initial commit / add all books

21 files changed, 709 insertions, 0 deletions

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