Lecture Notes

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


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

Separation of Variables (PDF)

Various Lecture Notes (PDF)

1. Convergence of Numerical Schemes

2. Discrete Fourier Transform, Fast Fourier Transform, and Fourier Series