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A Short Course in Ordinary Differential Equations

Author(s):
Publisher:

Springer

Pages: 267
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Recommend to library

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Paperback - 9783319354262

10 September 2016

$69.99

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Hardcover - 9783319112381

06 November 2014

$69.99

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Ebook - 9783319112398

21 October 2014

$54.99

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This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two...

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This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.

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Focuses on the theoretical aspect of ODEs without emphasis on lengthy technical applications of special equations from physics and engineering

Uses carefully selected and organized material to cover all significant text with analytic, easily comprehensible explanations

Simplifies and/or modifies many statements and proofs of theorems and introduces symbolic abbreviations for frequently used concepts and terms

Gives hints for proof-oriented exercises and answers to computational exercises

Preface
Notation and Abbreviations
1. Initial Value Problems
2. Linear Differential Equations
3. Lyapunov Stability Theory
4. Dynamic Systems and Planar Autonomous Equations
5. Introduction to Bifurcation Theory
6. Second-Order Linear Equations
Answers and Hints
Bibliography
Index.
“All material is carefully organized and presentedin a transparent manner. The text contains a large number of solved problemswhich illustrate well theoretical material. Each chapter concludes with aselection of exercises for independent study; hints and answers to exercisesare collected in the end of the book along with a useful list of references anda subject index. … Undoubtedly, this book is a very valuable contribution toexisting texts on qualitative theory of differential equations.” (Yuriy V.Rogovchenko, zbMATH, Vol. 1326.34007, 2016)
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Qingkai Kong is a Professor and Director of Undergraduate Studies in the Department of Mathematical Sciences at Northern Illinois University. He holds a M.Sc and Ph.D from the University of Alberta. Dr. Kong is a recipient of the Huo Ying-Dong Teaching Award and has refereed for over 50 journals.

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Qingkai Kong is a Professor and Director of Undergraduate Studies in the Department of Mathematical Sciences at Northern Illinois University. He holds a M.Sc and Ph.D from the University of Alberta. Dr. Kong is a recipient of the Huo Ying-Dong Teaching Award and has refereed for over 50 journals.

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