Handbook of Differential Equations (2nd ed.)

Description

1. Definition of Terms § (pp. 1ff. // PDF pp. 12ff.)
2. Method of Characteristics (PDF pp. 444ff.)

From the introduction: "This book is a compilation of the most important and widely applicable methods for solving and approximating differential equations. As a reference book, it provides convenient access to these methods and contains examples showing their use.
"The book is divided into four parts. The first part is a collection of transformations and general ideas about differential equations and how they are solved. This section of the book describes the techniques needed to determine whether a partial differential equation is well posed, what the `natural' boundary conditions are, and many other things. At the beginning of this section is a list of definitions for many of the important words describing differential equations and their solutions.
"The second part of the book is a collection of exact analytical solution techniques for differential equations. The third part of this book deals with approximate analytical solution techniques. For the methods in this part of the book, the format is similar to that used for the exact solution techniques.
"When an exact or an approximate solution technique cannot be found, it may be necesary to find the solution numerically. Other times, a numerical solution may convey more information than an exact or approximate analytic solution. The fourth part of this book is concerned with the most important methods for finding numerical solutions of common types of differential equations. When possible, a short FORTRAN program has been given. At the beginning of the fourth section is a brief introduction to the terms used in numerical methods. In that section, terms are defined and some general references are given.''