| LEC # | TOPICS |
|---|---|
| 1 | Introduction: Dense Granular Flow in a Silo |
| 2-3 | Linear Waves: PDE for Waves in an Elastic Medium, Characteristics, d'Alembert's Solution |
| 4-13 | Nonlinear Kinematic Waves: Lighthill-Whitham Theory of Traffic Flow, Density Waves, General Method of Characteristics, Hodograph Method, Expansion Fans, Wave Breaking, Shocks River Waves, Gas Compression Waves, Shallow Water Waves |
| Midterm Exam | |
| 14-16 | Dispersive Waves: Fourier Transform, Group Velocity and Caustics Envelope Equations, KdV Equation, Solitons |
| 17-18 | Linear Diffusion: Green Function for the Diffusion Equation, Some Fourier Analysis Similarity Solutions |
| 19-25 | Nonlinear Diffusion: Burgers Equation and Shock Structure, Cole-Hopf Transformation Porous Medium Equation, Similarity Solutions Regular and Singular Perturbations, Boundary Layers, Matched Asymptotic Expansions Nernst-Planck Equations |
| Final Exam |