Maxima

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series expansion, Laplace transforms, ordinary differential equations, systems of linear equations, vectors, matrices and tensors. It's based on a project created using the Macsyma program, an algebraic calculation tool created at the Massachusetts Institute of Technology. After becoming a reference in its field, it's served as the basis for applications including Mathematica and Maple.

With Maxima it's possible to produce high precision results using exact fractions, arbitrary precision integers and floating-point numbers with variable precision. Plus, it's possible to create graphs of functions and data in two and three dimensions. All this is done within a moderately accessible and easy-to-use working environment. Moreover, on the official website it's possible to find numerous tutorials to carry out almost any operation.

Maxima is an incredibly useful mathematical tool, that you can use to perform dozens of different operations, without complications and from a user-friendly interface.