Maple

Maple

Version	12
Download	OIT
Cost	$5 for CD $30 for student license
Manufacturer	Maplesoft
Web Page	maplesoft.com
Pundit Updated	1/14/2008

Introduction

Maple is a symbolic math package produced by Waterloo. It is available for free on the UNIX systems and can be started by typing xmaple at the command line. Maple is available to faculty and staff for $5 - the cost of the CD - while it is available for students at a cost of $30 for a perpetual license.

Maple Modes

There are two different ways Maple creates documents - worksheet mode and document mode. The information and screenshots below are presented assuming worksheet mode.

Duke CCP Tutorials

The Math Department at Duke has provided several tutorials on the fundamentals of Maple (in addition to many other tutorials on using Maple for specific purposes). They are a part of the Connected Curriculum Project (CCP) and are linked below. Please note the Copyright Information provided with respect to documents in the Connected Curriculum Project.

1. Maple Tutor for Precalculus, David Smith and Lawrence Moore
2. Maple Tutor for Differential Calculus, David Smith and Lawrence Moore
3. Maple Tutor for Integral Calculus, Lang Moore, Dick Schori, David Smith, and Jim Tomberg
4. Maple Tutor for Multivariable Calculus, Lang Moore, David Smith, and Jim Tomberg
5. Maple Tutor for Differential Equations, Lang Moore, David Smith, and Jim Tomberg
6. Maple Tutor for Linear Algebra, Lang Moore, David Smith, and Jim Tomberg
7. Maple Tutor for Engineering Mathematics, Lang Moore, David Smith, and Jim Tomberg

There are also two tutorials that assume document mode. These are:

1. Maple Tutor (Maple 10 and higher) for Differential Calculus, Joshua Holden, David Smith, and Lawrence Moore
2. Maple Tutor (Maple 10 and higher) for Multivariable Calculus, Joshua Holden, Lang Moore, David Smith, and Jim Tomberg

Additional Information

Below are some more example of specific tasks that may be done in Maple.

Symbolic Derivatives

There are at least three ways to take a symbolic derivative in Maple:

1. Using the diff command
2. Using the D operator
3. Using the "prime" operator

Handy Functions

Parallel Impedances (PAR)

If you need to calculate an equivalent impedance involving parallel constructions, you may want to define a function to simplify those parallel parts:

PAR := (Ra, Rb) -> simplify(Ra*Rb/(Ra+Rb))

Simplifying Fractions of Polynomials (SCS)

If you end up making calculations that involve fractions of polynomials, it can be useful to simplify the expression, collect the variable of interest, and then sort the results. For example, with Laplace transforms, s is the variable of interest so:

SCS := X -> sort(collect(simplify(X), s), s)

Example using PAR and SCS

PAR := (Ra, Rb) -> simplify(Ra*Rb/(Ra+Rb))

\( PAR := (Ra, Rb) \rightarrow {\it simplify}\left(\frac{Ra~Rb}{Ra+Rb}\right) \)

SCS := X -> sort(collect(simplify(X), s), s)

\( SCS := X \rightarrow {\it sort(collect(simplify(X), s), s)}\,\! \)

H:=PAR(1/s/C, R1+PAR(s*L, R2))

\( H:={\frac {{\it R1}\,sL+{\it R1}\,{\it R2}+s\,L\,{\it R2}}{s\,L+{\it R2}+{\it R1}\,{s}^{2}\,C\,L+{\it R1}\,s\,C\,{\it R2}+{s}^{2}\,L{\it R2}\,C}}\,\! \)

SCS(H)

\( {\frac { \left( {\it R1}\,L+L\,{\it R2} \right) s+{\it R1}\,{\it R2}}{ \left( {\it R1}\,CL+L\,{\it R2}\,C \right) {s}^{2}+ \left( L+{\it R1}\, C\,{\it R2} \right) s+{\it R2}}} \,\! \)

Inverse Laplace Transforms

For inverse Laplace transforms, a little bit of processing can go a long way. Specifically, consider the following:

with(inttrans)
x := exp(-t)+cos(80*t)
X1 := laplace(x, t, s)
X2 := simplify(X1)

At this point, X1 and X2 represent the laplace transform of the same function; they are just presented differently since X2 is the simplified version of X1. However, when taking the inverse:

x1 := invlaplace(X1, s, t)
x2 := invlaplace(X2, s, t)

a disaster happens - x1 returns the original x while x2 returns...a mess. One way around this is to have Maple split the Laplace transform into partial fractions, then take the inverse of those parts; writing

x2a := invlaplace(convert(X2, parfrac), s, t)

will yield the original x. One caveat - this only works if the Laplace transform is a ratio of polynomials; if there are any time shifts, represented by exponentials of s in the transform, the conversion to a partial fraction will fail. For this reason, you may want to construct two different versions of the inverse Laplace transform simplifier:

IL   := (X, s, t) -> simplify(convert(invlaplace(convert(X, parfrac), s, t), expsincos))

for taking the inverse of Laplace transforms that are ratios of polynomials and

ILTS := (X, s, t) -> simplify(convert(invlaplace(X), s, t), expsincos))

for those with time shifts. In both cases, the conversion to expsincos eliminates any complex exponentials (when possible).

Troubleshooting

Infinite startup time with X-Win 32

If you are trying to run Maple over X-Win 32 and the splash screen progress bar halts for a significant period of time, the following steps seem to work to correct the problem:

1. Hit CTRL-alt-delete
2. Choose the Task Manager
3. In the Processes tab, click Image Name to get the images in reverse alphabetical order - usually this means clicking it twice
4. Right-click the xwin32 image and select End Process Tree - do this for all instances of xwin32 that are running
5. Close the task manager
6. At the bottom right of your screen, point at the X-Win logos in the applications tray - they should disappear
7. Restart XWin on your computer
8. Type xterm in your PuTTY terminal to see if XWin is working - if it is, close the new xterm window
9. Try starting Maple again

Occasionally, this process has to be repeated - so far, the most recorded times for repeating it is three, but Maple did load on the fourth try!

Questions

Post your questions by editing the discussion page of this article. Edit the page, then scroll to the bottom and add a question by putting in the characters *{{Q}}, followed by your question and finally your signature (with four tildes, i.e. ~~~~). Using the {{Q}} will automatically put the page in the category of pages with questions - other editors hoping to help out can then go to that category page to see where the questions are. See the page for Template:Q for details and examples.

External Links

• Maple Tutor - Maple Tutor by Joshua Holden at Rose-Hulman Institute of Technology and Lang Moore, David Smith, and Jim Tomberg at Duke University. The stated purpose of this module is, "To learn the basics of Maple document mode (Maple 10 or higher) for use in a multivariable calculus course"