Outline

Mathematical Methods in Physics (PHY 230) - Fall 2003

• Special Functions (McQ 3)
  • principal parts
  • Gaussian integrals
  • error functions, gamma & beta functions, Riemann zeta functions, etc
• Infinite Series (McQ 2)
  • convergence and uniform convergence
  • summing series
  • power series
  • asymptotic series
• Ordinary Differential Equations (McQ 11-13)
  • general DEs
  • linear DEs
  • series expansions
  • Legendre polynomials, Bessel functions
  • qualitative nonlinear DEs
• Eigenfunction methods (McQ 14)
  • orthogonal functions and series
  • orthogonalization
  • Sturm-Liouville theorem and Hermitean operators
  • delta functions (McQ 3.6)
  • closure
  • 1D Green's functions
• Coordinates (McQ 8)
  • cylindrical and spherical coordinates
  • general orthogonal coordinates
  • grad, div, curl, Laplacian
• Partial Differential Equations (McQ 16)
  • PDE's of physics
  • separation of variables
  • Laplace and Helmholtz's equations
  • Bessel functions, spherical harmonics
• Integral Transforms (McQ 17)
  • Fourier transforms
  • power spectra
  • convolution and correlation
  • Laplace transforms
• Complex Variables (McQ 18-19)
  • analytic functions
  • poles, zeroes, branch points
  • Cauchy's theorem and integral formula
  • Taylor and Laurent series
  • residue theorem and contour integration
  • conformal transformations
• Probability (McQ 21)
  • permutations and combinations
  • probability distributions
  • binomial, Poisson, Gaussian, Lorentzian, uniform, exponential, and gamma
  • characteristic functions
  • central limit theorem