initial commit / add all books

9 files changed, 393 insertions, 0 deletions

diff --git a/964/CH21/EX21.1/21_1.sce b/964/CH21/EX21.1/21_1.sce
new file mode 100755
index 000000000..5f011f8bc
--- /dev/null
+++ b/964/CH21/EX21.1/21_1.sce
@@ -0,0 +1,25 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+tval=1.640533;

+a=0;

+b=0.8;

+fa=f(a);

+fb=f(b);

+l=(b-a)*((fa+fb)/2);

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+

+//by using approximate error estimate

+

+//the second derivative of f

+function y=g(x)

+    y=-400+4050*x-10800*x^2+8000*x^3

+endfunction

+f2x=intg(0,0.8,g)/(b-a);//average value of second derivative

+Ea=-(1/12)*(f2x)*(b-a)^3;

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

+disp(Ea,"The approximate error estimate without using the true value=")

diff --git a/964/CH21/EX21.2/21_2.sce b/964/CH21/EX21.2/21_2.sce
new file mode 100755
index 000000000..1f2e72374
--- /dev/null
+++ b/964/CH21/EX21.2/21_2.sce
@@ -0,0 +1,29 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+a=0;

+b=0.8;

+tval=1.640533;

+n=2;

+h=(b-a)/n;

+fa=f(a);

+fb=f(b);

+fh=f(h);

+l=(b-a)*(fa+2*fh+fb)/(2*n);

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+

+//by using approximate error estimate

+

+//the second derivative of f

+function y=g(x)

+    y=-400+4050*x-10800*x^2+8000*x^3

+endfunction

+f2x=intg(0,0.8,g)/(b-a);//average value of second derivative

+Ea=-(1/12)*(f2x)*(b-a)^3/(n^2);

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

+disp(Ea,"The approximate error estimate without using the true value=")

+

diff --git a/964/CH21/EX21.3/21_3.sce b/964/CH21/EX21.3/21_3.sce
new file mode 100755
index 000000000..5cbca050b
--- /dev/null
+++ b/964/CH21/EX21.3/21_3.sce
@@ -0,0 +1,141 @@
+clc;

+clear;

+g=9.8;//m/s^2; acceleration due to gravity

+m=68.1;//kg

+c=12.5;//kg/sec; drag coefficient

+function v=f(t)

+    v=g*m*(1-exp(-c*t/m))/c

+endfunction

+tval=289.43515;//m

+a=0;

+b=10;

+fa=f(a);

+fb=f(b);

+for i=10:10:20

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=50:50:100

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=100:100:200

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=200:300:500

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=1000:1000:2000

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=2000:3000:5000

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+for i=5000:5000:10000

+    n=i;

+    h=(b-a)/n;

+    disp(i,"No. of segments=")

+    disp(h,"Segment size=")

+    j=a+h;

+    s=0;

+    while j<b

+        s=s+f(j);

+        j=j+h;

+    end

+    l=(b-a)*(fa+2*s+fb)/(2*n);

+    Et=tval-l;//error

+    et=Et*100/tval;//percent relative error

+    disp("m",l,"Estimated d=")

+    disp(et,"et(%)")

+    disp("---------------------------------------------------------")

+end

+

+

diff --git a/964/CH21/EX21.4/21_4.sce b/964/CH21/EX21.4/21_4.sce
new file mode 100755
index 000000000..efa2bba58
--- /dev/null
+++ b/964/CH21/EX21.4/21_4.sce
@@ -0,0 +1,30 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+a=0;

+b=0.8;

+tval=1.640533;

+n=2;

+h=(b-a)/n;

+fa=f(a);

+fb=f(b);

+fh=f(h);

+l=(b-a)*(fa+4*fh+fb)/(3*n);

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+

+//by using approximate error estimate

+

+//the fourth derivative of f

+function y=g(x)

+    y=-21600+48000*x

+endfunction

+f4x=intg(0,0.8,g)/(b-a);//average value of fourth derivative

+Ea=-(1/2880)*(f4x)*(b-a)^5;

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

+disp(Ea,"The approximate error estimate without using the true value=")

+

diff --git a/964/CH21/EX21.5/21_5.sce b/964/CH21/EX21.5/21_5.sce
new file mode 100755
index 000000000..e5de4a916
--- /dev/null
+++ b/964/CH21/EX21.5/21_5.sce
@@ -0,0 +1,41 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+a=0;

+b=0.8;

+tval=1.640533;

+n=4;

+h=(b-a)/n;

+fa=f(a);

+fb=f(b);

+j=a+h;

+s=0;

+count=1;

+while j<b

+    if (-1)^count==-1 then

+        s=s+4*f(j);

+    else

+        s=s+2*f(j);

+    end

+    count=count+1;

+    j=j+h;

+end

+l=(b-a)*(fa+s+fb)/(3*n);

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+

+//by using approximate error estimate

+

+//the fourth derivative of f

+function y=g(x)

+    y=-21600+48000*x

+endfunction

+f4x=intg(0,0.8,g)/(b-a);//average value of fourth derivative

+Ea=-(1/(180*4^4))*(f4x)*(b-a)^5;

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

+disp(Ea,"The approximate error estimate without using the true value=")

+

diff --git a/964/CH21/EX21.6/21_6.sce b/964/CH21/EX21.6/21_6.sce
new file mode 100755
index 000000000..60d21800a
--- /dev/null
+++ b/964/CH21/EX21.6/21_6.sce
@@ -0,0 +1,52 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+a=0;

+b=0.8;

+tval=1.640533;

+//part a

+n=3;

+h=(b-a)/n;

+fa=f(a);

+fb=f(b);

+j=a+h;

+s=0;

+count=1;

+while j<b

+    s=s+3*f(j);

+    count=count+1;

+    j=j+h;

+end

+l=(b-a)*(fa+s+fb)/(8);

+disp("Part A:")

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+

+//by using approximate error estimate

+

+//the fourth derivative of f

+function y=g(x)

+    y=-21600+48000*x

+endfunction

+f4x=intg(0,0.8,g)/(b-a);//average value of fourth derivative

+Ea=-(1/6480)*(f4x)*(b-a)^5;

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

+disp(Ea,"The approximate error estimate without using the true value=")

+

+//part b

+n=5;

+h=(b-a)/n;

+l1=(a+2*h-a)*(fa+4*f(a+h)+f(a+2*h))/6;

+l2=(a+5*h-a-2*h)*(f(a+2*h)+3*(f(a+3*h)+f(a+4*h))+fb)/8;

+l=l1+l2;

+disp("---------------------------------------------------")

+disp("Part B:")

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

diff --git a/964/CH21/EX21.7/21_7.sce b/964/CH21/EX21.7/21_7.sce
new file mode 100755
index 000000000..82bc6b812
--- /dev/null
+++ b/964/CH21/EX21.7/21_7.sce
@@ -0,0 +1,19 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+tval=1.640533;

+x=[0 0.12 0.22 0.32 0.36 0.4 0.44 0.54 0.64 0.7 0.8];

+for i=1:11

+    func(i)=f(x(i));

+end

+l=0;

+for i=1:10

+    l=l+(x(i+1)-x(i))*(func(i)+func(i+1))/2;

+end

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

diff --git a/964/CH21/EX21.8/21_8.sce b/964/CH21/EX21.8/21_8.sce
new file mode 100755
index 000000000..6e46267ad
--- /dev/null
+++ b/964/CH21/EX21.8/21_8.sce
@@ -0,0 +1,22 @@
+clc;

+clear;

+function y=f(x)

+    y=(0.2+25*x-200*x^2+675*x^3-900*x^4+400*x^5)

+endfunction

+tval=1.640533;

+x=[0 0.12 0.22 0.32 0.36 0.4 0.44 0.54 0.64 0.7 0.8];

+for i=1:11

+    func(i)=f(x(i));

+end

+l1=(x(2)-x(1))*((f(x(1))+f(x(2)))/2);

+l2=(x(4)-x(2))*(f(x(4))+4*f(x(3))+f(x(2)))/6;

+l3=(x(7)-x(4))*(f(x(4))+3*(f(x(5))+f(x(6)))+f(x(7)))/8;

+l4=(x(9)-x(7))*(f(x(7))+4*f(x(8))+f(x(9)))/6;

+l5=(x(10)-x(9))*((f(x(10))+f(x(9)))/2);

+l6=(x(11)-x(10))*((f(x(11))+f(x(10)))/2);

+l=l1+l2+l3+l4+l5+l6;

+disp(l,"l=")

+Et=tval-l;//error

+et=Et*100/tval;//percent relative error

+disp(Et,"The Error Et=")

+disp("%",et,"The percent relative error et=")

diff --git a/964/CH21/EX21.9/21_9.sce b/964/CH21/EX21.9/21_9.sce
new file mode 100755
index 000000000..c9a62a048
--- /dev/null
+++ b/964/CH21/EX21.9/21_9.sce
@@ -0,0 +1,34 @@
+clc;

+clear;

+function t=f(x,y)

+    t=2*x*y+2*x-x^2-2*y^2+72

+endfunction

+len=8;//m,length

+wid=6;//m,width

+a=0;

+b=len;

+n=2;

+h=(b-a)/n;

+a1=0;

+b1=wid;

+h1=(b1-a1)/n;

+

+fa=f(a,0);

+fb=f(b,0);

+fh=f(h,0);

+lx1=(b-a)*(fa+2*fh+fb)/(2*n);

+

+fa=f(a,h1);

+fb=f(b,h1);

+fh=f(h,h1);

+lx2=(b-a)*(fa+2*fh+fb)/(2*n);

+

+fa=f(a,b1);

+fb=f(b,b1);

+fh=f(h,b1);

+lx3=(b-a)*(fa+2*fh+fb)/(2*n);

+

+l=(b1-a1)*(lx1+2*lx2+lx3)/(2*n);

+

+avg_temp=l/(len*wid);

+disp(avg_temp,"The average termperature is=")