Maple

General Description

Maple is a general purpose computer algebra system, that can be used to solve mathematical problems and produce high-quality technical graphics. Maple uses a high-level programming language, which gives users a way to define their own procedures. it also has some built in packages, which may be loaded to do work in group theory, linear algebra, and statistics, as well as in other fields. It can be used interactively or in batch mode.

Home Page: http://www.maplesoft.com/applications/

General Tutorials

• http://www.maplesoft.com/applications/

Cluster specific use

Prism

• Open an X11 terminal (if you do not use an X windows enabled terminal Maple will run in the command-line mode).
• From an SCS managed desktop (e.g., hostname is dskscs***.scs.fsu.edu) type:

qlogin -l maple

• From all other machines first log in to pamd.scs.fsu.edu

ssh -Y pamd.scs.fsu.edu

• then type:

qlogin -l maple

• This command logs you onto the least loaded prism node
• Type:

 xmaple 

• To use the non-graphical version of Maple type:

 maple 

Maple Examples on Prism

*Maple is especially nice for performing symbolic calculations such as indefinite integration, differentiation, integral transformations, and plottoing symbolic functions.

* The purpose of providing these few examples is so that you can literally cut and paste these commands as a test to be sure that Maple is working correctly in the case where a more complicated procedure is failing and to provide a simple starting point for new users.

* In the 1D examples I will use two simple functions to illustrate the use of integration, differentiation, Fourier transforms, and plotting.

Basic Symbolic Calculations

*Integration,Differentiation,Fourier Transforms

 f(x):=(sin(x))/x:
diff( f(x), x );
diff( f(x), x, x );

In the first case we took just the first derivative and in the second we took a second derivative both of which will be computed and displayed symbolically.

int( f(x), x );
int( f(x), x = 0 .. infinity );
with(inttrans):
fourier( f(x), x, w );                      

In the first example we compute the indefinite integral symbolically and in the second we compute the definite integral of f(x) from zero to infinity which for the sinc function defined as f the answer is (1/2)Pi which will be displayed using Pi and not numerically. In the last case we computed symbolically the Fourier transform of the sinc function f which will be given symbolically in terms of the Heavyside function. Note that here I have told Maple, with(inttrans) which will include all of the Maple routines involving integral transformations. With this inclusion one has access to all of their favotrite integral transformations such as Fourier, Laplace, Hilbert, Hankel, Mellin, etc...

Basic Plotting Commands

with(plots):
f(x):=(sin(x))/x:
g(x):=cos(x^2):
plot( f(x) , x = -3 .. 3 );
plot( [ f(x), g(x) ], x = -3 .. 3 );

* plot1.pdf: Plot of f(x) alone

* plot2.pdf: Plot of both f(x) and g(x)

These are the most basic form of a 2D plot. Again I have loaded all of the plotting commands and options by typing 'with(plots)'. To plot in 2D the only information needed is the function to be plotted and the range in x. There is an entire host of plot options that one can include to produce plots with titles, rename the axis, put in a legend, set the color of the curves, set line width, set the tick marks on the axis etc ... In the last example I have shown how to plot multiple functions simply list them as in a vector and however many components you use will be the number of functions plotted in the same window frame.

with(plots):
f(x):=(sin(x))/x:
g(x):=cos(x^2):
plot([f(x),g(x)],x=-3 .. 3,y=-1 .. 1,labels=[B,S],color=[magenta,cyan],title="Plot of f(x) and g(x)",legend=[ f, g ]);

* plot3.pdf: Plot of f and g with plot options used

Here is an example with several plot options being employed.

with(plots):
f(x,y):= sin( x / y ):
plot3d( f(x,y) , x = -1 .. 1, y = -1 .. 1, axes = boxed );

* plot4.pdf: 3D plot example

In this example we see how to plot a a surface in 3D. It is very similar to the 2D case with the slight difference of now we need to specify the range on x and on y. In the example I included a specification on the axes which was not necessary but makes the image easier to see.

Here is a copy of the actual Mapleworksheet that can be opened in Maple and run therein.

* TSGexamples.mw: Maple Worksheet of these examples

VisLab

• Open an X11 terminal (if you do not use an X windows enabled terminal this package will not work).
• Maple is installed locally on all VisLab machines so to run in GUI mode, type:

xmaple

• Alternatively, run Maple in console mode with:

maple