AMath 574 Catalog Description

Theory of linear and nonlinear hyperbolic conservation laws modeling wave propagation in gases, fluids, and solids. Shock and rarefaction waves. Finite volume methods for numerical approximation of solutions; Godunov’s method and high-resolution TVD methods. Stability, convergence, and entropy conditions.

Contents

• Course information
  • Instructor / Office Hours
  • Class meeting times
  • Canvas page
  • Grading
  • Recommended Background
  • Textbook
  • Some other resources:
  • Goals
  • Topics
• Outline and schedule
  • Schedule (tentative)
• Some examples
  • Advection
  • Burgers’ equation
  • Linear Acoustics
  • Two dimensional Burgers’ equation

• Lecture videos and slides

• Homework and midterm

• Jupyter notebooks
• Installing Clawpack
• Python

• Class GitHub Repository

• Some other references
  • Hyperbolic problems and finite volume methods
  • Entropy
  • Python
  • Latex