****INSTANT DOWNLOAD****PDF****Solutions Manual for Numerical and Analytical Methods with MATLAB 1st Edition by Bober

Chapters 2 – 14 Covered
c c c c




SOLUTIONS

, SOLUTIONMANUAL c




NUMERICALANDANALYTICALMETHODSWITH
c c c c




MATLAB

Table of Contents
c c




Page

Chapter 2 c 1

Chapter 3 c 46

Chapter 4 c 58

Chapter 5 c 98

Chapter 6 c 107

Chapter 7 c 176

Chapter 8 c 180

Chapter 9 c 188

Chapter 10 c 214

Chapter 11 c 271

Chapter 12 c 303

Chapter 13 c 309

Chapter 14 c 339




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, CHAPTER 2 c




P2.1. Taylor series expansion of f (x) about x = 0 is:
c c c c c c c c c c c c




f''(0) 2 f'''(0) 3 f 1V 4
f (x) = f (0)+ f '(0) x+ x + x + x +...
c c c c c c c c


c c c c c c c c c c c c c



4!
c c



2! 3! c c




For f (x)=cos(x), c c c c c c c f (0) =1,
c c c




f (x) =−sin(x), f '(0)=0,
c c c c c c c c c c c




f ''(x) = −cos(x), f ''(0)=−1,
c c c c c c c c c c c c c c




f '''(x) = +sin(x), f '''(0)=0,
c c c c c c c c c c c c c c c c




f1V(x)=+cos(x), f 1V(0)=1
c c c c c c c c c c c c




We can see that c c c




x x 4 x6 8 2
cos(x) =1− + − + x −+−+...
c c c


c c c c c




2! 4! 6! 8! c c c



c




and that c




x2
term(k)=−term(k −1)
c




2k (2k −1)
c c c c c c c c



c c c c




The following program evaluates cos(x)by both an arithmetic statement and bythe above
c c c c c c c c c c c c c c




c series for -π ≤ x ≤ π in step of 0.1  .
c c c c c c c c c c c c




% cosf.m
c




% This program evaluates cos(x) by both arithmetic statement and by
c c c c c c c c c c




% series for -π ≤ x ≤ π in steps of 0.1 π
c c c c c c c c c c c c




clear; clc; c




xi=-pi;dx=0.1*pi; c




c for j=1:21
c




x(j)=xi+(j-1)*dx;

cos_arith(j)= cos(x(j)); c




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, sum=1.0;term=1.0; c




for k=1:50
c c




den=2*k*(2*k-1);

term=-term*x(j)^2/den;

sum=sum+term;
c




test=abs(sum*1.0e-6);
c




if abs(term) <= test;
c c c c




break;

end

end

cos_ser(j)=sum;
c




nterms(j)=k;
c




end

fo=fopen('output.dat','w');
c




fprintf(fo,'x cos(x) cos (x) c terms inc c \n');

fprintf(fo,'
c by arith stm
c c by series
c the series
c c \n');

fprintf(fo,'=====================================================\n');
c




for j=1:21
c




fprintf(fo,'%10.5f %10.5f %10.5f %3i\n',...
c




x(j),cos_arith(j),cos_ser(j),nterms(j));
c




fprintf(fo,' \n');

end

fclose(fo);
c




plot(x,cos_arith),xlabel('x'),ylabel('cos(x)'),

title('cos(x) vs. x'),grid;
c c c




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