Teaching

Please note that all class announcements and class materials are published on Canvas. Feel free to contact me if you are not enrolled in my class but would like to have additional class information.

Math 552: Applications of Scientific Computing 

Semester: Spring

Offered: 2026

Introduction to the application of computational methods to models arising in science and engineering, concentrating mainly on the solution of partial differential equations. Topics include finite differences, finite element method, boundary value problems, numerical ODEs, and spectral methods.

Math 646: Applied Mathematics and Mathematical Modelin 

Semester: Spring

Offered: 2026

This course covers classical methods in applied mathematics and math modeling. The topics include dimensional analysis, asymptotics, regular and singular perturbation theory, calculus of variation, random walks and the diffusion limit, classical solution techniques for PDE, common methods for parameter estimation like Maximum Likelihood Estimation (MLE), Maximum a Posteriori (MAP) estimation, Bayesian estimation. The techniques will be applied to models arising throughout the natural sciences.

Math 645: Differential Equations and Dynamical Systems 

Semester: Fall

Offered: 2025

Classical theory of ordinary differential equations and some of its modern developments in dynamical systems theory. Linear systems and exponential matrix solutions. Well-posedness for nonlinear systems. Qualitative theory: limit sets, invariant set and manifolds. Stability theory: linearization about an equilibrium, Lyapunov functions. Autonomous two-dimensional systems and other special systems. Prerequisites: advanced calculus, linear algebra and basic ODE.