matlab

Actually stands for Matrix Laboratory and not for Mathematics Laboratory, as many thinks. Very easy to get addicted to since it saves a lot of time, but then, you must ask your employer to buy it and it's very expensive. Matlab can be seen as a game where the goal is to vectorize your code to speed it up. When coupled to Simulink, Matlab gets from very powerful to inescapably essential.

Lately, The MathWorks' strategy seems to be heading towards making the industry use Matlab at every level from design and development to production, thanks to products like the Matlab Compiler, the Real Time Workshop, the Data Acquisition Toolbox and the Stateflow packages.

Matlab is a numerical simulation/mathmatical analysis environment. It has its own programming language and is optimized to do matrix manipulations. It is often used by scientists and engineers to solve problems using numerical methods that can not be solved analytically.

For instance, you may want to know exactly what the motion of a ball flying through the air is. Isaac Newton's equations of motion give the base understanding but if you want to include the spin of the ball (for instance to model a baseball pitch) or the friction/drag due to air, you can't just write down the answer, you need to sort-of 'follow' the ball and apply numerical methods at each time step to see how it acts. Matlab is a good tool for doing this so that a solution can be obtained with minimal programming and without a deep understanding of the innards of the computer (who can keep the difference between a longint on unix and on windows straight anyway?)

There are some open source alternatives to matlab called scilab and octave (thanks to spiregrain for alerting me to octave). I could never get scilab to do what I wanted but I haven't tried octave yet (YMMV).