MATLAB Programming for Numerical Analysis

238 Pages·2014·12.29 MB·English

by  César Pérez López (auth.)

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MATLAB Programming for Numerical Analysis
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MATLAB is a high-level language and environment for numerical computation, visualization, and pro-
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gramming. Using MATLAB, you can analyze data, develop algorithms, and create models and appli-
cations. The language, tools, and built-in math functions enable you to explore multiple approaches
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and reach a solution faster than with spreadsheets or traditional programming languages, such as
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C/C++ or Java. o
Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical g
hands-on instructions and results, allowing you to quickly achieve your goals. You will first become
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familiar with the MATLAB environment, and then you will begin to harness the power of MATLAB. You a
will learn the MATLAB language, starting with an introduction to variables, and how to manipulate num- m
bers, vectors, matrices, arrays and character strings. You will learn about MATLAB’s high-precision
capabilities, and how you can use MATLAB to solve problems, making use of arithmetic, relational m
and logical operators in combination with the common functions and operations of real and complex
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analysis and linear algebra. n
You will learn to implement various numerical methods for optimization, interpolation and solving g
non-linear equations. You will discover how MATLAB can solve problems in differential and integral

calculus, both numerically and symbolically, including techniques for solving ordinary and partial dif- f
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ferential equations, and how to graph the solutions in brilliant high resolution. You will then expand your
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knowledge of the MATLAB language by learning how to use commands which enable you to investi-
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gate the convergence of sequences and series, and explore continuity and other analytical features of
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functions in one and several variables.
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· Use the MATLAB environment
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· Program the MATLAB language from first principles
· Analyze data by developing MATLAB algorithms r
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· Perform numerical analysis in MATLAB with hands-on examples you create c
· Understand how MATLAB can be used to investigate convergence of sequences and series and a
analytical properties of functions
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· Learn how to numerically and symbolically solve differential equations using MATLAB, and graph the solutions
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ISBN 978-1-4842-0296-8
54999
Shelve in
Applications/Mathematical &
9781484202968 Statistical Software
For your convenience Apress has placed some of the front
matter material after the index. Please use the Bookmarks
and Contents at a Glance links to access them.
Contents at a Glance
About the Author �����������������������������������������������������������������������������������������������������������������ix
■ Chapter 1: The MATLAB Environment ��������������������������������������������������������������������������������1
■ Chapter 2: MATLAB Language: Variables, Numbers, Operators and Functions ���������������29
■ Chapter 3: MATLAB Language: Development Environment Features �������������������������������83
■ Chapter 4: MATLAB Language: M-Files, Scripts, Flow Control and
Numerical Analysis Functions ���������������������������������������������������������������������������������������121
■ Chapter 5: Numerical Algorithms: Equations, Derivatives and Integrals ����������������������191
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Chapter 1
The MATLAB Environment
Starting MATLAB on Windows. The MATLAB working environment
To start MATLAB, simply double-click on the shortcut icon to the program on the Windows desktop. Alternatively,
if there is no desktop shortcut, the easiest and most common way to run the program is to choose programs from the
Windows Start menu and select MATLAB. Having launched MATLAB by either of these methods, the welcome screen
briefly appears, followed by the screen depicted in Figure 1-1, which provides the general environment in which the
program works.
Figure 1-1.
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Chapter 1 ■ the MatLaB environMent
The most important elements of the MATLAB screen are the following:
• The Command Window: This runs MATLAB functions.
• The Command History: This presents a history of the functions introduced in the Command
Window and allows you to copy and execute them.
• The Launch Pad: This runs tools and gives you access to documentation for all MathWorks
products currently installed on your computer.
• The Current Directory: This shows MATLAB files and execute files (such as opening and search
for content operations).
• Help (support): This allows you to search and read the documentation for the complete family
of MATLAB products.
• The Workspace: This shows the present contents of the workspace and allows you to make
changes to it.
• The Array Editor: This displays the contents of arrays in a tabular format and allows you to edit
their values.
• The Editor/Debugger: This allows you to create, edit, and check M-files (files that contain
MATLAB functions).
The MATLAB Command Window
The Command Window (Figure 1-2) is the main way to communicate with MATLAB. It appears on the desktop when
MATLAB starts and is used to execute all operations and functions. The entries are written to the right of the
prompt >> and, once completed, they run after pressing Enter. The first line of Figure 1-3 defines a matrix and, after
pressing Enter, the matrix itself is displayed as output.
Figure 1-2.
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Chapter 1 ■ the MatLaB environMent
Figure 1-3.
In the Command Window, it is possible to evaluate previously executed operations. To do this, simply select
the syntax you wish to evaluate, right-click, and choose the option Evaluate Selection from the resulting pop-up
menu (Figures 1-4 and 1-5). Choosing Open Selection from the same menu opens in the Editor/Debugger an M-file
previously selected in the Command Window (Figures 1-6 and 1-7).
Figure 1-4.
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Chapter 1 ■ the MatLaB environMent
Figure 1-5.
Figure 1-6.
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Chapter 1 ■ the MatLaB environMent
Figure 1-7.
MATLAB is sensitive to the use of uppercase and lowercase characters, and blank spaces can be used before and
after minus signs, colons and parentheses. MATLAB also allows you to write several commands on the same line,
provided they are separated by semicolons (Figure 1-8). Entries are executed sequentially in the order they appear on
the line. Every command which ends with a semicolon will run, but will not display its output.
Figure 1-8.
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Chapter 1 ■ the MatLaB environMent
Long entries that will not fit on one line can be continued onto a second line by placing dots at the end of the
first line (Figure 1-9).
Figure 1-9.
The option Clear Command Window from the Edit menu (Figure 1-10) allows you to clear the Command
Window. The command clc also performs this function (Figure 1-11). Similarly, the options Clear Command History
and Clear Workspace in the Edit menu allow you to clean the history window and workspace.
Figure 1-10.
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Chapter 1 ■ the MatLaB environMent
Figure 1-11.
To help you to easily identify certain elements as if/else instructions, chains, etc., some entries in the Command
Window will appear in different colors. Some of the existing rules for colors are as follows:
1. Chains appear in purple while they are being typed. When they are finished properly (with
a closing quote) they become brown.
2. Flow control syntax appears in blue. All lines between the opening and closing of the flow
control functions are correctly indented.
3. Parentheses, brackets, and keys are briefly illuminated until their contents are properly
completed. This allows the user to easily see if mathematical expressions are properly closed.
4. Comments in the Command Window, preceded by the symbol %, appear in green.
5. System commands such as ! appear in gold.
6. Errors are shown in red.
Below is a list of keys, arrows and combinations that can be used in the Command Window.
Key Control key Operation
� CTRL+ p Calls to the last entry submitted.
¯ CTRL+ n Calls to the next line.
← CTRL+ b Moves one character backward.
→ CTRL+ f Moves one character forward.
CTRL+→ CTRL+ r Moves one word to the right.
CTRL+← CTRL+ l Moves one word to the left.
Home CTRL+ a Moves to the beginning of the line.
(continued)
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