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**Unformatted text preview: **Ordinary and Partial Differential Equations An Introduction to Dynamical Systems John W. Cain, Ph.D. and Angela M. Reynolds, Ph.D. Mathematics Textbook Series. Editor: Lon Mitchell 1 . Book of Proof by Richard Hammack 2 . Linear Algebra by Jim Hefferon 3 . Abstract Algebra: Theory and Applications by Thomas Judson 4 . Ordinary and Partial Differential Equations by John W. Cain and Angela Reynolds Department of Mathematics & Applied Mathematics Virginia Commonwealth University Richmond, Virginia, 23284 Publication of this edition supported by the Center for Teaching Excellence at vcu Ordinary and Partial Differential Equations: An Introduction to Dynamical Systems Edition 1 . 2010 by John W. Cain and Angela Reynolds This work is licensed under the Creative Commons Attribution-NonCommercial-No Derivative Works 3 . License and is published with the express permission of the authors. Typeset in 10 pt Palladio L with Pazo Math fonts using PDFL A T E X Acknowledgements John W. Cain expresses profound gratitude to his advisor, Dr. David G. Scha- effer, James B. Duke Professor of Mathematics at Duke University. The first five chapters are based in part upon Professor Schaeffers introductory gradu- ate course on ordinary differential equations. The material has been adapted to accommodate upper-level undergraduate students, essentially by omitting technical proofs of the major theorems and including additional examples. Other major influences on this book include the excellent texts of Perko [ 8 ], Strauss [ 10 ], and Strogatz [ 11 ]. In particular, the material presented in the last five chapters (including the ordering of the topics) is based heavily on Strauss book. On the other hand, our exposition, examples, and exercises are more user-friendly, making our text more accessible to readers with less background in mathematics....

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