I use Maple as my CAS. Sometimes I don't have a calculator handy so I use Maple (overkill
).
It's handy if you want to make numerical approximations, make graphs (2D, 3D,vector fields,animations), check your answers, solve DE's etc.
IIRC, it's a bit expensive. If you're a student, I`m almost positive you can download it somewhere (legally) and get a campus-license from your university. It's probably 'only' Maple6 (I have), but suits my purpose.
Maple is capable of symbolic manipulation. Which means you can use expressions with arbitrary constants like a or b. Also, when you use, for example, \pi in your expression. Maple will work with \pi and not some approximation of \pi like a calculator. It will only give the decimals when you ask for an approximation (you can specify the number of digits. 5,10,100 or more).
I've heard MatLab is the program for matrices, but Maple can deal with them as well. But, not as efficient and extensive as MatLab I gather.
What Maple doesn't do is providing step by step solutions. It can solve a difficult integral in a jiffy, but it will not show any steps.
Sometimes it can not find an 'exact' solution. I once had a limit which looked complex, but could be solved by a human (since the expression could be simplified by a substitution which a human could spot). Maple could not solve it, but after making the substitution manually, it could.
Those are my two cents. It's a nice program to have. I had fun illustrating how the terms of a Fourier series approximate the function. And plotting nonstationary wavefunctions was nice too. Didn't use it for much else though.
