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 |