Outline

Mathematical Methods in Physics (PHY 230) - Fall 2006

These following topics are usually in order.
"McQ x" means the sections for "x" in the textbook Donald A. McQuarrie.

Special Functions (McQ 3)
- principal parts
- Gaussian integrals
- error functions, gamma & beta functions, Riemann zeta functions, etc
- delta functions
Infinite Series (McQ 2)
- convergence and uniform convergence
- expanding series
- summing series
Ordinary Differential Equations (McQ 11-13)
- general DEs
- linear DEs
- series expansions, method of Frobenius
- Legendre polynomials/functions, Bessel functions
- qualitative nonlinear DEs
Eigenfunction methods (McQ 14)
- orthogonal functions and series
- convergence and closure
- Sturm-Liouville theorem and Hermitean operators
- orthogonalization
- 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 15, 17)
- Fourier series
- 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
- stochastic processes
- characteristic functions
- central limit theorem

These following topics are not in order. They are mixing in the Computer Labs, the Mathematica Notebooks and the lectures.