## Elementary Differential Equations, 4/e

C. Henry Edwards, University of Georgia
David E. Penney

Published September, 1999 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-011290-9

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Differential Equations-Mathematics

For courses in differential equations. This book provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics students take following calculus. This is a strongly algebraic-oriented text with some computer enhancements for numerical methods. Matters of definition, classification, and logical structure deserve (and receive here) careful attention for the first time in the mathematical experience of many of the students. While it is neither feasible nor desirable to include proofs of the fundamental existence and uniqueness theorems along the way in an elementary course, students need to see precise and clear-cut statements of these theorems and understand their role in the subject. Appropriate existence and uniqueness proofs in the Appendix are included and referenced where appropriate in the main body of the text.

NEW—Stongest collection of problem sets available—Total is now 1600, of which 160 are new.
NEW—Applications are a highlight of this text:
—What explains the commonly observed lag time between indoor and outdoor daily temperature oscillations? (Section 1.5)
—What makes the difference between doomsday and extinction in alligator populations? (Section 1.7)
—How do a unicycle and a two-axle car react differently to road bumps? (Sections 2.6 and 5.5)
—Why are flagpoles hollow instead of solid? (Section 3.6)
—Why might an earthquake demolish one building and leave standing the one next door? (Section 5.5)
—How can you predict the time of next perihelion passage of a newly observed comet? (Section 6.4)
—Why and when does non-linearity lead to chaos in biological and mechanical systems? (Section 7.6)
NEW—Almost 275 computer-generated graphics throughout the text—Edwards/Penney is by far the most graphic and visually oriented of the competing elementary DE textbooks.

• Students are shown vivid pictures of slope fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life. NEW—Ten new student projects follow key computational sections in the book.
• Add concrete applied emphasis and engage students in more extensive investigations than afforded by typical exercises and problems.
A solid numerical methods emphasis is provided where appropriate—by the inclusion of generic numerical algorithms and a limited number of illustrative calculator, BASIC, and MATLAB routines.
A contemporary perspective—shaped by the availability of computational aids—permits a more streamlined coverage of certain standard topics (like exact equations and variation of parameters) in Chapters 1, 2, and 5.

1. First-Order Differential Equations.
2. Linear Equations of Higher Order.
3. Power Series Methods.
4. Laplace Transform Methods.
5. Linear Systems of Differential Equations.
6. Numerical Methods.
7. Nonlinear Systems and Phenomena.