Differential Equations, Dynamical Systems, and an Introduction to Chaos, Volume 60

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Academic Press, 2004 - Mathematics - 417 pages
4 Reviews
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.

* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon

NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems
  

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Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

User Review  - Joecolelife - Goodreads

this is an excellent introduction for beginners. in fact, this reference has explained the differential equations, the dynamical system and the chaos as clear as possible. the elementary mathematical ... Read full review

Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

User Review  - DJ - Goodreads

Big boy dynamical systems theory for once I've graduated from Strogatz's preschool. Read full review

Contents

Chapter 1 FirstOrder Equations
1
Chapter 2 Planar Linear Systems
21
Chapter 3 Phase Portraits for Planar Systems
39
Chapter 4 Classification of Planar Systems
61
Chapter 5 Higher Dimensional Linear Algebra
75
Chapter 6 Higher Dimensional Linear Systems
107
Chapter 7 Nonlinear Systems
139
Chapter 8 Equilibria in Nonlinear Systems
159
Chapter 11 Applications in Biology
235
Chapter 12 Applications in Circuit Theory
257
Chapter 13 Applications in Mechanics
277
Chapter 14 The Lorenz System
303
Chapter 15 Discrete Dynamical Systems
327
Chapter 16 Homoclinic Phenomena
359
Chapter 17 Existence and Uniqueness Revisited
383
Bibliography
407

Chapter 9 Global Nonlinear Techniques
189
Chapter 10 Closed Orbits and Limit Sets
215

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About the author (2004)

Robert L. Devaney is Professor of Mathematics at Boston University. Robert was raised in Methuen, Massachusetts. He received his undergraduate degree from Holy Cross College and his Ph.D. from the University of California, Berkeley. He has taught at Boston University since 1980. His main area of research is complex dynamical systems, and he has lectured extensively throughout the world on this topic. In 1996 he received the National Excellence in Teaching Award from the Mathematical Association of America. When he gets sick of arguing with his coauthors over which topics to include in the differential equations course, he either turns up the volume of his opera CDs, or heads for waters off New England for a long distance sail.

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