| Latest revision |
Your text |
| Line 1: |
Line 1: |
| <blockquote>"Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If
| | *[[Bessel functions]] |
| mathematical analysis should ever hold a prominent place in chemistry – an aberration which is happily almost impossible – it would occasion a rapid and widespread degeneration of that science." '''Auguste Comte''' (1830) <ref>[http://gallica.bnf.fr/ark:/12148/bpt6k109113f/f4.item.r=Cours%20de%20philosophie%20positive%20Tome%203 Auguste Comte"Cours de philosophie positive" (Tome 3) 35e Leçon. Considérations philosophiques sur l'ensemble de la chimie (1830)]</ref></blockquote>
| | *[[Chebyshev polynomials]] |
| <blockquote>"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."
| | *[[Dirac delta distribution]] |
| '''David Hilbert''' (1900) <ref>David Hilbert, excerpt from problem VI of his lecture [http://www.mathunion.org/ICM/ICM1900/Main/icm1900.0058.0114.ocr.pdf "Sur les problèmes futurs des Mathématiques", Second International Congress of Mathematicians, pp. 58-114 Paris (1900)]</ref></blockquote>
| | *[[Elliptic integrals]] |
| <blockquote>"Every mathematician knows it is impossible to understand an elementary course in thermodynamics." '''Vladimir I. Arnold''' (1989)<ref> Vladimir I. Arnold "Contact geometry: The geometrical method of Gibbs' thermodynamics," in ''Proceedings of the Gibbs Symposium, Yale University, May 15-17, 1989'' Ed. D. G. Caldi and G. D. Mostow, American Mathematical Society (1990) ISBN 978-0-8218-0157-4 p. 163. </ref></blockquote>
| | *[[Fast Fourier transform]] |
| | | *[[Fourier analysis]] |
| | | *[[Gaussian distribution]] |
| Here are details of mathematical tools that have applications in [[classical thermodynamics]], [[statistical mechanics]] and [[computer simulation techniques]].
| |
| ==General==
| |
| *[[Clebsch-Gordan coefficients]] | |
| *[[Euler angles]] | |
| *[[Gauss theorem]] | |
| *[[Green's theorem]] | | *[[Green's theorem]] |
| *[[Lagrange multipliers]] | | *[[Heaviside step distribution]] |
| *[[Laplace's equation]] | | *[[Kronecker delta]] |
| *[[Lee-Yang circle theorem]] | | *[[Laguerre polynomials]] |
| *[[Linear algebra]] | | *[[Legendre polynomials]] |
| *[[Liouville's theorem]] | | *[[Legendre transform]] |
| *[[Lyapunov exponents]]
| |
| *[[Padé approximants]] | | *[[Padé approximants]] |
| *[[Perron-Frobenius theorem]] | | *[[Perron-Frobenius theorem]] |
| *[[Poincaré theorem]]
| |
| *[[Power series]] | | *[[Power series]] |
| *[[Predictor-corrector methods]] | | *[[Ramp function]] |
| *[[Quaternions]]
| |
| *[[Random numbers]]
| |
| *[[Root finding]] | | *[[Root finding]] |
| *[[Runge-Kutta method]]
| |
| *[[Spherical harmonics]] | | *[[Spherical harmonics]] |
| | *[[Standard integrals]] |
| *[[Stirling's approximation]] | | *[[Stirling's approximation]] |
| *[[Substantive derivative]]
| |
| *[[Taylor expansion]] | | *[[Taylor expansion]] |
| *[[Trotter formula]]
| | *[[Wigner rotation matrices]] |
| *[[Wigner D-matrix]] | |
| *[[Wigner D-matrix |Wigner rotation matrices]]
| |
| | |
| ==Functions and distributions==
| |
| *[[Bessel functions]]
| |
| *[[Dirac delta distribution]]
| |
| *[[Gamma function]]
| |
| *[[Gaussian distribution]]
| |
| *[[Heaviside step distribution]]
| |
| *[[Kronecker delta]]
| |
| *[[Poisson distribution]]
| |
| *[[Ramp function]]
| |
| | |
| ==Geometry==
| |
| *[[Alpha shape]]
| |
| *[[Delaunay simplexes]]
| |
| *[[Dual lattice]]
| |
| *[[Lattice Structures]]
| |
| *[[Voronoi cells]]
| |
| ==Integrals and quadrature==
| |
| *[[Standard integrals]]
| |
| *[[Elliptic integrals]]
| |
| *[[Newton-Cotes formulas]]
| |
| *[[Gauss-Chebyshev quadrature]]
| |
| *[[Gauss-Legendre quadrature]]
| |
| ==Polynomials==
| |
| *[[Chebyshev polynomials]]
| |
| *[[Laguerre polynomials]]
| |
| *[[Legendre polynomials]]
| |
| **[[Associated Legendre functions]]
| |
| | |
| ==Transforms==
| |
| *[[Fast Fourier transform]]
| |
| *[[Fourier analysis]]
| |
| *[[Laplace transform]]
| |
| *[[Legendre transform]]
| |
| ==Computer assisted mathematics==
| |
| {| class="wikitable sortable" border="1" cellpadding="5" cellspacing="0"
| |
| |-
| |
| ! Packages !! Program or library !! class="unsortable" | Notes !! License
| |
| |-
| |
| |[[BLAS]]
| |
| |routines
| |
| | '''B'''asic '''L'''inear '''A'''lgebra '''S'''ubprograms
| |
| |free source
| |
| |-
| |
| |[[CGAL]]
| |
| |library
| |
| |'''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary
| |
| |free, Open Source
| |
| |-
| |
| |[http://freemat.sourceforge.net/ FreeMat]
| |
| |program
| |
| |
| |
| |free (GNU General Public License)
| |
| |-
| |
| |-
| |
| |[[IMSL Numerical Libraries]]
| |
| |library
| |
| |
| |
| |
| |
| |-
| |
| |[[LAPACK]]
| |
| |routines
| |
| |'''L'''inear '''A'''lgebra '''PACK'''age
| |
| |free source
| |
| |-
| |
| |[[ScaLAPACK]]
| |
| |library
| |
| |'''Sca'''lable '''LAPACK'''
| |
| |free source
| |
| |-
| |
| |[[Magma]]
| |
| |
| |
| |
| |
| |
| |
| |-
| |
| |[[Maple]]
| |
| |program
| |
| |
| |
| |commercial
| |
| |-
| |
| |[[Mathematica]]
| |
| |program
| |
| |
| |
| |commercial
| |
| |-
| |
| |[[Math Kernel Library]]
| |
| |library
| |
| |
| |
| |
| |
| |-
| |
| |[[MATLAB]]
| |
| |program
| |
| |
| |
| |commercial
| |
| |-
| |
| |[[Maxima]]
| |
| |program
| |
| |
| |
| |free (General Public License)
| |
| |-
| |
| |[[NAG]]
| |
| |routines
| |
| |'''N'''umerical '''A'''lgorithms '''G'''roup
| |
| |commercial
| |
| |-
| |
| |[[Numerical Recipes]]
| |
| |routines
| |
| |
| |
| |
| |
| |-
| |
| |[[Octave]]
| |
| |program
| |
| |
| |
| |free (GNU)
| |
| |-
| |
| |[[QUADPACK]]
| |
| |routines
| |
| |
| |
| |free
| |
| |-
| |
| |[[SAGE]]
| |
| |program
| |
| |
| |
| |free (General Public License)
| |
| |-
| |
| |[[Scilab]]
| |
| |program
| |
| |
| |
| |free, Open Source
| |
| |}
| |
| | |
| ==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/10.1063/1.2435629 Frank Wilczek "Reasonably Effective: I. Deconstructing a Miracle", Physics Today '''November''' pp. 8-9 (2006)]
| |
| **[http://dx.doi.org/10.1063/1.2743102 Frank Wilczek "Reasonably Effective: II. Devil's Advocate", Physics Today '''May''' pp. 8-9 (2007)]
| |
| *[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)]
| |
| ==References==
| |
| <references/>
| |
| ==External links==
| |
| *[http://www.mathematics.thetangentbundle.net/wiki/Main_Page TheTangentBundle mathematics wiki]
| |
| *[http://mathworld.wolfram.com/ Wolfram MathWorld]
| |
| [[category: mathematics]] | | [[category: mathematics]] |