Solutions Manual for Numerical and Analytical Methods with MATLAB 1st Edition by Bober

Chapters 2 – 14 Covered




SOLUTIONS

, SOLUTION MANUAL

NUMERICAL AND ANALYTICAL METHODS WITH

MATLAB

Table of Contents

Page

Chapter 2 1

Chapter 3 46

Chapter 4 58

Chapter 5 98

Chapter 6 107

Chapter 7 176

Chapter 8 180

Chapter 9 188

Chapter 10 214

Chapter 11 271

Chapter 12 303

Chapter 13 309

Chapter 14 339




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, CHAPTER 2

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

f '' f ''' f
f ( x) f (0) f ' (0) x x2 x3 1V x 4 ...
(0) (0)
4!
2! 3!

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

f ( x) sin( x), f ' (0) 0,

f ' ' ( x) cos( x), f ' ' (0) 1,

f ' ' ' ( x) sin( x), f ' ' ' (0) 0,

f 1V ( x) cos( x), f 1V (0) 1

We can see that

x2 x4 x6 8
cos( x) 1 x
4! 6! ...
8!
2!

and that

x2
term (k) term (k 1)
2 k (2 k
1)

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

by the above series for -π ≤ x ≤ π in step of 0.1 .

% cosf.m

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

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

clear; clc;

xi=-pi; dx=0.1*pi; for j=1:21

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

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




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