Outline

Mathematical Methods in Physics (PHY 230) - Fall 2002

• Special Functions (RHB Appendix)
  • gamma functions and beta functions
  • error functions
• Coordinates (RHB 8.9-10 / 10.9-10)
  • cylindrical and spherical coordinates
  • generally orthogonal coordinates
  • grad, div, curl, Laplacian
• Partial Differential Equations (RHB 16.1, 17-17.3 / 18.1, 19-19.3)
  • PDE's of physics
  • separation of variables
  • Laplace and Helmholtz's equations
  • Bessel functions, spherical harmonics
• Ordinary Differential Equations (RHB 12-14 / 14-16 except Laplace transform and Green's)
  • general DEs
  • linear DEs
  • series expansions
• Eigenfunction methods (RHB 15-15.5 / 17-17.5)
  • orthogonal series
  • Sturm-Liouville theorem
  • completeness
  • orthogonalization
• Green's Functions (RHB 11.1.3, 13.2.5, 15.6-15.7, 17.5 / 13.1.3, 15.2.5, 17.5-17.6, 19.5)
  • delta functions
  • 1D Green's functions
  • 3D Green's functions
  • closure
  • eigenfunction expansions
• Infinite Series (RHB 3 / 4)
  • summing series
  • expanding series
  • asymptotic series
• Complex Variables (RHB 18-18.15 / 20-20.15)
  • analytic functions
  • complex potentials and conformal transformations
  • Cauchy's theorem and integral formula
  • Taylor and Laurent series
  • poles, zeroes, branch points
  • residue theorem
• Integration (RHB 18.16-18.20 / 20.16-20.20)
  • contour integration
• Integral Transforms (RHB 11 / 13)
  • Fourier transforms
  • power spectra
  • convolution and correlation
  • Laplace transforms
• Probability (RHB 24-24.10 / 26-26.10)
  • permutations and combinations
  • probability distributions
  • random walks and random events
  • binomial, Poisson, Gaussian, and gamma
  • moment generating functions
  • central limit theorem