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

Interesting reading