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