ABSTRACT

Elementary Differential Equations presents the standard material in a first course on differential equations, including all standard methods which have been a part of the subject since the time of Newton and the Bernoulli brothers. The emphasis in this book is on theory and methods and differential equations as a part of analysis.

Differential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented first with theoretical considerations following. Essentially all proofs of the theorems used are included, making the book more useful as a reference.

The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values.

Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for finding solutions are included.

chapter 1|16 pages

Some Prerequisite Topics

part I|60 pages

First Order Scalar Equations

chapter 2|10 pages

The idea of a differential equation

chapter 3|48 pages

Methods

part II|78 pages

Scalar Linear Differential Equations, Methods

chapter 4|26 pages

Homogeneous Linear Equations

chapter 5|28 pages

Nonhomogeneous Equations

chapter 6|22 pages

Laplace Transform Methods

part III|68 pages

Series Methods

chapter 7|18 pages

A Review of Power Series

chapter 8|48 pages

Power Series Methods

part IV|108 pages

First Order Systems

chapter 9|24 pages

Methods for First Order Linear Systems

chapter 10|14 pages

First Order Linear Systems, Theory

chapter 11|26 pages

Theory of Ordinary Differential Equations

chapter 12|42 pages

Equilibrium Points and Limit Cycles

part V|64 pages

Partial Differential Equations

chapter 13|32 pages

Boundary Value Problems, Fourier Series

chapter 14|30 pages

Some Partial Differential Equations