Mathematica is a good product.
I have been told that Mathematica is the premier application of this type. The student edition costs about $100.00 to $150.00 (American), while the regular edition costs $800.00 to $1000.00, and is hard to find at a discount.
I have a student edition which I have never used. It is password protected and you have to prove that you are a student to get the password. I have never bothered to crack it or get some student to register it for me because I use MathCad7, which is a similar product and does everything I need.
I am told that Mathematica does more than mathCad7, so the following list of MathCad7 features might give you an idea of what Mathematica can do.- It allows entry of almost any mathematical notation, including summations and integrals. It has optional floating toolbars with all the symbols not found on your keyboard: Greek letters, Pi, e, summation & integral symbols, root symbols, et cetera. The Pi & e symbols in a formula stand for the actual value. It takes one click to get a trig function or root symbol inserted and ready for entry of arguments.
- It very intelligently formats the math notation as you enter it.
- You can assign values to variables. Like a spreadsheet, changing a variable value causes recalculation of all formulae. Variable names can use upper/lower cased words like VB variables.
- It has evaluated every formula I ever entered, including summations and integrals.
- Remarks can be interspersed with formulae. It will print all the formulae, results, et cetera, resulting in a really fancy document, which would put many math texts to shame.
- It will solve simultaneous equations and invert matrices. I think it will solve for roots of polynomials, but I have never tried this.
- It will produce graphs of Y = Function(X) for any function you can enter. It will also produce draw surfaces with contour lines.
- It will produce tables if you describe a variable as having a range of values.
- It will do symbolic math. For example give it (A + B + C}^4 and it will show you all the terms in the expansion. I think it will simplify expressions, but I have not tried this capability.
- It probably has many more features which I have not yet used.
- It is user friendly. I have not read more than 5-10 pages of the 680 page manual, which was enough to allow me to use all the features I need.