initial commit / add all books

14 files changed, 420 insertions, 0 deletions

diff --git a/1670/CH7/EX7.1/7_1.sce b/1670/CH7/EX7.1/7_1.sce
new file mode 100755
index 000000000..45238c2cc
--- /dev/null
+++ b/1670/CH7/EX7.1/7_1.sce
@@ -0,0 +1,12 @@
+//Example 7.1

+//Differentiation

+//Page no. 230

+clc;close;clear;

+deff('y=f(x)','y=sin(x)')

+deff('y=f1(x,h)','y=(f(x+h)-f(x-h))/(2*h)')

+deff('y=f2(x,h)','y=(-f(x+2*h)+8*f(x+h)-8*f(x-h)+f(x-2*h))/(12*h)')

+h=0.01;x=0.5

+d=f1(x,h)

+d1=f2(x,h)

+printf('Centred Formula of Order O(h2) = %g\n',d)

+printf('\n Centred Formula of Order O(h4) = %g',d1)
\ No newline at end of file
diff --git a/1670/CH7/EX7.10/7_10.sce b/1670/CH7/EX7.10/7_10.sce
new file mode 100755
index 000000000..4a512749d
--- /dev/null
+++ b/1670/CH7/EX7.10/7_10.sce
@@ -0,0 +1,9 @@
+//Example 7.10

+//Lagrange's Differentiation

+//Page no. 246

+clc;close;clear;

+

+z=[0,0.989992;0.1,0.999135;0.2,0.998295;0.3,0.987480];

+h=0.1;

+deff('y=f(x)','y=(-3*z(x,2)+4*z(x+1,2)-z(x+2,2))/(2*h)')

+printf('\n f`(0) = %g\n\n f`(0.1) = %g',f(1),f(2))
\ No newline at end of file
diff --git a/1670/CH7/EX7.11/7_11.sce b/1670/CH7/EX7.11/7_11.sce
new file mode 100755
index 000000000..bd997839a
--- /dev/null
+++ b/1670/CH7/EX7.11/7_11.sce
@@ -0,0 +1,57 @@
+//Example 7.11

+//Newton's Divided Difference Interpolation

+//Page no. 247

+clc;close;clear;

+

+x=[-1,1,2,3]

+y=[-21,15,12,3];

+y1=y;h=0.0000001

+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=1:4-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=1:4

+        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=poly(0,'x');

+p=1;f=y1(1);

+for i=1:3

+    for j=1:i

+        p=p*(x1-x(j))

+    end

+    p=p*z(1,i)

+    f=f+p

+    p=1;

+end

+disp(f,"f(x) = ")

+f1=y1(1)

+x2=poly(h,'x');

+for i=1:3

+    for j=1:i

+        p=p*(x2-x(j))

+    end

+    p=p*z(1,i)

+    f1=f1+p

+    p=1;

+end

+f1=(f1-f)/h

+disp(f1,"f`(x) = ")

+r=roots(f1)

+disp(r,"Roots = ")

+x1=r(2)

+p=1;f=y1(1);

+for i=1:3

+    for j=1:i

+        p=p*(x1-x(j))

+    end

+    p=p*z(1,i)

+    f=f+p

+    p=1;

+end

+disp(f,"Maximum Value = ")
\ No newline at end of file
diff --git a/1670/CH7/EX7.12/7_12.sce b/1670/CH7/EX7.12/7_12.sce
new file mode 100755
index 000000000..f66bf046f
--- /dev/null
+++ b/1670/CH7/EX7.12/7_12.sce
@@ -0,0 +1,31 @@
+//Example 7.12

+//Stirlings Central Difference Derivatives

+//Page no. 248

+clc;close;clear;

+printf('   x\t    y\t    d\t    d2\t    d3\t    d4\n')

+printf('------------------------------------------------')

+function [x]=f(x1)

+    x=0;

+    for i=3:6

+        x=x+(-1)^(i-1)*(z(x1,i))/((i-2)*h)

+    end

+endfunction

+h=1;

+z=[-3,-33;-2,-12;-1,-3;0,0;1,3;2,12;3,33];

+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 j==1

+            printf('   %g\t    ',z(i,j))

+        else

+            printf('%i\t    ',z(i,j))

+        end

+    end

+    printf('\n')

+end

+printf("\n\nf`(-3) = %g\n\nf`(0) = %g",f(1),f(4))
\ No newline at end of file
diff --git a/1670/CH7/EX7.13/7_13.sce b/1670/CH7/EX7.13/7_13.sce
new file mode 100755
index 000000000..4a8b12a74
--- /dev/null
+++ b/1670/CH7/EX7.13/7_13.sce
@@ -0,0 +1,42 @@
+//Example 7.13

+//Newtons Backward Formula

+//Page no. 248

+clc;close;clear;

+printf('   x\t  y\t  d\t  d2\t  d3\t  d4\t  d5\n')

+printf('--------------------------------------------------------')

+h=0.5;

+deff('y=f2(x)','y=(z(x,4)-z(x,5)+z(x,6))/h^2')

+z=[1.5,3.375;2,7;2.5,13.625;3,24;3.5,38.875;4,59];

+for i=1:6

+    for j=3:7

+        z(i,j)=-1

+    end

+end

+for i=3:7

+    for j=1:8-i

+        z(j,i)=z(j+1,i-1)-z(j,i-1)

+    end

+end

+printf('\n')

+for i=1:6

+    for j=1:7

+        if z(i,j)==-1 then

+            printf(' \t')

+        elseif j==1

+            printf('   %.1f\t',z(i,j))

+        else

+            printf('%.3f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+

+j=1;y1=0;

+for i=3:6

+    y1=y1+(-1)^(i-1)*z(j,i)/(i-2)

+end

+y1=y1/h;

+y2(7)=f2(1);

+printf('\n\n f`(1.5)= %g',y1)

+printf('\n\n f``(1.5) = %g',y2(7))

+

diff --git a/1670/CH7/EX7.14/7_14.sce b/1670/CH7/EX7.14/7_14.sce
new file mode 100755
index 000000000..c8dd35868
--- /dev/null
+++ b/1670/CH7/EX7.14/7_14.sce
@@ -0,0 +1,13 @@
+//Example 7.14

+//Newtons Divided Difference

+//Page no. 249

+clc;close;clear;

+

+x=[3,5,11,27,34]

+y=[-13,23,899,17315,35606]

+deff('y=f(x1)','y=a1+a2*((x1-x(2))+(x1-x(3)))')

+a1=(y(3)-y(2))/(x(3)-x(2))

+a2=((y(4)-y(3))/(x(4)-x(3))-(y(3)-y(2))/(x(3)-x(2)))/(x(4)-x(2))

+disp(y,"y:",x,"x:")

+printf('\n\n a1 = %g\t\ta2 = %g\n\n',a1,a2)

+disp(f(10),"f`(10) = ")
\ No newline at end of file
diff --git a/1670/CH7/EX7.2/7_2.sce b/1670/CH7/EX7.2/7_2.sce
new file mode 100755
index 000000000..041900836
--- /dev/null
+++ b/1670/CH7/EX7.2/7_2.sce
@@ -0,0 +1,22 @@
+//Example 7.2

+//Differentiation

+//Page no. 232

+clc;close;clear;

+

+t=[1,1.1,1.2,1.3,1.4]

+I=[8.2277,7.2428,5.9908,4.5260,2.9122]

+L=0.05;R=2;h=0.1;

+deff('y=f(x)','y=L*i1(x)+R*I(x)')

+deff('y=f1(x,h1)','y=(I(x+h1)-I(x-h1))/(2*h)')

+deff('y=f2(x,h1)','y=(-I(x+2*h1)+8*I(x+h1)-8*I(x-h1)+I(x-2*h1))/(12*h)')

+x=3;h1=1;

+i1(x)=f1(x,h1)

+E=f(x)

+printf('Using Centred Tendency of Order O(h2)\n')

+printf('I`(1.2) = %g\n',i1(x))

+printf('\n E(1.2) = %g',E)

+i1(x)=f2(x,h1)

+E=f(x)

+printf('\n\n\nUsing Centred Tendency of Order O(h4)\n')

+printf('I`(1.2) = %g\n',i1(x))

+printf('\n E(1.2) = %g',E)
\ No newline at end of file
diff --git a/1670/CH7/EX7.3/7_3.sce b/1670/CH7/EX7.3/7_3.sce
new file mode 100755
index 000000000..ac94dd29e
--- /dev/null
+++ b/1670/CH7/EX7.3/7_3.sce
@@ -0,0 +1,18 @@
+//Example 7.3

+//Richardson Extrapolation

+//Page no. 233

+clc;close;clear;

+

+t=[1,1.1,1.2,1.3,1.4]

+I=[8.2277,7.2428,5.9908,4.5260,2.9122]

+h=0.1;

+deff('y=f1(x,h1)','y=(I(x+h1)-I(x-h1))/(2*h)')

+deff('y=f2(x,h1)','y=(I(x+2*h1)-I(x-2*h1))/(4*h)')

+deff('y=f3(x,h1)','y=(I(x+h1)-I(x-h1))/(2*h)')

+x=3;h1=1;

+D0h=f1(x,h1)

+printf('\nD0(h) = %g\n',D0h)

+D02h=f2(x,h1)

+printf('\nD0(2h) = %g\n',D02h)

+I1=(4*D0h-D02h)/x

+printf('\nI` (1.2) = %g',I1)
\ No newline at end of file
diff --git a/1670/CH7/EX7.4/7_4.sce b/1670/CH7/EX7.4/7_4.sce
new file mode 100755
index 000000000..e1afbb4e7
--- /dev/null
+++ b/1670/CH7/EX7.4/7_4.sce
@@ -0,0 +1,13 @@
+//Example 7.4

+//Differentiation

+//Page no. 233

+clc;close;clear;

+

+t=[1.2,1.3,1.4,1.5,1.6]

+I=[1.5095,1.6984,1.9043,2.1293,2.3756]

+h=0.1;

+deff('y=f2(x,h1)','y=(-I(x+2*h1)+8*I(x+h1)-8*I(x-h1)+I(x-2*h1))/(12*h)')

+x=3;h1=1;

+i1(x)=f2(x,h1)

+printf('\nUsing Centred Tendency of Order O(h4)\n')

+printf('f`(1.4) = %g\n',i1(x))
\ No newline at end of file
diff --git a/1670/CH7/EX7.5/7_5.sce b/1670/CH7/EX7.5/7_5.sce
new file mode 100755
index 000000000..e879350d9
--- /dev/null
+++ b/1670/CH7/EX7.5/7_5.sce
@@ -0,0 +1,36 @@
+//Example 7.5

+//Stirlings Central Difference Derivatives

+//Page no. 238

+clc;close;clear;

+printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\n')

+printf('-----------------------------------------------------------------------------------------')

+h=0.1;s=1;

+e=[1,6,30]

+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=[0.7,0.644218;0.8,0.717356;0.9,0.783327;1,0.841471;1.1,0.891207;1.2,0.932039;1.3,0.963558];

+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')

+        elseif j==1

+            printf('   %.1f\t\t',z(i,j))

+        else

+            printf('%.6f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+fp=0;i=5;

+for j=2:2:6

+    fp=fp+((-1)^(j/2+1))*(z(i,j)-z(i-2,j))/(2*h*e(j/2))

+    i=i-1;

+end

+printf('\n\nf`p (sin`(x))= %g',fp)
\ No newline at end of file
diff --git a/1670/CH7/EX7.6/7_6.sce b/1670/CH7/EX7.6/7_6.sce
new file mode 100755
index 000000000..e10954e41
--- /dev/null
+++ b/1670/CH7/EX7.6/7_6.sce
@@ -0,0 +1,39 @@
+//Example 7.6

+//Stirlings Central Difference Derivatives

+//Page no. 239

+clc;close;clear;

+printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\t\t    d5\n')

+printf('----------------------------------------------------------------------------------------------------------')

+h=0.2;s=1;

+deff('y=f1()','y=(z(4,3)+(3*p^2-1)*z(4,4)/factorial(3)-(3*p^2-6*p+2)*z(3,4)/factorial(3))/h')

+z=[0.2,2.10022;0.4,1.98730;0.6,1.90940;0.8,1.86672;1,1.85937;1.2,1.88737;1.4,1.95063];

+x0=0.8;p=poly(0,'p');

+for i=3:7

+    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=1:7

+        if z(i,j)==0 then

+            printf(' \t')

+        elseif j==1

+            printf('   %.1f\t\t',z(i,j))

+        else

+            printf('%.6f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+f1p=f1()

+disp(f1p)

+r=roots(f1p);

+for i=1:2

+    if abs(r(i))==r(i) then

+        r1=r(i)

+        disp(r(i),"p = ")

+    end

+end

+x=x0+r1*h;

+disp(x,"x = ")
\ No newline at end of file
diff --git a/1670/CH7/EX7.7/7_7.sce b/1670/CH7/EX7.7/7_7.sce
new file mode 100755
index 000000000..5da90a4fc
--- /dev/null
+++ b/1670/CH7/EX7.7/7_7.sce
@@ -0,0 +1,47 @@
+//Example 7.7

+//Stirlings Central Difference Derivatives

+//Page no. 240

+clc;close;clear;

+printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\n')

+printf('------------------------------------------------------------------------------------------')

+h=0.2;s=1;

+a=poly(0,'a');

+b=poly(0,'b');

+deff('y=f3(x)','y=z(x,1)*y2(x)+(z(x,1)-b)*z(x,2)')

+deff('y=f4(x)','y=y1(x)*a')

+deff('y=f1(x)','y=(z(x+1,2)-z(x-1,2)-(z(x,4)-z(x-2,4))/factorial(3)+4*(z(x-1,6)-z(x-3,6))/factorial(5))/(2*h)')

+deff('y=f2(x)','y=(z(x-1,4)-2*(z(x-2,6))/factorial(4))/h^2')

+z=[0.8,1.73036;1,1.95532;1.2,2.19756;1.4,2.45693;1.6,2.73309;1.8,3.02549;2,3.33334;2.2,3.65563];

+x0=0.8;

+for i=3:6

+    for j=1:10-i

+        z(j,i)=z(j+1,i-1)-z(j,i-1)

+    end

+end

+printf('\n')

+for i=1:8

+    for j=1:6

+        if z(i,j)==0 then

+            printf(' \t')

+        elseif j==1

+            printf('   %.1f\t\t',z(i,j))

+        else

+            printf('%.6f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+y1(4)=f1(4);

+y2(4)=f2(4);

+y1(5)=f1(5);

+y2(5)=f2(5);

+g=f3(4)

+printf('\n\ny`(1.4) = %g\n\ny``(1.4) = %g\n\ny`(1.6) = %g\n\ny``(1.6) = %g\n\n',y1(4),y2(4),y1(5),y2(5))

+disp(f3(4),f4(4))

+printf('\n\n')

+A=[y1(4),z(4,2);y1(5),z(5,2)];

+B=[z(4,1)*(y2(4)+z(4,2));z(5,1)*(y2(5)+z(5,2))];

+disp(f3(5),f4(5))

+

+C=inv(A)*B;

+printf('\n\n a = %g\n\n b = %g',C(1),C(2))
\ No newline at end of file
diff --git a/1670/CH7/EX7.8/7_8.sce b/1670/CH7/EX7.8/7_8.sce
new file mode 100755
index 000000000..1ca7401ab
--- /dev/null
+++ b/1670/CH7/EX7.8/7_8.sce
@@ -0,0 +1,43 @@
+//Example 7.8

+//Stirlings Central Difference Derivatives

+//Page no. 242

+clc;close;clear;

+printf('   x\t\t    y\t\t    d\t\t    d2\t\t    d3\t\t    d4\n')

+printf('------------------------------------------------------------------------------------------')

+h=0.01;

+a=poly(0,'n');

+deff('y=f3(x)','y=z(x,1)^2*y2(x)+z(x,1)*y1(x)+(z(x,1)^2-a^2)*z(x,2)')

+deff('y=f1(x)','y=(z(x+1,2)-z(x-1,2)-(z(x,4)-z(x-2,4))/factorial(3))/(2*h)')

+deff('y=f2(x)','y=(z(x-1,4)-2*(z(x-2,6))/factorial(4))/h^2')

+z=[85,0.0353878892;85.01,0.0346198696;85.02,0.0338490002;85.03,0.0330753467;85.04,0.032298975];

+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')

+        elseif j==1

+            printf('   %.2f\t',z(i,j))

+        else

+            printf('%.10f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+y1(3)=f1(3);

+y2(3)=f2(3);

+

+printf('\n\ny`(85.02) = %g\n\ny``(85.02) = %.7g\n\n',y1(3),y2(3))

+n=f3(3)

+disp(n,"0 =")

+n=roots(n)

+for i=1:2

+    if abs(n(i))==n(i) then

+        n1=n(i)

+    end

+end

+printf('\n\nn = %.2g',n1)
\ No newline at end of file
diff --git a/1670/CH7/EX7.9/7_9.sce b/1670/CH7/EX7.9/7_9.sce
new file mode 100755
index 000000000..08d554a09
--- /dev/null
+++ b/1670/CH7/EX7.9/7_9.sce
@@ -0,0 +1,38 @@
+//Example 7.9

+//Newtons Backward Formula

+//Page no. 243

+clc;close;clear;

+printf('   x\t  y\t  d\t  d2\t  d3\t  d4\t  d5\t  d6\n')

+printf('---------------------------------------------------------------')

+h=0.1;

+deff('y=f2(x)','y=(z(x-2,4)+z(x-3,5)+z(x-4,6))/h^2')

+z=[1,7.989;1.1,8.403;1.2,8.781;1.3,9.129;1.4,9.451;1.5,9.750;1.6,10.031];

+for i=3:8

+    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=1:8

+        if z(i,j)==0 then

+            printf(' \t')

+        elseif j==1

+            printf('   %.1f\t',z(i,j))

+        else

+            printf('%.3f\t',z(i,j))

+        end

+    end

+    printf('\n')

+end

+

+j=6;y1=0;

+for i=3:6

+    y1=y1+z(j,i)/(i-2)

+j=j-1 

+end

+y1=y1/h;

+y2(7)=f2(7);

+printf('\n\n dy\n -- = %.10g\n dx',y1)

+printf('\n\n\n d2y\n --- = %.5g\n dx2',y2(7))

+