MATHEMATICA, like MAPLE (the two are ‘twins’), is a formal or numerical calculation software that lets you solve equations, such as differential or integral equations, or systems of equations, obtain limits and draw graphs. Its user interface takes the form of a notebook, allowing you to write text, titles, paragraphs and formulas with a specific language (see at the end of this article).

Calculation results and curves are also displayed in the current notebook, unlike MATLAB, SCILAB or PYTHON, where curves are displayed in pop-up windows. It is possible to export the files as a report in LaTex, for example.

The online help is extremely well-stocked and has many examples. There is also a very active community. There are tutorials, videos, ready-to-use templates, etc.

MATHEMATICA was conceived in 1988 by Stephen Wolfram, and is still developed by Wolfram Research. The Wolfram Language is the programming language used in MATHEMATICA. I recognize that his language is very powerful and elegant. Nothing to do with some old-fashioned programming language as Python or MATLAB. It exists in two forms: an exhaustive form for "dummies" and an extra-compact form for "geeks".

Example of Mathematica notebook with Transfer Function Model

Example of Mathematica notebook using Dsolve instruction based on SSM equations: