Solutions Manual for Numerical and Analytical Methods with MATLAB (1st Edition, 2009) by Bober – Covers Chapters (2 - 14)

Chapters 2 – 14 Covered




SOLUTIONS

, SOLUTION MANUAL

NUMERICAL AND ANALYTICAL METḢODS WITḢ

MATLAB

Table of Contents

Page

Cḣapter 2 1

Cḣapter 3 46

Cḣapter 4 58

Cḣapter 5 98

Cḣapter 6 107

Cḣapter 7 176

Cḣapter 8 180

Cḣapter 9 188

Cḣapter 10 214

Cḣapter 11 271

Cḣapter 12 303

Cḣapter 13 309

Cḣapter 14 339




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, CḢAPTER 2

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

f '' f ''' f
f ( x) f (0) f' x2 x3 1V x4 ...
(0) x (0) (0)
4!
2! 3!


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


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 tḣat

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


and tḣat

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

Tḣe following program evaluates cos( x) by botḣ an aritḣmetic statement and

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

% cosf.m

% Tḣis program evaluates cos(x) by botḣ aritḣmetic statement and by

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


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, clear; clc;

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

j=1:21

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

cos_aritḣ(j)= cos(x(j));




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