From f35ea80659b6a49d1bb2ce1d7d002583f3f40947 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:38:01 +0530
Subject: updated the code

---
 75/CH5/EX5.4/ex_4.sce |  6 +++---
 75/CH5/EX5.5/ex_5.sce | 10 +++++-----
 75/CH5/EX5.7/ex_7.sce | 29 +++++++++++++++++++++++++++++
 75/CH5/EX5.8/ex_8.sce | 33 +++++++++++++++++++++++++++++++--
 4 files changed, 68 insertions(+), 10 deletions(-)

(limited to '75/CH5')

diff --git a/75/CH5/EX5.4/ex_4.sce b/75/CH5/EX5.4/ex_4.sce
index d14b592d2..d661f5067 100755
--- a/75/CH5/EX5.4/ex_4.sce
+++ b/75/CH5/EX5.4/ex_4.sce
@@ -1,4 +1,4 @@
-        //    PG (258)
+//    PG (258)
 
 deff('[y]=f(x)','y=exp(x)*cos(x)')
 x0=0;
@@ -7,7 +7,7 @@ x=x0:xn;
 
 //    True value
 
-I = integrate('exp(x)*cos(x)','x',x0,x1)
+I = integrate('exp(x)*cos(x)','x',x0,xn)
 
 //    Using Simpson's rule
 
@@ -35,4 +35,4 @@ x5=x0+5*h;
 x6=x0+6*h;
 x7=x0+7*h;
 x8=x0+8*h;
-    I3 = h*(f(x0)+4*f(x1)+2*f(x2)+4*f(x3)+2*f(x4)+4*f(x5)+2*f(x6)+4*f(x7)+f(x8))/3
+    I3 = h*(f(x0)+4*f(x1)+2*f(x2)+4*f(x3)+2*f(x4)+4*f(x5)+2*f(x6)+4*f(x7)+f(x8))/3
\ No newline at end of file
diff --git a/75/CH5/EX5.5/ex_5.sce b/75/CH5/EX5.5/ex_5.sce
index 541b7d0a3..cf8514ce0 100755
--- a/75/CH5/EX5.5/ex_5.sce
+++ b/75/CH5/EX5.5/ex_5.sce
@@ -1,4 +1,4 @@
-        //    PG (261)
+//    PG (261)
 
 //    Example 1
 
@@ -9,11 +9,11 @@ deff('[y]=fppp(x)','y=(105*sqrt(x))/8')
 deff('[y]=fpppp(x)','y=(105*x^(-0.5))/16')
 
 x0=0;
-x1=1;
-x=x0:x1;
+xn=1;
+x=x0:xn;
 
 //    True value
-I = integrate('x^(7/2)','x',x0,x1)
+I = integrate('x^(7/2)','x',x0,xn)
 
 //    Using Trapezoidal rule
 
@@ -43,4 +43,4 @@ x2=x0+2*h;
 x3=x0+3*h;
 x4=x0+4*h;
     I2 = h*(f(x0)+4*f(x1)+2*f(x2)+4*f(x3)+f(x4))/3
-    E2 = -h^4*(xn-x0)*fpppp(0.5)/180
+    E2 = -h^4*(xn-x0)*fpppp(0.5)/180
\ No newline at end of file
diff --git a/75/CH5/EX5.7/ex_7.sce b/75/CH5/EX5.7/ex_7.sce
index a1608ff35..6eb53781d 100755
--- a/75/CH5/EX5.7/ex_7.sce
+++ b/75/CH5/EX5.7/ex_7.sce
@@ -1,3 +1,32 @@
+function [pL] = legendrepol(n,var)
+
+//    Generates the Legendre polynomial
+//    of order n in variable var
+
+if n == 0 then
+	cc = [1];
+elseif n == 1 then
+	cc = [0 1];
+else
+	if modulo(n,2) == 0 then
+		M = n/2
+	else
+		M = (n-1)/2
+	end;
+
+	cc = zeros(1,M+1);
+	for m = 0:M
+	    k = n-2*m;
+	    cc(k+1)=...
+        (-1)^m*gamma(2*n-2*m+1)/(2^n*gamma(m+1)*gamma(n-m+1)*gamma(n-2*m+1));
+	end;
+end;
+
+pL = poly(cc,var,'coeff');
+endfunction
+
+//    End function legendrepol
+
         //    PG (277)
 
 deff('[y]=f(x)','y=exp(x)*cos(x)')
diff --git a/75/CH5/EX5.8/ex_8.sce b/75/CH5/EX5.8/ex_8.sce
index d0d40fc93..c5baa6329 100755
--- a/75/CH5/EX5.8/ex_8.sce
+++ b/75/CH5/EX5.8/ex_8.sce
@@ -1,3 +1,32 @@
+function [pL] = legendrepol(n,var)
+
+//    Generates the Legendre polynomial
+//    of order n in variable var
+
+if n == 0 then
+	cc = [1];
+elseif n == 1 then
+	cc = [0 1];
+else
+	if modulo(n,2) == 0 then
+		M = n/2
+	else
+		M = (n-1)/2
+	end;
+
+	cc = zeros(1,M+1);
+	for m = 0:M
+	    k = n-2*m;
+	    cc(k+1)=...
+        (-1)^m*gamma(2*n-2*m+1)/(2^n*gamma(m+1)*gamma(n-m+1)*gamma(n-2*m+1));
+	end;
+end;
+
+pL = poly(cc,var,'coeff');
+endfunction
+
+//    End function legendrepol
+
         //    PG (278)
 
 deff('[y]=f(x)','y=exp(-x^2)')
@@ -22,7 +51,7 @@ for j = 1:2
     A = [A 2/((1-xr(j)^2)*(horner(pd,xr(j)))^2)]
 end
 
-tr = ((x1-x0)/2.*xr)+((x1+x0)/2);
+tr = ((x1-x0)./2.*xr)+((x1+x0)./2);
 
-s = ((x1-x0)/2)*f(tr)
+s = ((x1-x0)./2).*f(tr)
 I = s*A
\ No newline at end of file
-- 
cgit