Cesar Perez Lopez - MATLAB Mathematical Analysis [2014].pdf
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Contents at a Glance
About the Author �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½xi
About the Technical Reviewer �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½xiii
Introduction �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½
xv
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Chapter 1: MATLAB Introduction and Working Environment �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½1
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Chapter 2: Numbers, Operators, Variables and Functions �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½13
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Chapter 3: Complex Numbers and Functions of Complex Variables �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½71
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Chapter 4: Graphics in MATLAB�½ Curves, Surfaces and Volumes �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½125
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Chapter 5: Limits of Sequences and Functions�½ Continuity in One
and Several Variables �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½183
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Chapter 6: Numerical Series and Power Series �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½203
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Chapter 7: Derivatives�½ One and Several Variables�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½225
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Chapter 8: Integration in One and Several Variables�½ Applications �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½279
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Chapter 9: Differential Equations�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½325
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Introduction
MATLAB is a platform for scientific computing that can work in almost all areas of the experimental sciences,
engineering, mathematics and financial solutions. Logically, this software allows you to work in the field of
mathematical analysis through a wide variety of commands and functions.
MATLAB Mathematical Analysis
is a
reference to these commands and brief discussions of how to solve a very wide array of problems. It is not meant to
be a tutorial on MATLAB, but a user of MATLAB should be able to follow the book easily and look up various types of
problems or commands and see quick examples of how they work. This book covers a wide array of content and so it
is a great place to find new features, topics or commands that you might not have known existed.
The book begins by introducing the reader to the use of numbers of all types and bases, operators, variables and
functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted
to working with developing graphical representations of curves, volumes, and surfaces. MATLAB functions allow
working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit,
implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours,
volumes and graphical interpolation.
Vectors and matrices are a major feature of MATLAB and so they are treated throughout the book as the topics
come up and include applications in many of the areas.
The following content block develops computation of limits and functions, continuity and numerical and power
series. Then differentiability is addressed in one and several variables including differential theorems for vector fields.
It continues to address integration in one or more variable, and multiple integrals and their applications. Finally
differential equations are treated and some of their applications.
MATLAB Mathematical Analysis
offers a broad resource for looking up commands. Unlike most references, it can
be read from start to finish and jumping into chapters to look up is not an issue. So one of the aspects of the book is its
flexibility and the other main benefit is the breadth of coverage.
xv
Chapter 1
MATLAB Introduction and Working
Environment
Introduction to Working with MATLAB
Whenever you use a program of this type, it is necessary to know the general characteristics of how the program
interprets notation. This chapter will introduce you to some of the practices used in the MATLAB environment. If you
are familiar with using MATLAB, you may wish to skip over this chapter.
The best way to learn MATLAB is to use the program. Each example in the book consists of the header with the
prompt for user input “>>” and the response from MATLAB appears on the next line. See Figure
1-1.
Figure 1-1.
1
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