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Symbolic Math Tool
box™ 5
User’s Guide
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How to Contact MathWorks
www.mathworks.
com
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comp.soft-sys.matlab Newsgroup
www.mathworks.com/contact_TS.html Technical Support
suggest@mathworks.com Product enhancement suggestions
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rks.com
Bug reports
doc@mathworks.com Documentation error reports
service@mathworks.com Order status, license renewals, passcodes
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rks.com
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ng, and general information
508-647-7000 (Phone)
508-647-7001 (Fax)
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098
For contact information about worldwide offices, see the MathWorks Web site.
Symbolic Math Toolbox™ User’s Guide
© COPYRIGHT 1993–2010 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or cop ied only un der the terms of the license agreement. No part of this manual may b e photocopied or
reproduced in any form wi thout prior writt en consent from The MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation
by, for, or through the federal government of the United States. By accepting delivery of the Program
or Documentation, the government hereby a grees that this software or documentation q u alifies as
commercial computer software or commercial computer software documentation as such terms are used
or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, th e terms and
conditions of this Agreement and on ly those rights specified in thi s Agr eement, shall pertain to and govern
theuse,modification,reproduction,release,performance,display,anddisclosureoftheProgramand
Documentation by the federal governm ent (or other entity ac quiring fo r or t hrough the federal government)
and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the
government’s needs or is inconsistent in any respect w ith federal procurement law, the government agrees
to return the Program and Documen tation, unused, to The MathWorks, Inc.
Trademarks
MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See
www.mathworks.com/trademarks for a list of additional trademarks. O ther product or brand
names may be trademarks or registered trademarks of their respective holders.
Patents
MathWorks products are protected by one or more U.S. patents. Please see
www.mathworks.com/patents for more information.
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Revision History
August 1993 First printing
October 1994 Second printing
May 1997 Third printing Revised for Version 2
May 2000 Fourth printing Minor changes
June 2001 Fifth printing Minor changes
July 2002 Online only Revised for Version 2.1.3 (Release 13)
October 2002 Online only Revised for Version 3.0.1
December 2002 Sixth p rinting
June 2004 Seventh printing Revised for Version 3.1 (Release 14)
October 2004 Online only Revised for Version 3.1.1 (Release 14SP1)
March 2005 Online only Revised for Version 3.1.2 (Release 14SP2)
September 2005 Online only Revised for Version 3.1.3 (Release 14SP3)
March 2006 Online only Revised for Version 3.1.4 (Release 2006a)
September 2006 Online only Revised for Version 3.1.5 (Release 2006b)
March 2007 Online only Revised for Version 3.2 (Release 2007a)
September 2007 Online only Revised for Version 3.2.2 (Release 2007b)
March 2008 Online only Revised for Version 3.2.3 (Release 2008a)
October 2008 Online only Revised for Version 5.0 (Release 2008a+)
October 2008 Online only Revised for Version 5.1 (Release 2008b)
November 2008 Online only Revised for Version 4.9 (Release 2007b+)
March 2009 Online only Revised for Version 5.2 (Release 2009a)
September 2009 Online only Revised for Version 5.3 (Release 2009b)
March 2010 Online only Revised for Version 5.4 (Release 2010a)
September 2010 Online only Revised for Version 5.5 (Release 2010b)
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Contents
Introduction
1
Product Overview ................................. 1-2
Accessing Symbolic Math Toolbox Functionality
..... 1-3
Key Features
..................................... 1-3
Working from MATLAB
............................ 1-3
Working from MuPAD
............................. 1-3
Getting Started
2
Symbolic Objects .................................. 2-2
Overview
........................................ 2-2
Symbolic Variables
................................ 2-2
Symbolic Numbers
................................ 2-3
Creating Symbolic Variables and Expressions
........ 2-6
Creating Symbolic Variables
........................ 2-6
Creating Symbolic Expressions
...................... 2-7
Creating Symbol ic Objects with Identical Names
........ 2-8
Creating a Matrix of Symbolic Variables
............... 2-9
Creating a Matrix of Symbolic Numbers
............... 2-10
Finding Symbolic Variables in Expressi ons and
Matrices
....................................... 2-11
Performing Symbolic Computations
................. 2-13
Simplifying Symbolic Expressions
.................... 2-13
Substituting in Symbolic Expressions
................. 2-15
Estimating the Precision of Numeric to Symbolic
Conversions
.................................... 2-18
Differentiating Symbolic Expressions
................. 2-20
Integrating Symbolic E xpressions
.................... 2-22
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