Aerospace Computational Engineering Lab


AER1418: Variational Methods for PDEs

This introductory graduate course introduces variational formulations and associated finite element methods for partial differential equations in continuum mechanics, including both elliptic and hyperbolic equations. An equal emphasis is placed on mathematical theory and practical implementation. Theoretical topics include discussions of well-posedness, optimality, and a priori and a posteriori error estimates. Practical topics include implementation of finite elements, matrix and vector assembly, and adaptive mesh refinement.

Course notes: AER1418: variational methods for PDEs (2022)

Terms: Winter 2018-2023

AER336: Scientific Computing

This third-year undergraduate course introduces numerical methods for scientific computation which are relevant to the solution of a wide range of engineering problems. Topics addressed include interpolation, integration, linear systems, least-squares fitting, nonlinear equations and optimization, initial value problems, and partial differential equations.

Course notes: AER336: scientific computing (2022)

Terms: Winter 2016-2020, 2022-2023

ESC384: Partial Differential Equations

This third-year undergraduate course introduces techniques to analyze and solve partial differential equations (PDEs). Concepts covered include Fourier series, Sturm-Liouville theory, separation of variables, fundamental solutions, Green’s functions, method of characteristics, and numerical methods. Applications are in model PDEs in continuum mechanics: heat, Laplace’s, wave, and transport equations.

Course notes: ESC384: partial differential equations (2021)

Terms: Fall 2019-2022

2.086 (MIT): Numerical Computation for Mechanical Engineers

In this project, we developed a curriculum for a sophomore-level course on computational mathematics, numerical methods, and programming taught at MIT and Singapore University of Technology and Design (SUTD). I co-authored and continuously updated a textbook used in the course since Fall 2011. In Fall 2014, we have also introduced a "nutshell" textbook and interactive MATLAB demos.

Materials developed for the course are available on MIT OpenCourseWare: