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A Short Course in Ordinary Differential Equations: Universitext

Autor Qingkai Kong
en Limba Engleză Hardback – 6 noi 2014
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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Specificații

ISBN-13: 9783319112381
ISBN-10: 3319112384
Pagini: 267
Ilustrații: XII, 267 p. 55 illus.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.57 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Public țintă

Graduate

Cuprins

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.

Recenzii

“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)

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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