http://www.sklogwiki.org/SklogWiki/api.php?action=feedcontributions&feedformat=atom&user=70.39.93.16 2026-04-30T20:56:05Z User contributions MediaWiki 1.41.0 http://www.sklogwiki.org/SklogWiki/index.php?title=Mathematics&diff=10944 2010-12-29T20:33:44Z

<p>70.39.93.16: </p> <hr /> <div>:'' &quot;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 [http://www.thesiswritingservice.com/ thesis writing services] that the discussion of the foundations of mechanics be taken up by mathematicians also.&quot; ''<br /> ::::: '''David Hilbert''' (excerpt from problem #6 of his lecture ''&quot;Mathematical Problems&quot;'', delivered before the Second International Congress of Mathematicians in Paris, 1900)<br /> Here are details of mathematical tools that have applications in [[classical thermodynamics]], [[statistical mechanics]] and [[computer simulation techniques]].<br /> ==General==<br /> *[[Clebsch-Gordan coefficients]]<br /> *[[Euler angles]]<br /> *[[Gauss theorem]]<br /> *[[Green's theorem]]<br /> *[[Lagrange multipliers]]<br /> *[[Laplace's equation]]<br /> *[[Lee-Yang circle theorem]]<br /> *[[Linear algebra]]<br /> *[[Liouville's theorem]]<br /> *[[Lyapunov exponents]]<br /> *[[Padé approximants]]<br /> *[[Perron-Frobenius theorem]]<br /> *[[Poincaré theorem]]<br /> *[[Power series]]<br /> *[[Predictor-corrector methods]]<br /> *[[Random numbers]]<br /> *[[Root finding]]<br /> *[[Runge-Kutta method]]<br /> *[[Spherical harmonics]]<br /> *[[Stirling's approximation]]<br /> *[[Substantive derivative]]<br /> *[[Taylor expansion]]<br /> *[[Trotter formula]]<br /> *[[Wigner D-matrix]]<br /> *[[Wigner D-matrix |Wigner rotation matrices]]<br /> <br /> ==Functions and distributions==<br /> *[[Bessel functions]]<br /> *[[Dirac delta distribution]]<br /> *[[Gamma function]]<br /> *[[Gaussian distribution]]<br /> *[[Heaviside step distribution]]<br /> *[[Kronecker delta]]<br /> *[[Poisson distribution]]<br /> *[[Ramp function]]<br /> <br /> ==Geometry==<br /> *[[Alpha shape]]<br /> *[[Delaunay simplexes]]<br /> *[[Dual lattice]]<br /> *[[Lattice Structures]]<br /> *[[Voronoi cells]]<br /> ==Integrals and quadrature==<br /> *[[Standard integrals]]<br /> *[[Elliptic integrals]]<br /> *[[Newton-Cotes formulas]]<br /> *[[Gauss-Chebyshev quadrature]]<br /> *[[Gauss-Legendre quadrature]]<br /> ==Polynomials==<br /> *[[Chebyshev polynomials]]<br /> *[[Laguerre polynomials]]<br /> *[[Legendre polynomials]]<br /> **[[Associated Legendre functions]]<br /> <br /> ==Transforms==<br /> *[[Fast Fourier transform]]<br /> *[[Fourier analysis]]<br /> *[[Laplace transform]]<br /> *[[Legendre transform]]<br /> ==Computer assisted mathematics==<br /> {| class=&quot;wikitable sortable&quot; border=&quot;1&quot; cellpadding=&quot;5&quot; cellspacing=&quot;0&quot;<br /> |-<br /> ! Packages !! Program or library !! class=&quot;unsortable&quot; | Notes !! License <br /> |- <br /> |[[BLAS]]<br /> |routines<br /> | '''B'''asic '''L'''inear '''A'''lgebra '''S'''ubprograms<br /> |free source<br /> |-<br /> |[[CGAL]]<br /> |library<br /> |'''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary<br /> |free, Open Source<br /> |-<br /> |[[IMSL Numerical Libraries]]<br /> |library<br /> |<br /> |<br /> |-<br /> |[[LAPACK]]<br /> |routines<br /> |'''L'''inear '''A'''lgebra '''PACK'''age<br /> |free source<br /> |-<br /> |[[ScaLAPACK]]<br /> |library<br /> |'''Sca'''lable '''LAPACK'''<br /> |free source<br /> |-<br /> |[[Magma]]<br /> |<br /> |<br /> |<br /> |-<br /> |[[Maple]]<br /> |program<br /> |<br /> |commercial<br /> |-<br /> |[[Mathematica]]<br /> |program<br /> |<br /> |commercial<br /> |-<br /> |[[Math Kernel Library]]<br /> |library <br /> |<br /> |<br /> |-<br /> |[[MATLAB]]<br /> |program<br /> |<br /> |commercial<br /> |-<br /> |[[Maxima]]<br /> |program<br /> |<br /> |free (General Public License)<br /> |-<br /> |[[NAG]] <br /> |routines<br /> |'''N'''umerical '''A'''lgorithms '''G'''roup<br /> |commercial<br /> |-<br /> |[[Numerical Recipes]]<br /> |routines<br /> |<br /> |<br /> |-<br /> |[[Octave]]<br /> |program<br /> |<br /> |free (GNU)<br /> |-<br /> |[[QUADPACK]]<br /> |routines<br /> |<br /> |free<br /> |-<br /> |[[SAGE]] <br /> |program<br /> |<br /> |free (General Public License)<br /> |-<br /> |[[Scilab]]<br /> |program<br /> |<br /> |free, Open Source<br /> |}<br /> <br /> ==Interesting reading==<br /> *[http://dx.doi.org/10.1002/cpa.3160130102 Eugene P. Wigner &quot;The unreasonable effectiveness of mathematics in the natural sciences&quot;, Communications on Pure and Applied Mathematics '''13''' pp. 1-14 (1960)]<br /> **[http://dx.doi.org/10.1063/1.2435629 Frank Wilczek &quot;Reasonably Effective: I. Deconstructing a Miracle&quot;, Physics Today '''November''' pp. 8-9 (2006)]<br /> **[http://dx.doi.org/10.1063/1.2743102 Frank Wilczek &quot;Reasonably Effective: II. Devil's Advocate&quot;, Physics Today '''May''' pp. 8-9 (2007)] <br /> *[http://www.ams.org/bull/1988-19-01/S0273-0979-1988-15634-0/S0273-0979-1988-15634-0.pdf David Ruelle &quot;Is our mathematics natural? The case of equilibrium statistical mechanics&quot;, Bulletin of the American Mathematical Society '''19''' pp. 259-268 (1988)]<br /> ==External links==<br /> *[http://www.mathematics.thetangentbundle.net/wiki/Main_Page TheTangentBundle mathematics wiki]<br /> *[http://mathworld.wolfram.com/ Wolfram MathWorld]<br /> [[category: mathematics]]</div>

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