initial commit / add all books

16 files changed, 223 insertions, 0 deletions

diff --git a/1332/CH13/EX13.1/13_1.pdf b/1332/CH13/EX13.1/13_1.pdf
new 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
new 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
new 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
new 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
new 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
new 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
new 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
new 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