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Catalogue Information
Field name	Details
Dewey Class	515.352
Title	Differential Equations: Theory and Applications ([Ebook]) / by David Betounes.
Author	Betounes, David
Other name(s)	SpringerLink (Online service)
Edition statement	Second edition
Publication	New York, NY : Springer , 2010.
Physical Details	XIII, 620 pages : online resource.
ISBN	9781441911636
Summary Note	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):
Contents note	Introduction -- Techniques, Concepts and Examples -- Existence and Uniqueness: The Flow Map.-Linear Systems -- Linearization and 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4419-1163-6
Links to Related Works	Subject References: Differentiable dynamical systems . Differential equation . Dynamical systems and ergodic theory . Mathematical Methods in Physics . Mathematical Physics . Mathematics . Numerical Analysis . Ordinary differential equations . Authors: Betounes, David . Corporate Authors: SpringerLink (Online service) . Classification: 515.352 . 515.352 (DDC 23) .

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Differential Equations: Theory and Applications

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