4347 Contents
Partial Differential Equations and the Method of Characteristics
James V. Herod*
Page maintained by
Evans M. Harrell, II,
harrell@math.gatech.edu.
TABLE OF CONTENTS
Part I. First Order Equations
Preface

Introduction to a Theme

PDE's Using ODE's

A Changing Population Hetrogeneous in Age

Stepping Up The Dimension

Complications: Nonlinear Equations

Shock in Traffic Flow

Finding the Direction for Shock Curves

Complications: Initial Geometry

Connections with the Geometry: From Surfaces to Equations
Part II. Second Order Equations

Language and Classification

Standard Forms

Translation Solutions for Constant Coefficient Equations

Hyperbolic, Second Order PDE's with Variable Coefficients

D'Alembert's Solution for the Wave Equation

Variations on the Wave Equation

D'Alembert's Solution on an Interval

Uniqueness: Alternate Methods, Same Solutions

Connections with the Geometry: From Surfaces to Equations

Second Order Equations as First Order Systems

The Domain of Dependence

Factorization

PDE's and Special ODE's

The Riemann Method