Symbolic Math Toolbox

Using the Symbolic Math Toolbox

Introduction
The Symbolic Math Toolboxes incorporate symbolic computation into MATLAB^®'s numeric environment. These toolboxes supplement MATLAB's numeric and graphical facilities with several other types of mathematical computation.

Facility
Covers

Calculus
Differentiation, integration, limits, summation, and Taylor series

Linear Algebra
Inverses, determinants, eigenvalues, singular value decomposition, and canonical forms of symbolic matrices

Simplification
Methods of simplifying algebraic expressions

Solution of Equations
Symbolic and numerical solutions to algebraic and differential equations

Special Mathematical Functions
Special functions of classical applied mathematics

Variable-Precision Arithmetic
Numerical evaluation of mathematical expressions to any specified accuracy

Facility	Covers
Calculus	Differentiation, integration, limits, summation, and Taylor series
Linear Algebra	Inverses, determinants, eigenvalues, singular value decomposition, and canonical forms of symbolic matrices
Simplification	Methods of simplifying algebraic expressions
Solution of Equations	Symbolic and numerical solutions to algebraic and differential equations
Special Mathematical Functions	Special functions of classical applied mathematics
Variable-Precision Arithmetic	Numerical evaluation of mathematical expressions to any specified accuracy

The computational engine underlying the toolboxes is the kernel of Maple®, a system developed primarily at the University of Waterloo, Canada, and, more recently, at the Eidgenössiche Technische Hochschule, Zürich, Switzerland. Maple is marketed and supported by Waterloo Maple, Inc.

These versions of the Symbolic Math Toolboxes are designed to work with MATLAB 5.3 or greater and Maple V Release 5.

There are two toolboxes. The basic Symbolic Math Toolbox is a collection of more than one-hundred MATLAB functions that provide access to the Maple kernel using a syntax and style that is a natural extension of the MATLAB language. The basic toolbox also allows you to access functions in Maple's linear algebra package. The Extended Symbolic Math Toolbox augments this functionality to include access to all nongraphics Maple packages, Maple programming features, and user-defined procedures. With both toolboxes, you can write your own M-files to access Maple functions and the Maple workspace.

The following sections of this Tutorial provide explanation and examples on how to use the toolboxes.


Section	Covers
Getting Help	How to get online help for Symbolic Math Toolbox functions
Getting Started	Basic symbolic math operations
Calculus	How to differentiate and integrate symbolic expressions
Simplifications and Substitutions	How to simplify and substitute values into expressions
Variable-Precision Arithmetic	How to control the precision of computations
Linear Algebra	Examples using the toolbox functions
Solving Equations	How to solve symbolic equations
Special Mathematical Functions	How to access Maple's special math functions
Using Maple Functions	How to use Maple's help, debugging, and user-defined procedure functions
Extended Symbolic Math Toolbox	Features of the Extended Symbolic Math Toolbox

Chapter 2, Reference provides detailed descriptions of each of the functions in the toolboxes.

Getting Help