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A Short Course in Ordinary Differential Equations

Qingkai Kong (Autor)

Buch | Hardcover

XII, 267 Seiten

2014 | 2014
Springer International Publishing (Verlag)
978-3-319-11238-1 (ISBN)

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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 seniorundergraduates as well.

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.

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 presented in a transparent manner. The text contains a large number of solved problems which illustrate well theoretical material. Each chapter concludes with a selection of exercises for independent study; hints and answers to exercises are collected in the end of the book along with a useful list of references and a subject index. ... Undoubtedly, this book is a very valuable contribution to existing texts on qualitative theory of differential equations." (Yuriy V. Rogovchenko, zbMATH, Vol. 1326.34007, 2016)

Erscheint lt. Verlag	6.11.2014
Reihe/Serie	Universitext
Zusatzinfo	XII, 267 p. 55 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	584 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Bifurcation Theory • Linear Differential Equations • Lyapunov function method • Ordinary differential equations • Poincaré-Bendixson theorem • Stability Theory • Sturm-Liouville problems • Sturm–Liouville problems
ISBN-10	3-319-11238-4 / 3319112384
ISBN-13	978-3-319-11238-1 / 9783319112381
Zustand	Neuware