From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:27:19 +0530
Subject: initial commit / add all books

---
 260/CH4/EX4.1/4_1.sce   | 70 +++++++++++++++++++++++++++++++++++++++++++
 260/CH4/EX4.10/4_10.sce | 29 ++++++++++++++++++
 260/CH4/EX4.11/4_11.sce | 31 +++++++++++++++++++
 260/CH4/EX4.12/4_12.sce | 28 ++++++++++++++++++
 260/CH4/EX4.13/4_13.sce | 25 ++++++++++++++++
 260/CH4/EX4.14/4_14.sce | 23 ++++++++++++++
 260/CH4/EX4.15/4_15.sce | 19 ++++++++++++
 260/CH4/EX4.16/4_16.sce | 21 +++++++++++++
 260/CH4/EX4.17/4_17.sce | 32 ++++++++++++++++++++
 260/CH4/EX4.18/4_18.sce | 32 ++++++++++++++++++++
 260/CH4/EX4.19/4_19.sce | 28 ++++++++++++++++++
 260/CH4/EX4.2/4_2.sce   | 23 ++++++++++++++
 260/CH4/EX4.20/4_20.sce | 79 +++++++++++++++++++++++++++++++++++++++++++++++++
 260/CH4/EX4.21/4_21.sce | 28 ++++++++++++++++++
 260/CH4/EX4.3/4_3.sce   | 25 ++++++++++++++++
 260/CH4/EX4.4/4_4.sce   | 32 ++++++++++++++++++++
 260/CH4/EX4.5/4_5.sce   | 40 +++++++++++++++++++++++++
 260/CH4/EX4.6/4_6.sce   | 52 ++++++++++++++++++++++++++++++++
 260/CH4/EX4.7/4_7.sce   | 37 +++++++++++++++++++++++
 260/CH4/EX4.8/4_8.sce   | 23 ++++++++++++++
 260/CH4/EX4.9/4_9.sce   | 32 ++++++++++++++++++++
 21 files changed, 709 insertions(+)
 create mode 100644 260/CH4/EX4.1/4_1.sce
 create mode 100644 260/CH4/EX4.10/4_10.sce
 create mode 100644 260/CH4/EX4.11/4_11.sce
 create mode 100644 260/CH4/EX4.12/4_12.sce
 create mode 100644 260/CH4/EX4.13/4_13.sce
 create mode 100644 260/CH4/EX4.14/4_14.sce
 create mode 100644 260/CH4/EX4.15/4_15.sce
 create mode 100644 260/CH4/EX4.16/4_16.sce
 create mode 100644 260/CH4/EX4.17/4_17.sce
 create mode 100644 260/CH4/EX4.18/4_18.sce
 create mode 100644 260/CH4/EX4.19/4_19.sce
 create mode 100644 260/CH4/EX4.2/4_2.sce
 create mode 100644 260/CH4/EX4.20/4_20.sce
 create mode 100644 260/CH4/EX4.21/4_21.sce
 create mode 100644 260/CH4/EX4.3/4_3.sce
 create mode 100644 260/CH4/EX4.4/4_4.sce
 create mode 100644 260/CH4/EX4.5/4_5.sce
 create mode 100644 260/CH4/EX4.6/4_6.sce
 create mode 100644 260/CH4/EX4.7/4_7.sce
 create mode 100644 260/CH4/EX4.8/4_8.sce
 create mode 100644 260/CH4/EX4.9/4_9.sce

(limited to '260/CH4')

diff --git a/260/CH4/EX4.1/4_1.sce b/260/CH4/EX4.1/4_1.sce
new file mode 100644
index 000000000..21dd2091e
--- /dev/null
+++ b/260/CH4/EX4.1/4_1.sce
@@ -0,0 +1,70 @@
+//Eg-4.1
+//pg-139
+
+clear
+clc
+
+A=[-3 0 1];
+ xl=1;
+ xu=3;
+ fx=poly(A,'x','c')
+
+//This  is used determine true root with less errors using bisection method
+//input arguments--xl(lower bound of x),xu(upper bound of x),es(stopping criterion error),f(given function)
+//output arguments--root(final value of x) obtained from my code,pre-percent relative error,itns-number of itertions used in the code
+
+xrold=(xl+xu)/2;
+
+//Verying whether in given interval,function are applicable for bisecion method
+
+if horner(fx,xl)*horner(fx,xu)>0 then
+    disp("there are more than 2 roots or no root ,so bisection method is not applicable")
+elseif horner(fx,xl)*horner(fx,xu)==0 then
+    disp("there is no need to apply any method since one of bound is a root")
+elseif horner(fx,xl)*horner(fx,xrold)==0|horner(fx,xrold)*horner(fx,xu)==0 then
+    disp("(xl+xu)/2 is the required root")
+    
+else
+    //BISECTION METHOD  
+    disp("The given function has only one root in the given interval ,so by applying bisection method root can be determined")
+    test=horner(fx,xl)*horner(fx,xrold);
+    if test<0 then
+        xu=xrold;
+    elseif test>0 then
+        xl=xrold;
+    else 
+        root=xrold;
+    end
+    xrnew=(xl+xu)/2;
+    ea=abs(xrnew-xrold)*100/abs(xrnew);
+    pre(1,1)=ea;
+    iter=1;
+    itns(1,1)=1;
+    i=1;
+    while i<=10
+        printf('\n\nIteration No. %i \n',i);
+        printf('xlow=%f \n',xl);
+        printf('xhigh=%f \n',xu);
+        xrold=xrnew;
+        test=horner(fx,xl)*horner(fx,xrold);
+    if test<0 then
+        xu=xrold;
+    elseif test>0 then
+        xl=xrold;
+    else
+        root=xrold;
+        
+end
+    xrnew=(xl+xu)/2;
+    fnew=horner(fx,xrnew);
+    ea=abs(xrnew-xrold)*100/abs(xrnew);
+    iter=iter+1;
+    itns(iter,1)=iter;
+    pre(iter,1)=ea;
+    i=i+1;
+     printf('xnew=%f \n',xrnew);
+      printf('fnew=%f \n',fnew);
+end
+root=xrnew;//True root
+end
+
diff --git a/260/CH4/EX4.10/4_10.sce b/260/CH4/EX4.10/4_10.sce
new file mode 100644
index 000000000..255b61639
--- /dev/null
+++ b/260/CH4/EX4.10/4_10.sce
@@ -0,0 +1,29 @@
+//Eg-4.10
+//pg-161
+
+clear
+clc
+
+
+// Secant Method
+
+A=[-6 5 -3 2];
+x1=0.5;
+x2=0.7;
+eps=10^(-10);
+fx=poly(A,'x','c');
+iter=1;
+Abserr=100;
+while Abserr>eps
+    printf('iteration number %i\n',iter);
+    xnew1=x2-horner(fx,x2)*(x2-x1)/(horner(fx,x2)-horner(fx,x1));
+    printf('xnew1 = %f \n',xnew1);
+    Abserr = abs(horner(fx,xnew1) - horner(fx,x1))/abs(horner(fx,xnew1));
+    x1=x2;
+    x2=xnew1;
+   iter=iter+1;
+end
+
+disp("result was found in iterations")
+disp(iter-1)
+
diff --git a/260/CH4/EX4.11/4_11.sce b/260/CH4/EX4.11/4_11.sce
new file mode 100644
index 000000000..740616998
--- /dev/null
+++ b/260/CH4/EX4.11/4_11.sce
@@ -0,0 +1,31 @@
+//Eg-4.11
+//pg-163
+
+clear
+clc
+
+// Secant Method
+
+clear ;
+close ;
+clc ;
+
+deff('[z]=f(x)','z=1.55*x^(-0.5)-7.2*x+8.1*x^2-4*x^3-1.3');
+iter=1;
+eps=10^(-10);
+x1=0.5;
+x2=1;
+imax=20;
+
+Abserr=100;
+while Abserr>eps&iter<imax
+    //printf('iteration number %i\n',iter);
+    xnew1=x2-feval(x2,f)*(x2-x1)/(feval(x2,f)-feval(x1,f));
+    //printf('xnew1 = %f \n',xnew1);
+    Abserr=abs(xnew1-x1)/abs(xnew1);
+    x1=x2;
+    x2=xnew1;
+   iter=iter+1;
+end
+
+printf('The result of %f has been found after %d iterations',x2,iter-1)
\ No newline at end of file
diff --git a/260/CH4/EX4.12/4_12.sce b/260/CH4/EX4.12/4_12.sce
new file mode 100644
index 000000000..da24f074f
--- /dev/null
+++ b/260/CH4/EX4.12/4_12.sce
@@ -0,0 +1,28 @@
+//Eg-4.12
+//pg-165
+
+clear
+clc
+
+deff('[z]=f0(x0,x1)','z=x0^3-2.5*x1^2+4*x0-3.7');
+deff('[z]=f1(x0,x1)','z=0.7*x1^2+3*x1-1.8*x0+1');
+
+x0=0;
+x1=0;
+
+eps=10^-10;
+
+deff('[z]=df0(x0)','z=3*x0^2+4');
+deff('[z]=df1(x1)','z=-5*x1');
+deff('[z]=fd0(x0)','z=-1.8');
+deff('[z]=fd1(x1)','z=1.4*x1+3');
+for i=1:5
+Xold=[x0;x1];
+A=[feval(x0,df0) feval(x1,df1);feval(x0,fd0) feval(x1,fd1)];
+b=-[feval(x0,x1,f0);feval(x0,x1,f1)];
+Xnew=Xold+inv(A)*b;
+x0=Xnew(1);
+x1=Xnew(2);
+end
+
+disp(Xnew)
\ No newline at end of file
diff --git a/260/CH4/EX4.13/4_13.sce b/260/CH4/EX4.13/4_13.sce
new file mode 100644
index 000000000..25d671f2a
--- /dev/null
+++ b/260/CH4/EX4.13/4_13.sce
@@ -0,0 +1,25 @@
+//Eg-4.13
+//pg-173
+
+clear
+clc
+
+clc;
+clear;
+
+
+x0=0.5;
+x1=0.5;
+x2=0.5;
+
+for i=1:6
+Xold=[x0;x1;x2];
+A=[2*cos(x0)*(sin(x0)-1)+2*sin(x0)*(cos(x1)-cos(x0)) 2*cos(x1)*(sin(x1)-1)+2*sin(x1)*(cos(x0)-cos(x1)) -2*(x2+0.25);cos(x0)*(x2+.25)+2*x2*(cos(x1)*cos(x0)+sin(x0))  -2*x2*sin(x0)*sin(x1) sin(x0)+2*(cos(x1)*sin(x0)-cos(x0));-2*x2*sin(x0)*sin(x1) (x2+.25)*cos(x1)+2*x2*(cos(x0)*cos(x1)+1.5*sin(x1)) sin(x1)+2*(sin(x1)*cos(x0)-1.5*cos(x1))   ];
+b=-[(1-sin(x0))^2+(1.5-sin(x1))^2+(cos(x0)-cos(x1))^2-(x2+0.25)^2;(x2+0.25)*sin(x0)+2*x2*(cos(x1)*sin(x0)-cos(x0));(x2+0.25)*sin(x1)+2*x2*(cos(x0)*sin(x1)-1.5*cos(x1))];
+Xnew=Xold+inv(A)*b;
+x0=Xnew(1);
+x1=Xnew(2);
+x2=Xnew(3);
+end
+
+disp(Xnew)
\ No newline at end of file
diff --git a/260/CH4/EX4.14/4_14.sce b/260/CH4/EX4.14/4_14.sce
new file mode 100644
index 000000000..8785b761b
--- /dev/null
+++ b/260/CH4/EX4.14/4_14.sce
@@ -0,0 +1,23 @@
+//Eg-4.14
+//pg-179
+
+clear
+clc
+
+deff('[z]=f(x)','z=4*x^3+3*x^2+2*x+1');
+
+
+deriv=0;
+a=[1 2 3 4];
+F5=feval(5,f);
+F=a(4);
+x=5;
+for i=1:3
+    deriv=deriv*x+F;
+    F=F*x+a(4-i);
+end
+
+
+
+printf('The value of the function at x = 5 is %f\n',F5)
+printf(' The value of the derivative of the function at x = 5 is %f\n',deriv)
diff --git a/260/CH4/EX4.15/4_15.sce b/260/CH4/EX4.15/4_15.sce
new file mode 100644
index 000000000..be7e89720
--- /dev/null
+++ b/260/CH4/EX4.15/4_15.sce
@@ -0,0 +1,19 @@
+//Eg-4.15
+//pg-180
+
+clear
+clc
+
+
+//co-efficients of the polynomial
+a=[-6 11 -6 1];
+//one root
+l=1;
+n=4;
+for i=n-2:-1:1
+    b(n-1)=a(n);
+    b(i)=b(i+1)*l+a(i+1)
+end
+
+fdef=poly(b,'x','c');
+disp(fdef)
\ No newline at end of file
diff --git a/260/CH4/EX4.16/4_16.sce b/260/CH4/EX4.16/4_16.sce
new file mode 100644
index 000000000..7952ea328
--- /dev/null
+++ b/260/CH4/EX4.16/4_16.sce
@@ -0,0 +1,21 @@
+//Eg-4.16    
+//pg-182
+
+clear
+clc
+
+
+//co-efficients of the polynomial
+a=[6.3825 -21.52 21.26 -8 1];
+//one root
+l=3.7;
+n=5;
+for i=n-2:-1:1
+    b(n-1)=a(n);
+    b(i)=b(i+1)*l+a(i+1)
+end
+
+fdef=poly(b,'x','c');
+disp(fdef)
+printf('\nOr\n    The coefficient matrix is \n')
+disp(b)
\ No newline at end of file
diff --git a/260/CH4/EX4.17/4_17.sce b/260/CH4/EX4.17/4_17.sce
new file mode 100644
index 000000000..8fc0ef2b7
--- /dev/null
+++ b/260/CH4/EX4.17/4_17.sce
@@ -0,0 +1,32 @@
+//Eg-4.17
+//pg-184
+
+clear
+clc
+
+
+clc;
+clear;
+Aold=[1 -3 2 0 0];//4-7 terms are added inorder to satisfy condition no.84 in book
+n=0;
+r=1;
+//iterations are continued till 10^35
+while r/10^35 <= 1
+    for i=1:2
+        summ=0;
+        for k=1:i
+            summ=summ+2*((-1)^k)*Aold(i+k+1)*Aold(i+1-k); 
+        end
+        Anew(i)=((-1)^i)*((Aold(i+1))^2+summ);
+    end
+    Aold=[1 Anew(1) Anew(2) 0 0 ];
+    r=max(abs(Anew));
+    n=n+1;
+end
+
+
+r1=abs(Anew(1))^(1/2^n);
+r2=abs(Anew(2)/Anew(1))^(1/2^n);
+
+disp(r1);
+disp(r2);
\ No newline at end of file
diff --git a/260/CH4/EX4.18/4_18.sce b/260/CH4/EX4.18/4_18.sce
new file mode 100644
index 000000000..9828b90c5
--- /dev/null
+++ b/260/CH4/EX4.18/4_18.sce
@@ -0,0 +1,32 @@
+//Eg-4.18
+//pg-190
+
+clc;
+clear;
+
+//using the function graeffe.sci created.
+
+exec graf.sci
+clc
+eps1 = 0.01;
+eps2 = 0.001;
+
+
+printf('The solution to the problem (a) is \n')
+A1 = [1 3];
+q1 = graf(A1,eps1)
+printf('------------------------------------------------------\n')
+
+printf('The solution to the problem (b) is \n')
+A2 = [1 -4 3];
+q2 = graf(A2,eps1)
+printf('------------------------------------------------------\n')
+
+printf('The solution to the problem (c) is \n')
+A3 = [1 -7 14 -8];
+q3 = graf(A3,eps1);
+printf('------------------------------------------------------\n')
+
+printf('The solution to the problem 2 is \n')
+A = [1 -0.01678 1.76232*10^-5 -4.17671*10^-9];
+q4 = graf(A,eps2);
diff --git a/260/CH4/EX4.19/4_19.sce b/260/CH4/EX4.19/4_19.sce
new file mode 100644
index 000000000..f5ac2db40
--- /dev/null
+++ b/260/CH4/EX4.19/4_19.sce
@@ -0,0 +1,28 @@
+//Eg-4.19
+//pg-193
+
+clear
+clc
+
+
+a=[1 -14 71.74 -153.9 122.2525];
+
+b0=0;
+b01=1;
+g=-1;
+d=1;
+printf('The results for 10 iterations are presented below\n\n')
+printf(' i        g          d            b1            b2            r1          r2\n')
+for i=1:10
+  b1=a(2)-g*b01-d*b0;
+  b2=a(3)-g*b1-d*b01;
+  r1=a(4)-g*b2-d*b1;
+  r2=a(5)-d*b2;
+  dnew=a(5)/b2;
+  gnew=(a(4)-dnew*b1)/b2;
+  d=dnew;
+  g=gnew;
+  printf(' %d    %f    %f    %f    %f    %f    %f\n',i,g,d,b1,b2,r1,r2)
+end
+
+  
\ No newline at end of file
diff --git a/260/CH4/EX4.2/4_2.sce b/260/CH4/EX4.2/4_2.sce
new file mode 100644
index 000000000..4b0c67a63
--- /dev/null
+++ b/260/CH4/EX4.2/4_2.sce
@@ -0,0 +1,23 @@
+//Eg-4.2
+//pg-143
+
+clear
+clc
+
+xl=0;
+xu=1;
+for i=1:20
+    fl=xl-cos(xl);
+    fu=xu-cos(xu);
+    rt=(xl+xu)/2;
+    fr=rt-cos(rt);
+    if fl*fr<0 then
+        xu=(xl+xu)/2;
+    elseif fr*fu<0 then
+        xl=(xl+xu)/2;
+    else
+        rt=(xl+xu)/2; 
+    end
+   
+end
+printf('The solution after 20 iterations is %f',rt)
diff --git a/260/CH4/EX4.20/4_20.sce b/260/CH4/EX4.20/4_20.sce
new file mode 100644
index 000000000..fcc9a9743
--- /dev/null
+++ b/260/CH4/EX4.20/4_20.sce
@@ -0,0 +1,79 @@
+//Eg-4.20
+//pg-198
+
+clear
+clc
+
+
+a=[1 -10  50 -120 144];
+
+b0=0;
+b01=1;
+g=-1;
+d=1;
+for i=1:60
+  b1=a(2)-g*b01-d*b0;
+  b2=a(3)-g*b1-d*b01;
+  r1=a(4)-g*b2-d*b1;
+  r2=a(5)-d*b2;
+  dnew=a(5)/b2;
+  gnew=(a(4)-dnew*b1)/b2;
+  d=dnew;
+  g=gnew;
+end
+disp("Hence gamma delta b1 b2 are respectively")
+disp(g);
+disp(d);
+disp(b1);
+disp(b2);
+
+m=[8 -4 1];
+f=poly(m,'x','c');
+p=roots(f);
+disp("two roots are")
+disp(p);
+
+m=[18 -6 1];
+f=poly(m,'x','c');
+p=roots(f);
+disp("other two roots are");
+disp(p);
+
+
+disp("second part")
+
+a=[1 -8 27 -50 50];
+
+b0=0;
+b01=1;
+g=-1;
+d=1;
+for i=1:60
+  b1=a(2)-g*b01-d*b0;
+  b2=a(3)-g*b1-d*b01;
+  r1=a(4)-g*b2-d*b1;
+  r2=a(5)-d*b2;
+  dnew=a(5)/b2;
+  gnew=(a(4)-dnew*b1)/b2;
+  d=dnew;
+  g=gnew;
+end
+disp("Hence gamma delta b1 b2 are respectively")
+disp(g);
+disp(d);
+disp(b1);
+disp(b2);
+
+m=[5 -2 1];
+f=poly(m,'x','c');
+p=roots(f);
+disp("two roots are")
+disp(p);
+
+m=[10 -6 1];
+f=poly(m,'x','c');
+p=roots(f);
+disp("other two roots are");
+disp(p);
+
+
diff --git a/260/CH4/EX4.21/4_21.sce b/260/CH4/EX4.21/4_21.sce
new file mode 100644
index 000000000..8f9ea9d5c
--- /dev/null
+++ b/260/CH4/EX4.21/4_21.sce
@@ -0,0 +1,28 @@
+//Eg-4.21
+//pg-202
+
+clear
+clc
+
+
+//After complex root substitution a+ib
+
+deff('[z]=u(a,b)','z=a^2-b^2-2*a+2');
+deff('[z]=v(a,b)','z=2*a*b-2*b');
+deff('[z]=ua(a)','z=2*a-2');
+deff('[z]=ub(b)','z=-2*b');
+ain=0.5;
+bin=.5;
+
+for i=1:6
+    U=feval(ain,bin,u);
+    V=feval(ain,bin,v);
+    UA=feval(ain,ua);
+    UB=feval(bin,ub);
+    anew=ain+(V*UB-U*UA)/(UA^2+UB^2);
+    bnew=bin+(V*UA-U*UB)/(UA^2+UB^2);
+    ain=anew;
+    bin=bnew;
+end
+
+printf('\nThe complex root is %f + i(%f) \n',ain,bin)
diff --git a/260/CH4/EX4.3/4_3.sce b/260/CH4/EX4.3/4_3.sce
new file mode 100644
index 000000000..d6ec28d2d
--- /dev/null
+++ b/260/CH4/EX4.3/4_3.sce
@@ -0,0 +1,25 @@
+//Eg-4.3
+//pg-145
+
+clear
+clc
+
+ 
+ A=[-3 0 1];
+ [r,c] = size(A);
+ n = r;
+ 
+ xl=1;
+ xu=3;
+ fx=poly(A,'x','c')
+ 
+ // using formula |xnew^n-alpha|<=xhigh-xlow/2^n
+ 
+ xhigh=3;
+ xlow=1;
+ 
+ t = 1+ (6*2.303/log(2));
+ disp(t)
+ printf('Analytically 2^(1-n)<10^(-6), solving that implies n > %f\n so n = %d',t,t+1)
+ 
+ 
\ No newline at end of file
diff --git a/260/CH4/EX4.4/4_4.sce b/260/CH4/EX4.4/4_4.sce
new file mode 100644
index 000000000..cf59e091f
--- /dev/null
+++ b/260/CH4/EX4.4/4_4.sce
@@ -0,0 +1,32 @@
+//Eg-4.4
+//pg-147
+
+clear
+clc
+
+
+//False Position Method
+
+clear ;
+close ;
+clc ;
+//Coefficients of polynomial in increasing order of power of x
+A = [-2 1 -2 1];
+x1 = 1 ;
+x2 = 3 ;
+fx = poly(A,'x','c');
+for i = 1:20
+    printf('\n\nIteration No. %i \n',i);
+    fx1 = horner(fx,x1);
+    fx2 = horner(fx,x2);
+    x0 = x1 - fx1*(x2-x1)/(fx2-fx1) 
+    printf('xnew = %f \n',x0);
+    fx0 = horner(fx,x0);
+    if fx1*fx0 < 0 then
+        x2 = x0 ;
+    else
+        x1 = x0 ;
+    end    
+end
+
+printf('\n\nPlease note that the author has considered only 5 decimal places, but here we have taken 6 decimal places, so a minor difference in the answer may occur')
\ No newline at end of file
diff --git a/260/CH4/EX4.5/4_5.sce b/260/CH4/EX4.5/4_5.sce
new file mode 100644
index 000000000..6703a8b09
--- /dev/null
+++ b/260/CH4/EX4.5/4_5.sce
@@ -0,0 +1,40 @@
+//Eg-4.5
+//pg-149
+
+clear
+clc
+
+
+//False Position Method
+
+clear ;
+close ;
+clc ;
+//Coefficients of polynomial in increasing order of power of x
+A = [-3.1622777 -1.2649111 -0.1264911 0 0 100];
+x1 = 0 ;
+x2 = 2 ;
+fx = poly(A,'x','c');
+printf('\n\nThe given equation can be modified and written in the following form after substituting the values of given constants\n')
+disp(fx)
+i = 0;
+eps = 1;
+
+while(eps > 10^(-6))
+    i = i+1;
+    //printf('\n\nIteration No. %i \n',i);
+    fx1 = horner(fx,x1);
+    fx2 = horner(fx,x2);
+    xnew = (x1*fx2 - x2*fx1)/(fx2-fx1); 
+    fxnew = horner(fx,xnew);
+    //printf('xnew = %f \nfxnew = %f',xnew,fxnew);
+    
+    if fx1*fxnew < 0 then
+        x2 = xnew ;
+    else
+        x1 = xnew ;
+    end
+    eps = abs(fxnew);
+end
+
+printf('\n\nThe result obtained after %d iterations is x = %f\n',i,xnew)
\ No newline at end of file
diff --git a/260/CH4/EX4.6/4_6.sce b/260/CH4/EX4.6/4_6.sce
new file mode 100644
index 000000000..1695ccb55
--- /dev/null
+++ b/260/CH4/EX4.6/4_6.sce
@@ -0,0 +1,52 @@
+//Eg-4.6
+//pg-151
+
+clear
+clc
+
+// Method of Sucessive substitution
+
+clear ;
+close ;
+clc ;
+//Coefficients of polynomial in increasing order of power of x
+A = [0 0 1];
+
+//when G(x)=x^2
+x01 = 0.5;
+x02 = 1.5;
+t(1) = x01;
+fx = poly(A,'x','c');
+printf('\nFor G(x) = x^2\n\n')
+printf('  x0        itr        xnew\n')
+for(i = 1:5)
+    xnew(i) = horner(fx,t(i))
+    t(i+1) = xnew(i);
+    printf('%f     %d        %f\n',x01,i,xnew(i))
+end
+p(1) = x02;
+for(i = 1:5)
+    xnew(i) = horner(fx,p(i))
+    p(i+1) = xnew(i);
+    printf('%f     %d        %f\n',x02,i,xnew(i))
+end
+
+
+//when g(x)=x^1/2
+
+deff('z=f(x)','z=x^(1/2)');
+printf('\nFor G(x) = x^0.5\n\n')
+printf('  x0        itr        xnew\n')
+for i=1:5
+    xnew(i) = feval(t(i),f);
+    t(i+1) = xnew(i);
+    printf('%f     %d        %f\n',x01,i,xnew(i))
+end
+for i=1:5
+    xnew(i) = feval(p(i),f);
+    p(i+1) = xnew(i);
+    printf('%f     %d        %f\n',x02,i,xnew(i))
+end
+
+
+
diff --git a/260/CH4/EX4.7/4_7.sce b/260/CH4/EX4.7/4_7.sce
new file mode 100644
index 000000000..e520d423b
--- /dev/null
+++ b/260/CH4/EX4.7/4_7.sce
@@ -0,0 +1,37 @@
+//Eg-4.7
+//pg-154
+
+
+
+// Method of Sucessive substitution
+
+clear ;
+close ;
+clc ;
+//Coefficients of polynomial in increasing order of power of x
+
+x1=0.5;
+deff('[z]=f(x)','z=0.3*exp(x)');
+errorcheck=1;
+iter=1;
+eps=10^-8;
+imax=30;
+
+while errorcheck==1&iter<imax
+xnew=feval(x1,f);
+ printf('xnew  = %f\n',xnew);
+
+abserr=abs(xnew-x1)/abs(xnew);
+x1=xnew;
+if abserr<=eps then
+    errorcheck=2;
+end
+iter=iter+1;
+end
+
+disp("The solution is")
+disp(x1)
+disp("no of iterations required")
+disp(iter)
+
+printf('\nSince the number of decimals used for calculations and that displayed are different the number of iterations is different from the book.')
\ No newline at end of file
diff --git a/260/CH4/EX4.8/4_8.sce b/260/CH4/EX4.8/4_8.sce
new file mode 100644
index 000000000..f310fb243
--- /dev/null
+++ b/260/CH4/EX4.8/4_8.sce
@@ -0,0 +1,23 @@
+//Eg-4.8
+//pg-155
+
+clear
+clc
+
+
+// Newton Raphson Method
+
+A=[6 -5 1];
+x1=0.2;
+x2=4;
+fx=poly(A,'x','c');
+B=[-5 2];
+diffx=poly(B,'x','c');
+for i=1:6
+    printf('\niteration number %i\n',i-1);
+    xnew1=x1-horner(fx,x1)/horner(diffx,x1);
+    xnew2=x2-horner(fx,x2)/horner(diffx,x2);
+    printf('xnew1 = %f \nxnew2=%f\n',x1,x2);
+    x1=xnew1;
+    x2=xnew2;
+end
\ No newline at end of file
diff --git a/260/CH4/EX4.9/4_9.sce b/260/CH4/EX4.9/4_9.sce
new file mode 100644
index 000000000..44c818eb4
--- /dev/null
+++ b/260/CH4/EX4.9/4_9.sce
@@ -0,0 +1,32 @@
+//Eg-4.9
+//pg-157
+
+clear
+clc
+
+
+// Newton Raphson Method
+
+A = [-150-(%pi*0.12*298)-%pi*0.12*0.8*5.67*10^(-8)*298^4 %pi*0.12*25 0 0 %pi*.12*.8*5.67*10^(-8)];
+x1 = 298;
+fx = poly(A,'x','c');
+B = [%pi*0.12*25 0 0 %pi*.12*4*.8*5.67*10^(-8)];
+diffx = poly(B,'x','c');
+disp(fx)
+disp(diffx)
+iter=1;
+
+eps=10^(-10);
+errorcheck=1;
+abserr = 1;
+
+while (abserr > eps)
+    printf('\niteration number %i\n',iter);
+    xnew1 = x1 - horner(fx,x1)/horner(diffx,x1);
+    printf('xnew1 = %f \n',xnew1);
+    abserr = abs((xnew1 - x1)/(x1)*100);
+    x1 = xnew1;
+    iter = iter + 1;
+end
+
+printf('\nThe solution obtained after %d iterations is %f\n',iter-1,xnew1)
\ No newline at end of file
-- 
cgit