Mathematics
- "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 delivered before the 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
- 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
Integrals and quadrature
- Standard integrals
- Elliptic integrals
- Newton-Cotes formulas
- Gauss-Chebyshev quadrature
- Gauss-Legendre quadrature