MATLAB Differential Equations(1).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�½ix
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Chapter 1: Introducing MATLAB and the MATLAB 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�½1
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Chapter 2: First Order Differential Equations�½ Exact Equations, Separation of Variables,
Homogeneous and Linear 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�½�½�½�½
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Chapter 3: Higher Order Differential Equations�½ The Laplace Transform and
Special Types of 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�½�½�½�½�½�½�½�½�½�½�½�½45
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Chapter 4: Differential Equations Via Approximation Methods �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½61
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Chapter 5: Systems of Differential Equations and Finite Difference Equations �½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½67
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Chapter 6: Numerical Calclus with MATLAB�½ Applications to Differential Equations �½�½�½�½�½�½�½�½
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Chapter 7: Ordinary and Partial Differential Equations with Initial and
Boundary Values�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½101
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Chapter 8: Symbolic Differential and Integral Calculus�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�½�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 1
Introducing MATLAB and the MATLAB
Working Environment
Introduction
MATLAB is a platform for scientific calculation and high-level programming which uses an interactive environment
that allows you to conduct complex calculation tasks more efficiently than with traditional languages, such as C, C++
and FORTRAN. It is the one of the most popular platforms currently used in the sciences and engineering.
MATLAB is an interactive high-level technical computing environment for algorithm development, data
visualization, data analysis and numerical analysis. MATLAB is suitable for solving problems involving technical
calculations using optimized algorithms that are incorporated into easy to use commands.
It is possible to use MATLAB for a wide range of applications, including calculus, algebra, statistics, econometrics,
quality control, time series, signal and image processing, communications, control system design, testing and
measuring systems, financial modeling, computational biology, etc. The complementary toolsets, called
toolboxes
(collections of MATLAB functions for special purposes, which are available separately), extend the MATLAB
environment, allowing you to solve special problems in different areas of application.
In addition, MATLAB contains a number of functions which allow you to document and share your work.
It is possible to integrate MATLAB code with other languages and applications, and to distribute algorithms and
applications that are developed using MATLAB.
The following are the most important features of MATLAB:
•
•
•
•
•
•
•
It is a high-level language for technical calculation
It offers a development environment for managing code, files and data
It features interactive tools for exploration, design and iterative solving
It supports mathematical functions for linear algebra, statistics, Fourier analysis, filtering,
optimization, and numerical integration
It can produce high quality two-dimensional and three-dimensional graphics to aid data
visualization
It includes tools to create custom graphical user interfaces
It can be integrated with external languages, such as C/C++, FORTRAN, Java, COM, and
Microsoft Excel
The MATLAB development environment allows you to develop algorithms, analyze data, display data files and
manage projects in interactive mode (see Figure
1-1).
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Chapter 1
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IntroduCIng MatLaB and the MatLaB WorkIng envIronMent
Figure 1-1.
Developing Algorithms and Applications
MATLAB provides a high-level programming language and development tools which enable you to quickly develop
and analyze algorithms and applications.
The MATLAB language includes vector and matrix operations that are fundamental to solving scientific and
engineering problems. This streamlines both development and execution.
With the MATLAB language, it is possible to program and develop algorithms faster than with traditional
languages because it is no longer necessary to perform low level administrative tasks, such as declaring variables,
specifying data types and allocating memory. In many cases, MATLAB eliminates the need for ‘for’ loops. As a result,
a line of MATLAB code usually replaces several lines of C or C++ code.
At the same time, MATLAB offers all the features of traditional programming languages, including arithmetic
operators, control flow, data structures, data types, object-oriented programming (OOP) and debugging.
Figure
1-2
shows a communication modulation algorithm that generates 1024 random bits, performs the
modulation, adds complex Gaussian noise and graphically represents the result, all in just nine lines of MATLAB code.
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