Mathematics

Here are details of mathematical tools that have applications in classical thermodynamics, statistical mechanics and computer simulation techniques.

General

• Clebsch-Gordan coefficients
• Euler angles
• Green's theorem
• Laplace's equation
• Linear algebra
• Liouville's theorem
• Lyapunov exponents
• Padé approximants
• Perron-Frobenius theorem
• Poincaré theorem
• Power series
• Predictor-corrector methods
• Random numbers
• Root finding
• Runge-Kutta method
• Spherical harmonics
• Stirling's approximation
• Taylor expansion
• 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

• CGAL - Computational Geometry Algorithms Library
• LAPACK - Linear Algebra PACKage
• Maple
• Mathematica
• MATLAB
• NAG Numerical Algorithms Group
• Numerical Recipes
• Octave
• SAGE Open Source Mathematics Software
• ScaLAPACK