Mathematics: Difference between revisions

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m (→‎Computer assisted mathematics: Added an internal link to BLAS.)
m (→‎Computer assisted mathematics: Changed list to a wikitable.)
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*[[Legendre transform]]
*[[Legendre transform]]
==Computer assisted mathematics==
==Computer assisted mathematics==
*[[BLAS]] '''B'''asic '''L'''inear '''A'''lgebra '''S'''ubprograms
{| class="wikitable sortable" border="1" cellpadding="5" cellspacing="0"
*[[CGAL]] '''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary
|-
*[[IMSL Numerical Libraries]]
! Packages !! Program or library !! class="unsortable" | Notes !! License 
*[[LAPACK]] - '''L'''inear '''A'''lgebra '''PACK'''age
|-
**[[ScaLAPACK]] ('''Sca'''lable '''LAPACK''')
|[[BLAS]]
*[[Magma]]
|
*[[Maple]]
| '''B'''asic '''L'''inear '''A'''lgebra '''S'''ubprograms
*[[Mathematica]]
|
*[[Math Kernel Library]]
|-
*[[MATLAB]]
|[[CGAL]]
*[[Maxima]]
|
*[[NAG]] '''N'''umerical '''A'''lgorithms '''G'''roup
|'''C'''omputational '''G'''eometry '''A'''lgorithms '''L'''ibrary
*[[Numerical Recipes]]
|
*[[Octave]]
|-
*[[QUADPACK]]
|[[IMSL Numerical Libraries]]
*[[SAGE]] Open Source Mathematics Software
|
*[[Scilab]]
|
|
|-
|[[LAPACK]]
|
|'''L'''inear '''A'''lgebra '''PACK'''age
|
|-
|[[ScaLAPACK]]
|
|'''Sca'''lable '''LAPACK'''
|
|-
|[[Magma]]
|
|
|
|-
|[[Maple]]
|
|
|
|-
|[[Mathematica]]
|
|
|
|-
|[[Math Kernel Library]]
|
|
|
|-
|[[MATLAB]]
|
|
|
|-
|[[Maxima]]
|
|
|
|-
|[[NAG]]  
|
|'''N'''umerical '''A'''lgorithms '''G'''roup
|
|-
|[[Numerical Recipes]]
|
|
|
|-
|[[Octave]]
|
|
|
|-
|[[QUADPACK]]
|
|
|
|-
|[[SAGE]]  
|
|
|Free, Open Source
|-
|[[Scilab]]
|
|
|
|}


==Interesting reading==
==Interesting reading==

Revision as of 14:33, 18 February 2009

"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