Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition

PREFACE

This is a textbook for a first course in differential equations. The book is intended for science and engineering majors who have completed the calculus sequence, but not necessarily a first course in linear algebra. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science.

Differential equations is an old and venerable subject that will always play a central role in describing phenomena that change over time. Indeed, at least one course in differential equations is part of the curriculum of most engineering and science students. Our goal in writing this text is to provide these students with both an introduction to, and a survey of, modern methods, applications, and theory of this beautiful and powerful mathematical apparatus that is likely to serve them well in their chosen field of study. The subject matter is presented in a manner consistent with the way practitioners use differential equations in their work; technology is used freely, with more emphasis on methods, modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. For example, some important theoretical results, such as theorems guaranteeing existence and uniqueness of solutions to initial value problems, are not proved. Nevertheless, they are carefully stated, illustrated by examples, and used frequently.

Any student who studies major portions ...