorization to find R
+R(2,1)=0;R(3,1)=0;R(3,2)=0;
+for i=1:3
+ for j=1:3
+ if(i==j)
+ k=0;
+ for m=1:i-1
+ k=k+R(m,i)^2;
+ end
+ R(i,j)=sqrt(B(i,j)-k)
+ end
+ if(j>i)
+ k=0;
+ for m=1:i-1
+ k=k+R(m,j)*R(m,i);
+ end
+ R(i,j)=(B(i,j)-k)/R(i,i)
+ end
+ end
+end
+//cholesky factorization end
+disp(R,'Upper Triangular Matrix (R)=')
+R_1=inv(R);
+disp(R_1,'Inverse of R')
+Q=A*R_1;
+disp(Q,'Orthogonal Matrix Q=')
\ No newline at end of file diff --git a/1332/CH9/EX9.5/9_5.pdf b/1332/CH9/EX9.5/9_5.pdf Binary files differnew file mode 100755 index 000000000..d311586e4 --- /dev/null +++ b/1332/CH9/EX9.5/9_5.pdf diff --git a/1332/CH9/EX9.5/9_5.sce b/1332/CH9/EX9.5/9_5.sce new file mode 100755 index 000000000..b08b08d88 --- /dev/null +++ b/1332/CH9/EX9.5/9_5.sce @@ -0,0 +1,32 @@ +//Example 9.5
+//Vector Computation
+//Page no. 299
+clc;clear;close;
+
+X=[2,3,0,1];
+n=X(1);
+for i=2:4
+ if(n<X(i))
+ n=X(i);
+ end
+end
+printf('\nMaximum Value (n)=%i\n',n)
+for i=1:4
+ X(i)=X(i)/n;
+end
+disp(X,'Normalized X=')
+k=0;
+for i=1:4
+ k=k+X(i)^2;
+end
+sigma=X(1)*abs(1/X(1))*sqrt(k);
+printf('\nsigma=%f\n',sigma);
+X(1)=X(1)+sigma;
+printf('\nModified x1 = %g\n',X(1))
+for i=1:4
+ U(1,i)=X(i);
+end
+disp(U,'U=')
+p=sigma*X(1);sigma=n*sigma;
+printf('\n p = %f\n\n sigma = %f',p,sigma);
+printf('\n\n\nNote : There is a computation error in calculation of U1')
\ No newline at end of file diff --git a/1332/CH9/EX9.6/9_6.pdf b/1332/CH9/EX9.6/9_6.pdf Binary files differnew file mode 100755 index 000000000..36a5c4c29 --- /dev/null +++ b/1332/CH9/EX9.6/9_6.pdf diff --git a/1332/CH9/EX9.6/9_6.sce b/1332/CH9/EX9.6/9_6.sce new file mode 100755 index 000000000..6c9009740 --- /dev/null +++ b/1332/CH9/EX9.6/9_6.sce @@ -0,0 +1,24 @@ +//Example 9.6
+//House Holder Transformation
+//Page no. 300
+clc;clear;close;
+
+A=[4,2,1;2,5,-2;1,-2,7]
+disp(A,'A=')
+k=0;
+for j=2:3
+ k=k+A(j,1)^2;
+end
+a=A(2,1)*abs(1/A(2,1))*sqrt(k);
+disp(a,'alpha=')
+U=[0;a+A(2,1);A(3,1)];
+disp(U,'U=')
+U1=U'*U;
+disp(U1,'UT*U=')
+U2=U*U';
+disp(U2,'U*UT=')
+P=eye(3,3)-(2*U2)/U1;
+disp(P,'P=');
+B=P*A*P;
+disp(B,'B=');
+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)')
\ No newline at end of file diff --git a/1332/CH9/EX9.7/9_7.pdf b/1332/CH9/EX9.7/9_7.pdf Binary files differnew file mode 100755 index 000000000..b181eceb4 --- /dev/null +++ b/1332/CH9/EX9.7/9_7.pdf diff --git a/1332/CH9/EX9.7/9_7.sce b/1332/CH9/EX9.7/9_7.sce new file mode 100755 index 000000000..cf497efe8 --- /dev/null +++ b/1332/CH9/EX9.7/9_7.sce @@ -0,0 +1,47 @@ +//Example 9.7
+//Givens QR Method
+//Page no. 303
+clc;clear;close;
+
+A=[4,2,1;2,5,-2;1,-2,7]
+deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')
+deff('y=s(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')
+disp(A,'A=')
+R=A;Q=eye(3,3);
+m=1;
+for j=1:2
+ for i=j+1:3
+ for k=1:3 //C matrix evaluation
+ for l=1:3
+ if(k==l)
+ if(k==i | k==j)
+ C(k,l)=c(i,j)
+ else
+ C(k,l)=1
+ end
+ end
+ if(k>l)
+ if(k==i & l==j)
+ C(k,l)=-1*s(i,j)
+ else
+ C(k,l)=0
+ end
+ end
+ if(k<l)
+ if(k==j & l==i)
+ C(k,l)=s(i,j)
+ else
+ C(k,l)=0
+ end
+ end
+ end
+ end
+ printf('\n\n Iteration %i',m)
+ m=m+1
+ disp(C,'C=');
+ R=C*R;
+ Q=Q*C';
+ disp(Q,'Q=',R,'R=')
+ end
+end
+disp(Q*R,'Q*R=A=') //verification
\ No newline at end of file diff --git a/1332/CH9/EX9.8/9_8.pdf b/1332/CH9/EX9.8/9_8.pdf Binary files differnew file mode 100755 index 000000000..47c8cbef2 --- /dev/null +++ b/1332/CH9/EX9.8/9_8.pdf diff --git a/1332/CH9/EX9.8/9_8.sce b/1332/CH9/EX9.8/9_8.sce new file mode 100755 index 000000000..79e5f435f --- /dev/null +++ b/1332/CH9/EX9.8/9_8.sce @@ -0,0 +1,35 @@ +//Example 9.8
+//Recursive Least-Square Method
+//Page no. 308
+clc;clear;close;
+
+A0=[3,0;0,3;3,3];
+B0=[2;2;2];
+A1=[6,3];B1=[6];
+A0T=A0';
+G0=A0T*A0;
+disp(G0,'G0=')
+G0_1=inv(G0);
+disp(G0_1,'Inverse of G0=')
+X0=G0_1*A0T*B0;
+disp(X0,'X0=')
+
+//by recursive least square algorithm
+G1=G0+A1'*A1;
+disp(G1,'G1=');
+G1_1=inv(G1);
+disp(G1_1,'Inverse of G1')
+X1=X0+G1_1*A1'*(B1-A1*X0);
+disp(X1,'X1=')
+
+//verification
+A=[3,0;0,3;3,3;6,3];
+B=[2;2;2;6];
+AT=A';
+G=AT*A;
+disp(G,'G=')
+G_1=inv(G);
+disp(G_1,'Inverse of G=')
+X=G_1*AT*B;
+disp(X,'X=')
+disp('Thus X and X1 are Same')
\ No newline at end of file |
