An Introduction to Differential Equations and Their Applications

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Overview


Intended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition.
Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear differential equations and chaos, and partial differential equations. Numerous figures, problems with solutions, and historical notes clarify the text.
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Product Details

  • ISBN-13: 9780486445953
  • Publisher: Dover Publications
  • Publication date: 3/11/2006
  • Series: Dover Books on Mathematics Series
  • Pages: 640
  • Sales rank: 527,714
  • Product dimensions: 8.30 (w) x 10.90 (h) x 1.30 (d)

Meet the Author

Partial Differential Equations & Beyond
Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers is one of the most widely used textbooks that Dover has ever published. Readers of the many Amazon reviews will easily find out why. Jerry, as Professor Farlow is known to the mathematical community, has written many other fine texts — on calculus, finite mathematics, modeling, and other topics. We followed up the 1993 Dover edition of the partial differential equations title in 2006 with a new edition of his An Introduction to Differential Equations and Their Applications. Readers who wonder if mathematicians have a sense of humor might search the internet for a copy of Jerry's The Girl Who Ate Equations for Breakfast (Aardvark Press, 1998).

Critical Acclaim for Partial Differential Equations for Scientists and Engineers:
"This book is primarily intended for students in areas other than mathematics who are studying partial differential equations at the undergraduate level. The book is unusual in that the material is organized into 47 semi-independent lessonsrather than the more usual chapter-by-chapter approach.

"An appealing feature of the book is the way in which the purpose of each lesson is clearly stated at the outset while the student will find the problems placed at the end of each lesson particularly helpful. The first appendix consists of integral transform tables whereas the second is in the form of a crossword puzzle which the diligent student should be able to complete after a thorough reading of the text.

"Students (and teachers) in this area will find the book useful as the subject matter is clearly explained. The author and publishers are to be complimented for the quality of presentation of the material." — K. Morgan, University College, Swansea

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Table of Contents

1. Introduction to Differential Equations
2. First-Order Differential Equations
3. Second-Order Linear Equations
4. Series Solutions
5. The Laplace Transform
6. Systems of Differential Equations
7. Difference Equations
8. Nonlinear Differential Equations and Chaos
9. Partial Differential Equations
Appendix
Answers to Problems
Index
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