Outline

Mathematical Methods in Physics (PHY 230) - Fall 2002

• Special Functions
  • gamma functions and beta functions
  • error functions
• Coordinates
  • cylindrical and spherical coordinates
  • generally orthogonal coordinates
  • grad, div, curl, Laplacian
• Partial Differential Equations
  • PDE's of physics
  • separation of variables
  • Laplace and Helmholtz's equations
  • Bessel functions, spherical harmonics
• Ordinary Differential Equations
  • general DEs
  • linear DEs
  • series expansions
• Eigenfunction methods
  • orthogonal series
  • Sturm-Liouville theorem
  • completeness
  • orthogonalization
• Green's Functions
  • delta functions
  • 1D Green's functions
  • closure
  • eigenfunction expansions
  • 3D Green's functions
• Infinite Series
  • summing series
  • expanding series
  • asymptotic series
• Complex Variables
  • analytic functions
  • complex potentials and conformal transformations
  • Cauchy's theorem and integral formula
  • Taylor and Laurent series
  • poles, zeroes, branch points
  • residue theorem
• Integration
  • contour integration
  • saddle point integration
• Integral Transforms
  • Fourier transforms
  • power spectra
  • convolution and correlation
  • Laplace transforms
• Probability
  • permutations and combinations
  • probability distributions
  • random walks and random events
  • binomial, Poisson, Gaussian, and gamma
  • moment generating functions
  • central limit theorem