Differential Equations: Theory and Applications

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With Maple

ISBN:	1441911626
ISBN 13:	9781441911629
Autor:	Betounes, David
Verlag:	Springer Verlag GmbH
Umfang:	xiv, 626 S.
Erscheinungsdatum:	16.11.2009
Auflage:	2/2010
Produktform:	Gebunden/Hardback
Einband:	Gebunden

The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but also has a complete collection of proofs for the major theorems, ranging from the usual existence and uniqueness results to the Hartman-Grobman linearization theorem and the Jordan canonical form theorem. The book can be used almost exclusively in the traditional way for graduate math courses, or it can be used in an applied way for interdisciplinary courses involving physics, engineering, and other science majors. For this reason an extensive computer component using Maple is provided on Springer’s website. This new edition has been extensively revised throughout, particularly the chapters on linear systems, stability theory and Hamiltonian systems. The computer component is an in-depth supplement and complement to the material in the text and contains an introduction to discrete dynamical systems and iterated maps, special-purpose Maple code for animating phase portraits, stair diagrams, N-body motions, and rigid-body motions, and numerous tutorial Maple worksheets pertaining to all aspects of using Maple to study the topics in the text. Review from first edition: „This book is intended for first- and second- year graduate students in mathematics and also organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. The book is well written and provides many interesting examples. The author gives a comprehensive introduction to the theory on ordinary differential equations with a focus on mechanics and dynamical systems. The exposition is clear and easily understood.“ (Yuan Rong, Zentralblatt MATH, Vol. 993 (18), 2002)

Artikelnummer: 1616078 Kategorie: Analysis

Beschreibung

Beschreibung

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.

Inhaltsverzeichnis

Introduction.- Techniques, Conceptsand Examples.- Existenceand Uniqueness:The Flow Map.-Linear Systems.- Linearization & Transformation.- Stability Theory.- Integrable Systems.- Newtonian Mechanics.-Hamiltonian Systems.- Appendix A: Elementary Analysis.- Appendix B: Lipschitz Maps and Linearization.- Appendix C: Linear Algebra.-Appendix D: Electronic Contents.