# 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 I (ENGN 2810)

We will explore the basics of fluids dynamics in this course. We investigate flows to design and, if possible, take advantage of their behavior for engineering solutions. You will first learn the necessary mathematical concepts and notation to communicate integral and differential formulations of governing equations for fluid motion. We will then develop an intuitive understanding of the constitutive relations and balance principles governing fluid flow (e.g., Navier-Stokes equations). The Navier-Stokes equations will then be analyzed and, under specific assumptions, be reduced to simpler equations (e.g., inviscid flow and Bernoulli's equation). We will then consider exact, analytical solutions to the Navier-Stokes equations for simple flows (e.g., parallel shear flows, lubrication theory, and boundary layers).

### High Reynolds number flows (ENGN 1700)

You will explore the fluid mechanics of aerospace and energy systems in this course.

Aerospace fluid dynamics are the dynamics of flows involving air. 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 (e.g., extracting energy). You will first learn to identify a fluid and develop the mathematical framework (differential equations) that describe compressible flow motion/dynamics. We then study fundamental thin airfoil, wing, and boundary layer theory. We will then consider extracting energy from air flows using wind turbines. You will then solve the Euler equations using analysis and numerical methods. We will conclude the course by surveying advanced topics involving supersonics, hypersonics, and space propulsion.