initial commit / add all books

9 files changed, 130 insertions, 0 deletions

diff --git a/964/CH19/EX19.1/19_1.sce b/964/CH19/EX19.1/19_1.sce
new file mode 100755
index 000000000..abd1ff8b4
--- /dev/null
+++ b/964/CH19/EX19.1/19_1.sce
@@ -0,0 +1,43 @@
+clc;

+clear;

+function y=f(t)

+    y=1.7+cos(4.189*t+1.0472)

+endfunction

+deltat=0.15;

+t1=0;

+t2=1.35;

+omega=4.189;

+del=(t2-t1)/9;

+for i=1:10

+    t(i)=t1+del*(i-1);

+end

+sumy=0;

+suma=0;

+sumb=0;

+for i=1:10

+    y(i)=f(t(i));

+    a(i)=y(i)*cos(omega*t(i));

+    b(i)=y(i)*sin(omega*t(i));

+    sumy=sumy+y(i);

+    suma=suma+a(i);

+    sumb=sumb+b(i);

+end

+A0=sumy/10;

+A1=2*suma/10;

+B1=2*sumb/10;

+disp("The least square fit is y=A0+A1*cos(w0*t)+A2*sin(w0*t), where")

+disp(A0,"A0=")

+disp(A1,"A1=")

+disp(B1,"B1=")

+theta=atan(-B1/A1);

+C1=(A1^2 + B1^2)^0.5;

+disp("Alternatively, the least square fit can be expressed as")

+disp("y=A0+C1*cos(w0*t + theta), where")

+disp(A0,"A0=")

+disp(theta,"Theta=")

+disp(C1,"C1=")

+disp("Or")

+disp("y=A0+C1*sin(w0*t + theta + pi/2), where")

+disp(A0,"A0=")

+disp(theta,"Theta=")

+disp(C1,"C1=")
\ No newline at end of file
diff --git a/964/CH19/EX19.2/19_2.sce b/964/CH19/EX19.2/19_2.sce
new file mode 100755
index 000000000..e89dbbf72
--- /dev/null
+++ b/964/CH19/EX19.2/19_2.sce
@@ -0,0 +1,16 @@
+clc;

+clear;

+a0=0;

+//f(t)=-1 for -T/2 to -T/4

+//f(t)=1 for -T/4 to T/4

+//f(t)=-1 for T/4 to T/2

+//ak=2/T* (integration of f(t)*cos(w0*t) from -T/2 to T/2)

+//ak=2/T*((integration of f(t)*cos(w0*t) from -T/2 to -T/4) + (integration of f(t)*cos(w0*t) from -T/4 to T/4) + (integration of f(t)*cos(w0*t) from T/4 to T/2))

+//Therefore, 

+//ak=4/(k*%pi) for k=1,5,9,.....

+//ak=-4/(k*%pi) for k=3,7,11,.....

+//ak=0 for k=even integers

+//similarly we find the b's.

+//all the b's=0

+disp("The fourier approximtion is:")

+disp("4/(%pi)*cos(w)*t) - 4/(3*%pi)*cos(3*(w)*t) + 4/(5*%pi)*cos(5*(w)*t) - 4/(7*%pi)*cos(7*(w)*t) + .....")
\ No newline at end of file
diff --git a/964/CH19/EX19.3/19_3.jpeg b/964/CH19/EX19.3/19_3.jpeg
new file mode 100755
index 000000000..bc0a63a88
--- /dev/null
+++ b/964/CH19/EX19.3/19_3.jpeg
diff --git a/964/CH19/EX19.3/19_3.sce b/964/CH19/EX19.3/19_3.sce
new file mode 100755
index 000000000..4090562f0
--- /dev/null
+++ b/964/CH19/EX19.3/19_3.sce
@@ -0,0 +1,8 @@
+clc;

+clear;

+x=0.5:0.5:5.5;

+for i=1:11

+    y(i)=0.9846*ln(x(i))+1.0004;

+end

+plot(x,y)

+xtitle("y vs x","x","y")
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diff --git a/964/CH19/EX19.4/19_4.sce b/964/CH19/EX19.4/19_4.sce
new file mode 100755
index 000000000..78c5f1fd1
--- /dev/null
+++ b/964/CH19/EX19.4/19_4.sce
@@ -0,0 +1,18 @@
+clc;

+clear;

+s=[0.0002 0.0002 0.0005 0.0005 0.001 0.001];

+r=[0.2 0.5 0.2 0.5 0.2 0.5];

+u=[0.25; 0.5; 0.4; 0.75; 0.5; 1];

+logs=log10(s);

+logr=log10(r);

+logu=log10(u);

+for i=1:6

+    m(i,1)=1;

+    m(i,2)=logs(i);

+    m(i,3)=logr(i);

+end

+

+a=m\logu;

+disp(10^a(1),"alpha=")

+disp(a(2),"sigma=")

+disp(a(3),"rho=")
\ No newline at end of file
diff --git a/964/CH19/EX19.5/19_5.sce b/964/CH19/EX19.5/19_5.sce
new file mode 100755
index 000000000..75a18d953
--- /dev/null
+++ b/964/CH19/EX19.5/19_5.sce
@@ -0,0 +1,25 @@
+clc;

+clear;

+x=0:10;

+y=sin(x);

+xi=0:.25:10;

+//part a

+yi=interp1(x,y,xi);

+plot2d(xi,yi)

+xtitle("y vs x (part a)","x","y")

+//part b

+//fitting x and y in a fifth order polynomial

+clf();

+p=[0.0008 -0.0290 0.3542 -1.6854 2.586 -0.0915];

+

+for i=1:41

+    yi(i)=p(1)*(xi(i)^5)+p(2)*(xi(i)^4)+p(3)*(xi(i)^3)+p(4)*(xi(i)^2)+p(5)*(xi(i))+p(6);

+end

+plot2d(xi,yi);

+xtitle("y vs x (part b)","x","y")

+//part c

+clf();

+d=splin(x,y)

+yi-interp(xi,x,y,d)

+plot2d(xi,yi)

+xtitle("y vs x (part c)","x","y")

diff --git a/964/CH19/EX19.5/19_5a.jpeg b/964/CH19/EX19.5/19_5a.jpeg
new file mode 100755
index 000000000..abb4ab346
--- /dev/null
+++ b/964/CH19/EX19.5/19_5a.jpeg
diff --git a/964/CH19/EX19.5/19_5b.jpeg b/964/CH19/EX19.5/19_5b.jpeg
new file mode 100755
index 000000000..0f1805feb
--- /dev/null
+++ b/964/CH19/EX19.5/19_5b.jpeg
diff --git a/964/CH19/EX19.6/19_6.sce b/964/CH19/EX19.6/19_6.sce
new file mode 100755
index 000000000..3d823cf1f
--- /dev/null
+++ b/964/CH19/EX19.6/19_6.sce
@@ -0,0 +1,20 @@
+clc;

+clear;

+x=[0.05 0.12 0.15 0.3 0.45 0.7 0.84 1.05];

+y=[0.957 0.851 0.832 0.72 0.583 0.378 0.295 0.156];

+sx=sum(x);

+sxx=sum(x.*x);

+sx3=sum(x.*x.*x);

+sx4=sum(x.*x.*x.*x);

+sx5=sum(x.*x.*x.*x.*x);

+sx6=sum(x.*x.*x.*x.*x.*x);

+n=8;

+sy=sum(y);

+sxy=sum(x.*y);

+sx2y=sum(x.*x.*y);

+sx3y=sum(x.*x.*x.*y);

+m=[n sx sxx sx3;sx sxx sx3 sx4;sxx sx3 sx4 sx5;sx3 sx4 sx5 sx6];

+p=[sy;sxy;sx2y;sx3y];

+a=m\p;

+disp("The cubic polynomial is y=a0 + a1*x + a2*x^2 + a3*x^3, where a0, a1, a2 and a3 are")

+disp(a)
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