Teaching

I am teaching CMOR 527: Discontinuous Galerkin Methods this coming spring term at Rice University. If you have any specific questions about course topics, feel free to send me an email.

CMOR 500: Analysis

Institution: Rice University
Semester: Fall 2023

Real numbers, completeness, sequences and convergence, compactness, continuity, the derivative, the Riemann integral, fundamental theorem of calculus. Vector spaces, dimension, linear maps, inner products and norms, derivatives in R^d, inverse function theorem, implicit function theorem, multiple integration, change of variable theorem.

Upcoming

CMOR 527: Discontinuous Galerkin Methods

Institution: Rice University
Semester: Spring 2024

The course will present the theory and implementation of discontinuous Galerkin methods for partial differential equations common in engineering applications. Two main classes of problems are covered: steady-state and time-dependent elliptic/parabolic and hyperbolic equations. These include (but are not limited to) the Poisson and heat equations, linear wave equations, and nonlinear conservation laws.

CAAM 334: Matrix Analysis for Data Science

Institution: Rice University
Semester: Spring 2023

Solution of linear systems and linear least squares problems. Eigenvalue problem and singular value decomposition. Introduction to gradient based methods. Applications to data science. 

CAAM 335: Matrix Analysis

Institution: Rice University
Semester: Fall 2022

Equilibria and the solution of linear systems and linear least squares problems. Eigenvalue problem and its application to solve dynamical systems. Singular value decomposition and its application.

AMATH 231: Calculus IV

Institution: University of Waterloo
Semester: Spring 2022

The first part of the course introduces the concepts and main results of vector integral calculus: vector fields, line and surface integrals and the three famous theorems - Green's theorem, Gauss' Divergence theorem and Stokes' theorem. The second part of the course deals with Fourier analysis, that is, the remarkable idea that a variety of complicated functions can be synthesized from pure sine and cosine functions. Applications to physics and engineering are emphasized throughout the course.

MATH 207: Multivariable Calculus for Non-Specialists

Institution: University of Waterloo
Semester: Spring 2020

Multivariable functions and partial derivatives. Gradients. Optimization including Lagrange multipliers. Polar coordinates. Multiple integrals. Surface integrals on spheres and cylinders. Introduction to Fourier Series.