Differential Equations: Theory and Applications Theory and Applications
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- Engels
- Hardcover
- 9781441911629
- 16 november 2009
- 626 pagina's
Samenvatting
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 complementto 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)
This book was written as a comprehensive introduction to the theory of ordinary di?erential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. H- torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mat- matics, thematerial is organized sothatthebookcan alsobeusedin awider setting within today’s modern university and society (see “Ways to Use the Book” below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can bene?t from using this text. Working professionals in any of these ?elds should be able to pro?t too by study of this text. An important, but optional component of the book (based on the - structor’s or reader’s preferences) is its computer material. The book is one of the few graduate di?erential equations texts that use the computer to enhance the concepts and theory normally taught to ?rst- and second-year graduate students in mathematics. I have made every attempt to blend - gether the traditional theoretical material on di?erential equations and the new, exciting techniques a?orded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab. The electronic material for mastering and enjoying the computer component of this book is on Springer’s website.
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- Bindwijze
- Hardcover
- Oorspronkelijke releasedatum
- 16 november 2009
- Aantal pagina's
- 626
- Illustraties
- Nee
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- Hoofdauteur
- David Betounes
- Tweede Auteur
- Onbekend
- Co Auteur
- David Betounes
- Hoofduitgeverij
- Springer-Verlag New York Inc.
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- 9781441911629
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