Editing 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) | |||
'''David Hilbert''' ( | |||
Here are details of mathematical tools that have applications in [[classical thermodynamics]], [[statistical mechanics]] and [[computer simulation techniques]]. | Here are details of mathematical tools that have applications in [[classical thermodynamics]], [[statistical mechanics]] and [[computer simulation techniques]]. | ||
==General== | ==General== | ||
*[[Clebsch-Gordan coefficients]] | *[[Clebsch-Gordan coefficients]] | ||
*[[Euler angles]] | *[[Euler angles]] | ||
*[[Green's theorem]] | *[[Green's theorem]] | ||
*[[Laplace's equation]] | *[[Laplace's equation]] | ||
*[[Lee-Yang circle theorem]] | *[[Lee-Yang circle theorem]] | ||
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*[[Power series]] | *[[Power series]] | ||
*[[Predictor-corrector methods]] | *[[Predictor-corrector methods]] | ||
*[[Random numbers]] | *[[Random numbers]] | ||
*[[Root finding]] | *[[Root finding]] | ||
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*[[Spherical harmonics]] | *[[Spherical harmonics]] | ||
*[[Stirling's approximation]] | *[[Stirling's approximation]] | ||
*[[Taylor expansion]] | *[[Taylor expansion]] | ||
*[[Trotter formula]] | *[[Trotter formula]] | ||
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|'''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary | |'''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary | ||
|free, Open Source | |free, Open Source | ||
|- | |- | ||
|[[IMSL Numerical Libraries]] | |[[IMSL Numerical Libraries]] | ||
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==Interesting reading== | ==Interesting reading== | ||
*[http://dx.doi.org/10.1002/cpa.3160130102 Eugene P. Wigner "The unreasonable effectiveness of mathematics in the natural sciences", Communications on Pure and Applied Mathematics '''13''' pp. 1-14 (1960)] | *[http://dx.doi.org/10.1002/cpa.3160130102 Eugene P. Wigner "The unreasonable effectiveness of mathematics in the natural sciences", Communications on Pure and Applied Mathematics '''13''' pp. 1-14 (1960)] | ||
*[http://www.ams.org/bull/1988-19-01/S0273-0979-1988-15634-0/S0273-0979-1988-15634-0.pdf David Ruelle "Is our mathematics natural? The case of equilibrium statistical mechanics", Bulletin of the American Mathematical Society '''19''' pp. 259-268 (1988)] | *[http://www.ams.org/bull/1988-19-01/S0273-0979-1988-15634-0/S0273-0979-1988-15634-0.pdf David Ruelle "Is our mathematics natural? The case of equilibrium statistical mechanics", Bulletin of the American Mathematical Society '''19''' pp. 259-268 (1988)] | ||
[[category: mathematics]] | [[category: mathematics]] |