Matlab

MATLAB® is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java™.

You can use MATLAB for a range of applications, including signal processing and communications, image and video processing, control systems, test and measurement, computational finance, and computational biology. More than a million engineers and scientists in industry and academia use MATLAB, the language of technical computing.

http://www.mathworks.com/products/matlab/

Mathematica

What Is Mathematica?
Almost any workflow involves computing results, and that's what Mathematica does—from building a hedge fund trading website or publishing interactive engineering textbooks to developing embedded image recognition algorithms or teaching calculus.

Mathematica is renowned as the world's ultimate application for computations. But it's much more—it's the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions.

http://www.wolfram.com/mathematica/