# Teaching

## At the University of California San Diego:

#### MAE 108 - Probability and Statistical Methods for Mechanical and Environmnental Engineering

Course Webpage (Spring 2015)This undergraduate course focuses on concepts and methods of probabilities and statistics applied to the formulation and modeling of engineering problems. Covered topics include: probabilities and conditional probabilities, Bayes theorem, random variables, densities, expected values, characteristic functions, central limit theorem; engineering reliability, random sampling, hypothesis testing, confidence intervals; curve fitting and data analysis.

#### MAE 207 - Complex and Biological Fluids

Course Webpage (Winter 2015)This graduate-level special-topics course focuses on applications of low-Reynolds-number hydrodynamics to the description of complex and biological fluids. Covered topics include: Stokes flows, their properties and fundamental solutions; particulate suspensions: effective stress, Brownian motion, Fokker-Planck equation; polymer solutions: entropic dumbbell, dynamics and rheology; biological membranes and vesicles; locomotion, bioconvection, colletive motion; intracellular transport.

#### MAE 210A - Fluid Mechanics I

Course Webpage (Fall 2014)This course covers fundamentals of fluid mechanics at the beginning graduate level. It focuses on analytical methods and covers the following topics: kinematics of fluid flows; basic conservation laws; physical properties of fluids; derivation of the Navier-Stokes equations; analytical solutions (parallel flows); dimensional analysis and flow regimes; vorticity dynamics.

**Textbook:** *Fluid Mechanics*, Kundu, Cohen and Dowling (Academic Press 2012).

#### MAE 210C - Fluid Mechanics III

Course Webpage (Spring 2014)This course focuses on the theory of hydrodynamic stability and transition to turbulence. Topics covered include: stability of dynamical systems and bifurcations; Kelvin Helmholtz instability; Rayleigh-Benard thermal convection; Taylor-Couette flow and centrifugal instabilities; capillary instability; energy methods; stability of parallel flows; Orr-Sommerfeld equation; convective and absolute instabilities; secondary instability and transition to turbulence; Landau's theory of nonlinear stability.

**Textbook:** *Hydrodynamic Instabilities*, Charru (Cambridge University Press 2011).

## At the University of Illinois:

#### TAM 335 - Introductory Fluid Mechanics

This course provides an introduction to the field of fluid mechanics for undergraduate engineering students. Topics covered include: fluid statics; continuity, momentum, and energy principles via control volumes; ideal and real fluid flow; introduction to the Navier Stokes equations; dimensional analysis and similarity; closed-conduit flows; open-channel flows; and turbomachinery.

**Textbook:** *Fundamentals of Fluid Mechanics*, Munson et al. (Wiley 2009).

#### TAM 435 - Intermediate Fluid Mechanics

This course covers fundamentals of fluid mechanics, at the advanced undergraduate and beginning graduate level. It focuses on analytical methods and covers the following topics: kinematics of fluid flows; conservation laws; physical properties of fluids; derivation of the Navier-Stokes equations; analytical solutions (parallel flows); inviscid flows; two-dimensional potential flows; vorticity dynamics; boundary layer theory; one-dimensional compressible flow.

**Textbook:** *Incompressible Flow*, Panton (Wiley 2005).

#### TAM 536 - Instability and Transition

This course focuses on the theory of hydrodynamic stability and transition to turbulence. Topics covered include: stability of dynamical systems and bifurcations; Kelvin Helmholtz instability; Rayleigh-Benard thermal convection; Taylor-Couette flow and centrifugal instabilities; capillary instability; energy methods; stability of parallel flows; Orr-Sommerfeld equation; convective and absolute instabilities; secondary instability and transition to turbulence; Landau's theory of nonlinear stability.

**Textbook:** *Hydrodynamic Stability*, Drazin & Reid (Cambridge University Press 2004).

#### TAM 541 - Mathematical Methods I

This first course on Mathematical Methods focuses on linear algebra, ordinary differential equations and complex variables for engineering applications. Topics covered include: vector spaces; vector and tensor algebra; best approximation; ordinary differential equations: analytical solution methods, power series, special functions; Laplace transforms; complex variables; analytic functions; complex integrals; introduction to conformal mappings.

**Textbook:** *Advanced Engineering Mathematics*, Greenberg (Prentice-Hall 1998).

#### TAM 542 - Mathematical Methods II

This second course on Mathematical Methods focuses on partial differential equations for engineering applications. It covers the following topics: functions of several variables; types of PDEs; boundary conditions; derivation of the Laplace equation, wave equation, and heat equation from conservation laws; self-similarity; separation of variables; Green's functions; eigenfunction expansions; Fourier and other integral transforms; method of characteristics.

**Textbook:** *Applied Partial Differential Equations*, Haberman (Prentice-Hall 2003).