4347 Contents

Partial Differential Equations and the Method of Characteristics

James V. Herod*

*(c) Copyright 1993,1994,1995 by James V. Herodd, herod@math.gatech.edu. All rights reserved.

Page maintained by Evans M. Harrell, II, harrell@math.gatech.edu.


Part I. First Order Equations


  1. Introduction to a Theme
  2. PDE's Using ODE's
  3. A Changing Population Hetrogeneous in Age
  4. Stepping Up The Dimension
  5. Complications: Nonlinear Equations
  6. Shock in Traffic Flow
  7. Finding the Direction for Shock Curves
  8. Complications: Initial Geometry
  9. Connections with the Geometry: From Surfaces to Equations
    Part II. Second Order Equations

  10. Language and Classification
  11. Standard Forms
  12. Translation Solutions for Constant Coefficient Equations
  13. Hyperbolic, Second Order PDE's with Variable Coefficients
  14. D'Alembert's Solution for the Wave Equation
  15. Variations on the Wave Equation
  16. D'Alembert's Solution on an Interval
  17. Uniqueness: Alternate Methods, Same Solutions
  18. Connections with the Geometry: From Surfaces to Equations
  19. Second Order Equations as First Order Systems
  20. The Domain of Dependence
  21. Factorization
  22. PDE's and Special ODE's
  23. The Riemann Method