These lecture notes are from previous years, and touch upon many of the topics introduced in this course.

LECTURE TOPICS AND NOTES |
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Conservation Laws in Continuum Modeling (PDF) 1. Introduction 2. Continuum Approximation; Densities and Fluxes 3. Conservation Laws in Mathematical Form 4. Phenomenological Equation Closure 5. Concluding Remarks |

Stability of Numerical Schemes for PDEs (PDF) 1. Naive Scheme for the Wave Equation 2. Von Neumann Stability Analysis for PDEs 3. Numerical Viscosity and Stabilized Scheme |

Simplest Car Following Traffic Flow Model (PDF) 1. The Model; Nondimensionalization 2. Continuum Limit of Model 3. Numerical Issues; Stiffness of the Equations 4. Examples |

Discrete to Continuum Modeling (PDF) 1. Introduction 2. Wave Equations from Mass-Spring Systems 3. Torsion-Coupled Pendulums: Sine-Gordon Equation |

1. Convergence of Numerical Schemes 2. Discrete Fourier Transform, Fast Fourier Transform, and Fourier Series |