From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:27:19 +0530
Subject: initial commit / add all books

---
 260/CH9/EX9.1/9_1.sce |  8 ++++++
 260/CH9/EX9.2/9_2.sce | 14 ++++++++++
 260/CH9/EX9.3/9_3.sce | 56 +++++++++++++++++++++++++++++++++++++
 260/CH9/EX9.4/9_4.sce | 18 ++++++++++++
 260/CH9/EX9.5/9_5.sce | 35 ++++++++++++++++++++++++
 260/CH9/EX9.6/9_6.sce | 14 ++++++++++
 260/CH9/EX9.7/9_7.sce | 21 ++++++++++++++
 260/CH9/EX9.8/9_8.sce | 76 +++++++++++++++++++++++++++++++++++++++++++++++++++
 8 files changed, 242 insertions(+)
 create mode 100644 260/CH9/EX9.1/9_1.sce
 create mode 100644 260/CH9/EX9.2/9_2.sce
 create mode 100644 260/CH9/EX9.3/9_3.sce
 create mode 100644 260/CH9/EX9.4/9_4.sce
 create mode 100644 260/CH9/EX9.5/9_5.sce
 create mode 100644 260/CH9/EX9.6/9_6.sce
 create mode 100644 260/CH9/EX9.7/9_7.sce
 create mode 100644 260/CH9/EX9.8/9_8.sce

(limited to '260/CH9')

diff --git a/260/CH9/EX9.1/9_1.sce b/260/CH9/EX9.1/9_1.sce
new file mode 100644
index 000000000..3f7f3c85e
--- /dev/null
+++ b/260/CH9/EX9.1/9_1.sce
@@ -0,0 +1,8 @@
+//Eg-9.1
+//pg-386            
+
+clear
+clc
+
+//Theoretical Problem
+disp("given example is Theoretical")
\ No newline at end of file
diff --git a/260/CH9/EX9.2/9_2.sce b/260/CH9/EX9.2/9_2.sce
new file mode 100644
index 000000000..958135b3a
--- /dev/null
+++ b/260/CH9/EX9.2/9_2.sce
@@ -0,0 +1,14 @@
+//Eg-9.2
+//pg-387
+
+clear
+clc
+
+
+//zeros of T3(x)
+n=3;
+for i=1:3
+    lambda(i)=cosd((2*i-1)*180/(2*n));
+end
+disp("zeros of T3(x)")
+disp(lambda)
\ No newline at end of file
diff --git a/260/CH9/EX9.3/9_3.sce b/260/CH9/EX9.3/9_3.sce
new file mode 100644
index 000000000..8928547ee
--- /dev/null
+++ b/260/CH9/EX9.3/9_3.sce
@@ -0,0 +1,56 @@
+//Eg-9.2
+//pg-388
+
+clear
+clc
+
+a=[1 0 -1 1];
+fz=poly(a,'z','c');
+r=roots(fz);
+
+
+//bounds
+lb=1;
+ub=3;
+//using x=2z-b-a/b-a ---using fact that x=z-2 fx roots are obtained from subtracting 2 from fz 
+s=r-2;
+
+fx=poly(s,'x',['roots']);
+disp(fx)
+m=coeff(fx);
+
+for i=1:4
+    t0=m(1)*1+1/2*m(3);
+    t1=m(2)*1+3/4*m(4);
+    t2=1/2*m(3);
+    t3=1/4*m(4);
+    
+end
+
+//considering order greater than 1
+fx1=poly([t0 t1],'x','c');
+r=roots(fx1);
+s=r+2;
+fz1=poly(s,'z',['roots']);
+fz2=35/4*fz1;
+
+
+
+error1=fz-fz2;
+
+//order>2
+f2z=poly([15/2 -45/4 5],'z','c');
+error2=fz-f2z;
+
+
+//plotting f vs z
+z=.5:.5:3.5;
+plot(z,horner(fz,z));
+set(gca(),"auto_clear","off")
+plot(z,horner(fz2,z));
+plot(z,horner(f2z,z));
+
+
+//errors e vs z
+plot(z,horner(error1,z));
+plot(z,horner(error2,z));
\ No newline at end of file
diff --git a/260/CH9/EX9.4/9_4.sce b/260/CH9/EX9.4/9_4.sce
new file mode 100644
index 000000000..bc8e7b295
--- /dev/null
+++ b/260/CH9/EX9.4/9_4.sce
@@ -0,0 +1,18 @@
+
+//Eg-9.4
+//pg-394
+
+clear
+clc
+clc;
+clear;
+
+deff('[z]=f(x)','z=(x^4-2*x^2)*sin(x)');
+x1=-1:.2:1;
+//values of fx obtained manually
+
+fx1=[.841471;0.624387;.333365;.114645;.015576;0;-.015576;-.114645;-.333365;-.624387;-.841471];
+
+plot(x1,feval(x1,f));
+set(gca(),"auto_clear","off")
+plot(x1,fx1,'*');
diff --git a/260/CH9/EX9.5/9_5.sce b/260/CH9/EX9.5/9_5.sce
new file mode 100644
index 000000000..94ca8b44e
--- /dev/null
+++ b/260/CH9/EX9.5/9_5.sce
@@ -0,0 +1,35 @@
+//Eg-9.4
+//pg-396
+
+clc
+clear
+
+//from mclaurins series
+a=[0 1 0 -1/3 0 1/5 0 -1/7 0 1/9];
+
+
+//from R5,4x
+//subracting fx r45x and sloving for coefficients we end up with the matrices
+A=[1 0 -1.6667 0;0 1 0 -1.66667;-0.71429 0 1 0;0 -.71429 0 1];
+C=[0;0.71429;0;-.55556];
+
+B=inv(A)*C;
+//using these values we can compute values of a we represent set of a values using matrix P
+
+P(1)=0;
+P(2)=1;
+P(3)=B(1);
+P(4)=B(2)-1/3;
+P(5)=B(3)-B(1)/3;
+P(6)=B(4)-B(2)/3+1/5;
+
+T(1) = 1;
+for(i = 1:4)
+    T(i+1) = B(i);
+end
+
+j=poly(P,"x","coeff");
+k=poly(T,"x","coeff");
+
+disp("so required R5,4x is")
+disp(j/k)
\ No newline at end of file
diff --git a/260/CH9/EX9.6/9_6.sce b/260/CH9/EX9.6/9_6.sce
new file mode 100644
index 000000000..da872b020
--- /dev/null
+++ b/260/CH9/EX9.6/9_6.sce
@@ -0,0 +1,14 @@
+//Eg-9.6
+//pg-400
+
+clc
+clear
+
+x=0.6;
+p=.3275911;
+t=1/(1+p*x);
+
+erfx=1-(.254829592*t-.284496736*t^2+1.421413741*t^3-1.453152027*t^4+1.061405429*t^5)*exp(-x^2);
+
+disp("erf(.6)")
+disp(erfx)
\ No newline at end of file
diff --git a/260/CH9/EX9.7/9_7.sce b/260/CH9/EX9.7/9_7.sce
new file mode 100644
index 000000000..28ed4015f
--- /dev/null
+++ b/260/CH9/EX9.7/9_7.sce
@@ -0,0 +1,21 @@
+//Eg-9.7
+//pg-403
+
+clc
+clear
+
+p=6.5;
+n = 6;
+a = 0.5;
+prodd=1;
+
+for i = 1:n
+    prodd = prodd*(p-i);
+end
+
+req=prodd*(22/7)^.5
+
+disp("required value")
+disp(req)
+
+printf('\n\n The minor difference in the answer is because of using the value of 22/7 in the place of pi\n')
\ No newline at end of file
diff --git a/260/CH9/EX9.8/9_8.sce b/260/CH9/EX9.8/9_8.sce
new file mode 100644
index 000000000..15ab8d773
--- /dev/null
+++ b/260/CH9/EX9.8/9_8.sce
@@ -0,0 +1,76 @@
+//Eg-9.8
+//pg-413
+
+clc
+clear
+
+//After substituting alpha=lamda*R,z/L,r/R,L/R
+//Treq=T-Ta/T0-Ta
+//first three zeros are taken from appendix 9F
+
+
+alpha=[2.4048;5.5201;8.6537];
+
+a=[1;-2.2499997;1.2656208;-.3163866;.0444479;-.0039444;.00021];
+b=[.5;-.56249985;.21093573;-.03954289;.00443319;-.00031761;.00001109];
+c=[.36746691;.60559366;-.74350384;.25300117;-.04261214;.00427916;-.00024846];
+d=[-.6366198;.2212091;2.1682709;-1.31164827;.3123951;-.0400976;.0027873];
+e=[0.79788456;-.00000077;-.0055274;-.00009512;.00137237;-.00072805;.000014476];
+f=[.79788456;.00000156;.01659667;.00017105;-.00249511;.00113653;-.00020033];
+g=[-.78539816;-.04166397;-.00003954;.00262573;.00054125;-.00029333;.00013558];
+h=[-2.35619449;.12499612;.0000565;-.00637879;.00074348;.00079824;-.00029166];
+
+
+for i=1:3
+   
+x=alpha(i);
+
+p=x/3*x/3;
+q=3/x;
+
+if x<3 then
+ J0(i)=a(1)+p*(a(2)+p*(a(3)+p*(a(4)+p*(a(5)+p*(a(6)+p*(a(7)))))))  ;
+  J1(i)=x*(b(1)+p*(b(2)+p*(b(3)+p*(b(4)+p*(b(5)+p*(b(6)+p*(b(7))))))))  ;
+else
+    f0=e(1)+q*(e(2)+q*(e(3)+q*(e(4)+q*(e(5)+q*(e(6)+q*(e(7)))))));
+    f1=f(1)+q*(f(2)+q*(f(3)+q*(f(4)+q*(f(5)+q*(f(6)+q*(f(7))))))) ;
+    theta0=x+g(1)+q*(g(2)+q*(g(3)+q*(g(4)+q*(g(5)+q*(g(6)+q*(g(7))))))) ; 
+    theta1=x+h(1)+q*(h(2)+q*(h(3)+q*(h(4)+q*(h(5)+q*(h(6)+q*(h(7))))))) ; 
+    J0(i)=(1/x)^.5*f0*cos(theta0);
+    J1(i)=(1/x)^.5*f1*cos(theta1);
+end
+
+end
+for i=1:3
+   
+x=alpha(i)/2;
+
+p=x/3*x/3;
+q=3/x;
+
+if x<3 then
+ JJ0(i)=a(1)+p*(a(2)+p*(a(3)+p*(a(4)+p*(a(5)+p*(a(6)+p*(a(7)))))))  ;
+  JJ1(i)=x*(b(1)+p*(b(2)+p*(b(3)+p*(b(4)+p*(b(5)+p*(b(6)+p*(b(7))))))))  ;
+else
+    f0=e(1)+q*(e(2)+q*(e(3)+q*(e(4)+q*(e(5)+q*(e(6)+q*(e(7)))))));
+    f1=f(1)+q*(f(2)+q*(f(3)+q*(f(4)+q*(f(5)+q*(f(6)+q*(f(7))))))) ;
+    theta0=x+g(1)+q*(g(2)+q*(g(3)+q*(g(4)+q*(g(5)+q*(g(6)+q*(g(7))))))) ; 
+    theta1=x+h(1)+q*(h(2)+q*(h(3)+q*(h(4)+q*(h(5)+q*(h(6)+q*(h(7))))))) ; 
+    JJ0(i)=(1/x)^.5*f0*cos(theta0);
+    JJ1(i)=(1/x)^.5*f1*cos(theta1);
+end
+
+end
+
+Treq=0;
+
+for i=1:3
+Treq=(1/alpha(i)*JJ0(i)*sinh(.5*alpha(i))/J1(i)/sinh(2*alpha(i)))+Treq;
+end
+Tfinal=2*Treq;
+disp("values of alpha ,required bessel functions and final required value are respectively")
+disp(alpha)
+disp(JJ0)
+disp(J1)
+disp(Tfinal)
+
-- 
cgit