| 1 | Overview of Class | |
| 2 | General Framework. Discrete to Continuum Limits. | |
| 3 | Sources for Conservation Laws | |
| 4 | Conservation Laws in 2-D or 3-D, Dimensional Analysis, Fick's Law | Problem Set 1 Out Next Day |
| 5 | Conservation Laws and Partial Differential Equations (PDEs), Method of Characteristics, Traffic Flow | |
| 6 | Linearized Traffic Flow | |
| 7 | Characteristic Curves, Nonlinear Problems | |
| 8 | Nonlinear Kinematic Waves and Wave-Breaking | |
| 9 | Traffic Flow Examples | Problem Set 1 Due, Problem Set 2 Out |
| 10 | Shock Jump Condition | |
| 11 | Domain of Dependence, Characteristics, Shocks | |
| 12 | Flood Waves | Problem Set 2 Due Next Day, Problem Set 3 Out |
| 13 | Ordinary Differential Equations (ODEs), Shock and Rarefaction | |
| 14 | Arrow of Time | |
| 15 | Extended Theory | |
| 16 | EIKO, Waves and Caustics | |
| 17 | Whole Curves, Envelopes, Mach Cone | Problem Set 3 Due |
| 18 | Domain of Dependence, 1st Order PDEs | Problem Set 4 Out Day Before |
| 19 | Review of Theory: Expansion Fans, Shocks | |
| 20 | Review of Theory: Entropy Increase at Shocks | |
| 21 | Entropy, Quadratic Flow | |
| 22 | Envelopes and Relationship Between Conservation Laws and Shocks | |
| 23 | Shock Structure Due to Higher Order Effects | Problem Set 4 Due, Problem Set 5 Out Next Day |
| 24 | Gas Dynamics, Acoustics, and Strings | |
| 25 | Gas Dynamics, Polytropic Gas, Hyperbolic | |
| 26 | Linear Algebra for Gas Dynamics | |
| 27 | Linear Gas Dynamics: Acoustic in a Pipe | Problem Set 5 Due Next Day |
| 28 | Gauss / Stokes Theorem | Problem Set 6 Out |
| 29 | General Solution for the Wave Equation | |
| 30 | Multivariable Calculus, Differentiability, Properties of the Gradient, Taylor Expansion, Implicit Function Theorem | |
| 31 | Characteristics for Klein-Gordon | Problem Set 6 Due, Problem Set 7 Out Next Day |
| 32 | Characteristics, Simple Waves, and Shocks for Gas Dynamics, Numerical Method by Characteristics | |
| 33 | Separation of Variables and Normal Modes | |
| 34 | Scalar Product Definition of Self-Adjoint | |
| 35 | Generalize to Operators, Finite Differences Schemes for PDEs | Problem Set 7 Due Next Day, Problem Set 8 Out Next Day |
| 36 | FD Schemes | |
| 37 | Introduction to the vNSA Problem Series | |
| 38 | Artificial Viscosity | |
| 39 | von Neumann Stability Analysis for Numerical Schemes | Problem Set 8 Due |
