Teaching
Numerical methods of engineers (ENGN 1840)
In this course, I teach numerical analysis techniques relevant and fundamental to engineering problems. The course provides an overview of how to analytically solve Ordinary and Partial Differential Equations (ODEs & PDEs) as well as linear systems of equations. The four main fundamental numerical calculations by which all numerical approaches are based are presented: interpolation, numerical differentiation, numerical integration, and root finding/iteration. The properties of numerical methods, i.e., stability, accuracy, and convergence, are first presented in the course. Numerical methods are then applied to solving two types of ODEs: Initial-Value Problems (IVPs) and Boundary-Valued Problems (BVPs) and PDEs (i.e., parabolic, hyperbolic, elliptic).
Compressible fluid dynamics (ENGN 2830)
In this course, we explore compressible fluids dynamics. Such flows have a variable density over space and time. They can expand to take the shape of their volume or be compressed into an enclosing, confined space. These flows surround (air), inflate (air in lungs), compress (impact), hold/push (drag/thrust), and levitate (flight) us. We investigate flows to design and, if possible, take advantage of their behavior for engineering solutions. Students first learn to identify a fluid and develop the mathematical framework (differential equations) that describe compressible low motion/dynamics. We then study fundamental flow characteristics for 1D linear and non-linear systems. We will start by learning to solve steady 1D problems that can be built into realistic applications. Students then solve the Riemann problem for the Euler equations (unsteady 1D flow) using analysis and numerical methods. We conclude the course by surveying advanced topics in multi-dimensional flows (e.g., hypersonics, turbulence, and Computational Fluid Dynamics).
Fluid Mechanics of Energy and Aerospace Systems (ENGN 1700)
Coming 2023 Fall Semester.