A Short Course in Ordinary Differential Equations
Published on 21. October 2014
XII, 267 pages
978-3-319-11239-8 (ISBN)
Description
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.
Reviews / Votes
"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)
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
XII, 267 p. 55 illus.
File size
4,48 MB
ISBN-13
978-3-319-11239-8 (9783319112398)
DOI
10.1007/978-3-319-11239-8
Schweitzer Classification
Other editions
Additional editions
Qingkai Kong
A Short Course in Ordinary Differential Equations
Book
11/2014
Springer
€74.89
Shipment within 10-15 days
Person
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.
Content
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.
