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Numerical and Analytical Methods with MATLAB (1st Edition) by William Bober, Chi-Tay Tsai & Oren Masory — A comprehensive engineering mathematics text integrating MATLAB with analytical and numerical methods covering systems of linear equations, roots of

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Numerical and Analytical Methods with MATLAB (1st Edition) by William Bober, Chi-Tay Tsai & Oren Masory is an applied engineering mathematics textbook crafted to merge analytical techniques with modern computational tools. The book uses MATLAB (and Simulink when relevant) to help students see how “black-box” functions actually work, thereby strengthening both their programming skills and mathematical insight. Routledge+1 Starting from the basics, it reviews essential programming practices and MATLAB fundamentals—how to set up scripts, use matrices and vectors, generate plots, and debug. Then it delves into core numerical and analytical techniques: solving systems of linear equations via Gaussian elimination or matrix inversion; finding roots of algebraic and transcendental equations using search and Newton-Raphson methods (or MATLAB’s built-in functions) Routledge+1; numerical integration via Simpson’s rule or built-in quad/dblquad functions; solving ordinary differential equations through Runge-Kutta methods or MATLAB’s ODE solver functions; analyzing partial differential equations like heat conduction, sound waves and vibrating strings; curve fitting, optimization and even finite element analyses for stress or thermal problems; and finally control systems modelling in MATLAB/Simulink. Routledge+1 The book is structured so that the first six chapters are suitable for sophomore-level courses—introducing programming, matrices, linear systems, and equation solvers—while the later chapters target senior undergraduates or first-year graduate students with advanced topics like PDEs, FEM and control systems. Goodwill Books+1 For students, this text provides hands-on learning: most chapters include projects that require writing MATLAB scripts that produce tables, graphs, or interactive simulations. The sample program code gives guidance, reducing the barrier to entry into computational methods. Instructors can use the text as a course foundation for a computational engineering methods class, combining analytical reasoning with programming. For practising engineers looking to modernize their workflows, the book shows how to apply MATLAB to real modelling tasks frequently encountered in mechanical, civil or aerospace engineering. Key benefits include: bridging theory and computation, illustrating engineering applications of numerical methods, building MATLAB fluency, offering structured progression from basics to advanced. Whether your goal is to solve a set of linear equations, simulate a vibrating beam, fit data curves to experimental results, design an optimization routine, or code a simple finite element solver in MATLAB, this text gives you the path. In summary: if you’re taking a numerical methods, computational modelling or engineering mathematics course that involves MATLAB, Numerical and Analytical Methods with MATLAB (1st Edition) stands as a strong, modern resource. It blends analytical reasoning, numerical techniques and programming tools in a way that supports learning, teaching and practical engineering problem solving. If you like, I can generate 100+ extra tags/keywords optimized for listing platforms like Stuvia, and/or create alternate versions of the description (for shorter ad copy or instructor-focused messaging). Would you like me to do that?

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Uploaded on
November 9, 2025
Number of pages
442
Written in
2025/2026
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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

,




CHAPTER 2

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

f '' f ''' f
f ( x) f (0) f ' (0) x2 x3 1V x 4 ...
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 that

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

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

,



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

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