Differential equations and dynamical systems courses
This page collects some information about (ordinary) differential equations and dynamical systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on integrated ACM 106b, AM 125b and CDS 140a.
Contents
Overview of current course sequence
ACM 106b: Introductory Methods of Computational Mathematics
Catalog listing he sequence covers the introductory methods in both theory and implementation of numerical linear algebra, approximation theory, ordinary differential equations, and partial differential equations. The course covers methods such as direct and iterative solution of large linear systems; eigenvalue and vector computations; function minimization; nonlinear algebraic solvers; preconditioning; timefrequency transforms (Fourier, wavelet, etc.); root finding; data fitting; interpolation and approximation of functions; numerical quadrature; numerical integration of systems of ODEs (initial and boundary value problems); finite difference, element, and volume methods for PDEs; level set methods. Programming is a significant part of the course. Instructor: Yan. Dependent courses:
Partially overlapping courses

Topics (Winter 2010)

ACM 216: Markov Chain, Discret Stochastic Processes and Applications
Catalog listing Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bound Dependent courses Partially overlapping courses

Topics (Winter 2008)

Advanced courses
There are several advanced courses that build on ACM 116/216 and are offered on a semiregular basis: