At the simplest level, MATLAB is a powerful calculator. At the more advanced level, MATLAB is a high-performance language for technical computing. It integrates computation, visualisation and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical problems related to science and engineering, especially those involving data that can be held in matrices and vectors.

Because MATLAB has been designed around engineering and scientific applications, it requires only a fraction of the time to write a program compared to scalar non-interactive languages such as C or FORTRAN.

Matlab is structured using a large collection of files, called M-files. These are of two quite different types, namely script M-files and function M-files. You can use these M-files to do arithmetic calculations, numerically solve equations, create graphics, etc. You can usethe M-files supplied in MATLAB to build up sophisticated computer programs. But, most importantly, you will need to create and store your own M-files to supplement those already provided by MATLAB in order to solve your specific problems.

By using the Symbolic Math Toolbox, your MATLAB  M-files can also include differential and integral calculus, linear algebra, algebraic simplifications, algebraic solution of equations, variable-precision arithmetic, etc.