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

       Preface

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

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   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