"Praise and Commendations to all those wonderful people who write the fantastic free math-tools and programs that simplify life so much for so many users"

A selection of sites for Free Math Tools:

There are other free math tools not mentioned on the sites above, for example:

Two of the most popular tools are:

There are also many sites for scientific plotting, however Scilab and Maxima have powerful plotting facilities of their own (Maxima installs Gnuplot)

This site...

... is mainly intended for students of basic control theory and signal processing. They often need to use math tools to avoid trivial but tedious and boring computations 'by hand'. Computer simulation is never intended to replace understanding of fundamental principles, but they can add a dimension to the students learning that is not possible from strictly manipulating equations. Illustrative graphs can for example easily be created to visualize results.
Therefore an attempt is made to create a collection of examples that shows the use of Scilab and Maxima.
From a learning point of view it is important that the examples and test cases can be solved by hand so that the student can verify that the methods applied to the programs produce the expected results. This is why the examples are kept as simple as possible.

Scilab

Scilab is the well-known and powerful Matlab equivalent with a large number of built-in toolboxes, among them the Simulink equivalent Xcos (Scicos).
Scilab can be downloaded from the Scilab-site:
http://www.scilab.org
There you will find all you need, like a large selection of tutorials, additional toolboxes and much more.
Not found there, however, is the site http://techteach.no . This site contains, among other, two short and well-written tutorials: Master Scilab and Master Scicos and contain several tutorial examples from control theory.

Scilab plotting for beginners

The  Scilab graphics is powerful and contains a vast number of commands for plotting. The graphics is object oriented (Java-inspired), and the graphics window and the drawing it contains are represented by hierarchical entities. Type help graphics_entities  (note underscore) in the Scilab command window to see a detailed description of the graphics.  This may be overwhelming for the beginner.
*  For basic plotting of data to be presented in a report some simple commands are sufficient, and easy to understand and remember.
*  For complex graphs you may have to use the hierarchical  commands if you want to repeat the program several times.
*  For most types of graphs you can use the exellent graphics editor for a final  graph
*  For users used to Matlab, there is the plotlib that was created by Stephane Motelet .  In Scilab 5.2 console (command window) you may select Applications -> Module manager - Atoms. You will obtain a list of available add on libraries. Select plotlib and it will automatically be downloaded and installed. This plotlib is still being adapted to the new graphics, some commands (like the grid-functions) may not work yet

Here is a zip file, ScilabPlotting.zip , containing some hints and plotting examples, and two data files for use with an example (Plotting map data)
(This file now works also in scilab 5.2.1)

Modelling of data with Scilab.  

Download here:  modellingOfData.pdf


Maxima

Maxima is a powerful symbolic-based mathematical software providing a huge number of functions for algebraic manipulation, calculus operations, matrix and linear algebra, and other mathematical calculations. It comes in two flavors: XMaxima and wxMaxima. While both allow the user access to the Maxima commands, the difference is in the graphic user interface (GUI) used to communicate with Maxima. For both versions a growing number of add-on packages are available.
The user interface of wxMaxima is more suited for students, many commands are available by using button panes, text and mathematical expressions can be mixed to produce note-book like documents and more. wxMaxima is the preferred version below.

(wx)Maxima documentation and tutorials.

Maxima is very well documented, there is a large number of tutorials and guides. Below a small selection: Note that wxMaxima has a very good and well organized built in help-manual

The package COMA (COntrol engineering with MAxima)

COMA is a well designed package for (wx)Maxima. It is not yet included in wxMaxima but will be in the next release. It has functions for studies of linear continuous systems in the time domain and Laplace domain. It contains state space methods and functions for optimizing and computing stability limits and stability areas.
The newest version (still not yet included in Maxima) can be found at

http://sourceforge.net/apps/phpbb/maxima/viewforum.php?f=3

That site is directly accessible from the Maxima Homepage via  "Third Party Code",  "A collection of user-contributed code"

2009-12-22, 'Scilab Plotting'  added, 2009-12,23 'Modelling' added