Teaching for Winter 2024
Undergraduate
AMATH 353 Partial Differential Equations I : Second order linear partial differential equations - the diffusion equation, wave equation, and Laplace's equation. Methods of solution - separation of variables and eigenfunction expansions, the Fourier transform. Physical interpretation of solutions in terms of diffusion, waves and steady states. First order non-linear partial differential equations and the method of characteristics. Applications are emphasized throughout.
Course information, and my lecture notes, are posted here (password protected).
Graduate
AMATH 777 Stochastic Processes in the Physical Sciences : Basic concepts and classification of stochastic processes. Stochastic differentiation and integration, Markov processes, Chapman-Kolmogorov equation, Fokker-Planck equation, Master equations: mesoscopic vs. macroscopic description. Spectral representation of stationary processes. Correlation function theory.
Course information, and my lecture notes, are posted here (password protected).