initial commit / add all books

16 files changed, 326 insertions, 0 deletions

diff --git a/1332/CH12/EX12.1/12_1.pdf b/1332/CH12/EX12.1/12_1.pdf
new 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
new 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
new 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
new 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
new 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
new 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
new 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
new 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