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

See also Condensed Table of Contents without subsections

• Course information
  • Instructor
  • Class meeting times
  • Discussion board
  • Canvas page
  • Grading
  • Recommended Background
  • Textbook
  • Goals
  • Topics
• Outline and reading assignments
  • Schedule (tentative)
• Some examples
  • Advection
  • Burgers’ equation
  • Linear Acoustics
  • Two dimensional Burgers’ equation
• Riemann problems and solutions
  • Acoustics
  • Nonconvex Scalar conservation laws
  • Shallow water equations
• Jupyter notebooks
  • Running notebooks on your computer
  • Viewing notebooks on Github
  • Running notebooks on the Windows Azure notebook server

• Lecture videos and slides
  • Lectures for the first week of classes:
  • Lectures for February 27, 2017
  • Tutorials
• Homework and project
  • Schedule
  • Midterm
  • Course Project
  • Homework format
  • Peer Review
• Course Projects
  • Feedback and peer review
  • Timeline
  • The course project paper
  • Presentations
• Possible project topics

• Computing Options
  • SageMathCloud
  • Docker image
• Downloading and installing software for this class
  • Git
  • Clawpack
  • Fortran and Python
• Class GitHub Repository
  • AM574 environment variable
  • To update
  • Your copy of these files
• Using SageMathCloud
  • Making a plot via a Python script
  • Making a plot in Jupyter notebooks
  • Viewing a png file
  • Viewing an html file
  • Editing files
  • Collaborating
• Python
  • Some Python resources

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