The GNU Octave project began with good intentions as a more flexible tool for students to learn chemical engineering by providing solutions for chemical reactor design problems. It is now a widely used language and software package by educational organizations, students, and commercial operations.

GNU Octave is an open sourced numerical computing software package for solving and developing solutions for linear and nonlinear problems through numerical/matrix/array mathematics. GNU boasts that their software language is mostly compatible with MATLAB and that it can be extended by loading in modules written in C++, C, Fortran, and other languages.

Feature list – solve common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations.

https://www.gnu.org/software/octave/

R-project (Free, Open Source)