User manual MATLAB SYMBOLIC MATH TOOLBOX 5

[. . . ] Symbolic Math ToolboxTM 5 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, 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 ToolboxTM User's Guide © COPYRIGHT 1993­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] · Expressions returned by evalin and feval. 3-142 4 MuPAD in Symbolic Math Toolbox · "Understanding MuPAD" on page 4-2 · "MuPAD for MATLAB Users" on page 4-10 · "Integration of MuPAD and MATLAB" on page 4-25 4 MuPAD® in Symbolic Math ToolboxTM Understanding MuPAD In this section. . . "Introduction to MuPAD" on page 4-2 "The MATLAB Workspace and MuPAD Engines" on page 4-2 "Introductory Example Using a MuPAD Notebook from MATLAB" on page 4-3 Introduction to MuPAD Version 5 of Symbolic Math Toolbox is powered by the MuPAD symbolic engine. · Nearly all Symbolic Math Toolbox functions work the same way as in previous versions. To read about the differences with the new engine, see the transition Release Notes. · MuPAD notebooks provide a new interface for performing symbolic calculations, variable-precision calculations, plotting, and animations. "Introductory Example Using a MuPAD Notebook from MATLAB" on page 4-3 contains an introductory example of how to use this interface. · Symbolic Math Toolbox functions allow you to copy variables and expressions between the MATLAB workspace and MuPAD notebooks. For more information, see "Copying Variables and Expressions Between the MATLAB Workspace and MuPAD Notebooks" on page 4-25. · You can call MuPAD functions and procedures from the MATLAB environment. For more information, see "Calling MuPAD Functions at the MATLAB Command Line" on page 4-28. The MATLAB Workspace and MuPAD Engines A MuPAD engine is a separate process that runs on your computer in addition to a MATLAB process. A MuPAD engine starts when you first call a function that needs a symbolic engine, such as syms. Symbolic Math Toolbox functions that use the symbolic engine use standard MATLAB syntax, such as y = int(x^2). 4-2 Understanding MuPAD® Conceptually, each MuPAD notebook has its own symbolic engine, with associated workspace. You can have any number of MuPAD notebooks open simultaneously. One engine exists for use by Symbolic Math Toolbox. MATLAB workspace Each MuPAD notebook also has its own engine. MuPAD notebook 1 MuPAD notebook 2 MuPAD engine Engine 1 Engine Workspace MuPAD engine Engine 2 Engine Workspace MuPAD engine Engine 3 Engine Workspace The engine workspace associated with the MATLAB workspace is generally empty, except for assumptions you make about variables. For more information, see "Clearing Assumptions and Resetting the Symbolic Engine" on page 4-31. Introductory Example Using a MuPAD Notebook from MATLAB This example shows how to use a MuPAD notebook to calculate symbolically the mean and variance of a normal random variable that is restricted to be positive. For more information on using a MuPAD notebook, see "Calculating in a MuPAD Notebook" on page 4-15. The density function of the normal and positive random variable is e- x 2 / 2 2 / f ( x) = 0 if x > 0 otherwise. 4-3 4 MuPAD® in Symbolic Math ToolboxTM 1 At the MATLAB command line, enter the command mupad 2 A blank MuPAD notebook opens. You perform calculations by typing in the input area, demarcated by a left bracket. Input area 3 In the input area, type f := exp(-x^2/2)*sqrt(2/PI) and press Enter. 4-4 Understanding MuPAD® Note Assignment in a MuPAD notebook uses :=, not the MATLAB syntax =. Also, the MuPAD syntax for the mathematical constant is PI, not the MATLAB syntax pi. For more information on common syntax differences, see "Differences Between MATLAB and MuPAD Syntax" on page 4-21. The MuPAD notebook displays results in real math notation. [. . . ] ym f ( x, y) m =0 y= a a is real and n is a positive integer n-1 taylor(f, n, y, a) a is real and n is a positive integer. See Also symvar, taylortool 6-197 taylortool Purpose Syntax Description Taylor series calculator taylortool taylortool('f') taylortool initiates a GUI that graphs a function against the Nth partial sum of its Taylor series about a base point x = a. The default function, value of N, base point, and interval of computation for taylortool are f = x*cos(x), N = 7, a = 0, and [-2*pi, 2*pi], respectively. taylortool('f') initiates the GUI for the given expression f. Examples taylortool('sin(tan(x)) - tan(sin(x))') 6-198 taylortool See Also funtool, rsums 6-199 tril Purpose Syntax Description Return lower triangular part of symbolic matrix tril(A) tril(A, k) tril(A) returns a triangular matrix that retains the lower part of the matrix A. The upper triangle of the resulting matrix is padded with zeros. [. . . ]