Mathematics

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"Important investigations by physicists on the foundations of mechanics are at hand; I refer to the writings of Mach, Hertz, Boltzmann and Volkmann. It is therefore very desirable that the discussion of the foundations of mechanics be taken up by mathematicians also."
David Hilbert (excerpt from problem #6 of his lecture "Mathematical Problems", delivered before the Second International Congress of Mathematicians in Paris, 1900)

Here are details of mathematical tools that have applications in classical thermodynamics, statistical mechanics and computer simulation techniques.

General

Functions and distributions

Geometry

Integrals and quadrature

Polynomials

Transforms

Computer assisted mathematics

Packages Program or library Notes License
BLAS Basic Linear Algebra Subprograms
CGAL Computational Geometry Algorithms Library
IMSL Numerical Libraries
LAPACK Linear Algebra PACKage
ScaLAPACK Scalable LAPACK
Magma
Maple
Mathematica
Math Kernel Library
MATLAB
Maxima
NAG Numerical Algorithms Group
Numerical Recipes
Octave
QUADPACK
SAGE Free, Open Source
Scilab

Interesting reading