Differential Equations, Dynamical Systems, and Linear Algebra

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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
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About the author

James S. Hirsch is former reporter for"The New York Times" and "The Wall Street Journal". He is the author of four nonfiction books, including the "New York Times" bestseller. "Hurricane: The Miraculous Journey of Rubin Carter", which was the basis for the film of the same name starring Denzel Washington. Hirsch is a graduate of the University of Missouri School of Journalism and has a master's degree from the LBJ School of Public Affairs at the University of Texas. He lives in the Boston area with his wife, Sheryl, and their children, Amanda and Garrett. Born and raised in St. Louis, he remains a diehard Cardinal fan.

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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Additional Information

Publisher
Academic Press
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Published on
Jun 28, 1974
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Pages
358
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ISBN
9780080873763
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Best For
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Language
English
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Genres
Mathematics / Algebra / General
Mathematics / Algebra / Linear
Mathematics / Differential Equations / General
Mathematics / General
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Content Protection
This content is DRM protected.
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Eligible for Family Library

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Stephen Smale
Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems.

The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems.

This book will be particularly useful to advanced students and practitioners in higher mathematics.

* 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
Stephen Smale
Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems.

The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems.

This book will be particularly useful to advanced students and practitioners in higher mathematics.

* 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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