Stanley J. Farlow - An Introduction to Differential Equations and Their Applications

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FARLOW University of Maine DOVER PUBLICATIONS, INC.
Mineola, New York Copyright Copyright 1994 by Stanley J. Farlow All rights reserved. Bibliographical Note This Dover edition, first published in 2006, is an unabridged republication of
the work originally published by McGraw-Hill, Inc., New York, in 1994. All color
materials have been reprinted in black and white. International Standard Book NumberISBN-13: 978-0-486-44595-3ISBN-10: 0-486-44595-X Manufactured in the United States by Courier Corporation 44595X03 www.doverpublications.com ABOUT THE AUTHOR Stanley J. Farlow has academic degrees from Iowa State University, the University of Iowa, and Oregon State University.

He is a former Lieutenant Commander and Public Health Service Fellow who served for several years as a computer analyst at the National Institutes of Health in Bethesda, Maryland. In 1968 he joined the faculty of the University of Maine, where he is currently Professor of Mathematics. He is also the author of Partial Differential Equations for Scientists and Engineers, (currently being published by Dover Publications, Inc.), Finite Mathematics (McGraw-Hill, 1988, 1994), Applied Mathematics (McGraw-Hill, 1988), Introduction to Calculus (McGraw-Hill, 1990), and Calculus and Its Applications (McGraw-Hill, 1990). He has also edited The GMDH Method: Self-Organizing Methods in Modeling (Marcel Dekker, 1984). To Dorothy and Susan PREFACE An Introduction to Differential Equations and Their Applications is intended for use in a beginning one-semester course in differential equations. It is designed for students in pure and applied mathematics who have a working knowledge of algebra, trigonometry, and elementary calculus.

The main feature of this book lies in its exposition. The explanations of ideas and concepts are given fully and simply in a language that is direct and almost conversational in tone. I hope I have written a text in differential equations that is more easily read than most, and that both your task and that of your students will be helped. Perhaps in no other college mathematics course is the interaction between mathematics and the physical sciences more evident than in differential equations, and for that reason I have tried to exploit the reader's physical and geometric intuition. At one extreme, it is possible to approach the subject on a highly rigorous lemma-theoremcorollary level, which, for a course like differential equations, squeezes out the lifeblood of the subject, leaving the student with very little understanding of how differential equations interact with the real world. At the other extreme, it is possible to wave away all the mathematical subtleties until neither the student nor the instructor knows what's going on.