Differential Equations, Dynamical Systems, and an Introduction to Chaos
2nd Edition
Published on 6. December 2003
Book
Hardback
432 pages
978-0-12-349703-1 (ISBN)
Description
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.
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.
Reviews / Votes
"The exposition is excellent. I particularly liked how the proofs are fairly easy to follow... There are several instances where 'What if...?' questions come up naturally and the authors explore these as though they were reading your mind." --Gareth Roberts, Holy Cross"This text contains exactly what a student entering graduate school in Dynamical Systems needs to know; it is Dynamical Systems from three mathematicians who are not only among the world's most prominent experts in dynamical systems, but who are also among the world's best mathematical expositors. The book contains the benchmark models of chaos to which much of current research is compared" --Bruce Peckham, University of Minnesota
"The presentation is very clear and often supported by carefully selected key-examples. The book meets very high pedagogical standards and certainly is a worthy successor of the original version." --R. Steinbauer, Wien, in MONATSHEFTE FUR MATHEMATIC, VOL 147
More details
Edition
2nd edition
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
Professional and scholarly
Advanced students, practitioners, and scientists in applied mathematics.
Dimensions
Height: 229 mm
Width: 152 mm
Weight
790 gr
ISBN-13
978-0-12-349703-1 (9780123497031)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Morris W. Hirsch | Stephen Smale | Robert L. Devaney
Differential Equations, Dynamical Systems, and an Introduction to Chaos
Book
10/2018
3rd Edition
Academic Press
€75.51
The article will not be published
Morris W. Hirsch | Stephen Smale | Robert L. Devaney
Differential Equations, Dynamical Systems, and an Introduction to Chaos
Book
04/2012
3rd Edition
Academic Press
€98.00
Shipment within 15-20 days
Additional editions
Morris W Hirsch | Stephen Smale | Morris W. Hirsch
Differential Equations, Dynamical Systems, and an Introduction to Chaos
E-Book
05/2014
2nd Edition
Academic Press
€85.95
Available for download
Previous edition
M.W. Hirsch | Sverre O. Smale
Differential Equations, Dynamical Systems and Linear Algebra
Book
04/1974
Academic Press
€68.08
Article exhausted; check for reprint
Persons
Morris W. Hirsch works at the University of Wisconsin, Madison, USA. Stephen Smale works in the Department of Mathematics at University of California, Berkeley, USA. Robert L. Devaney works in the Department of Mathematics at Boston University, MA, USA.
Content
First Order Equations
Planar Linear Systems
Phase Portraits for Planar Systems
Classification of Planar Systems
Higher Dimensional Linear Algebra
Higher Dimensional Linear Systems
Nonlinear Systems
Equilibria in Nonlinear Systems
Global Nonlinear Techniques
Closed Orbits and Limit Sets
Applications in Biology
Applications in Circuit Theory
Applications in Mechanics
The Lorenz System
Discrete Dynamical Systems
Homoclinic Phenomena
Existence and Uniqueness Revisited
Planar Linear Systems
Phase Portraits for Planar Systems
Classification of Planar Systems
Higher Dimensional Linear Algebra
Higher Dimensional Linear Systems
Nonlinear Systems
Equilibria in Nonlinear Systems
Global Nonlinear Techniques
Closed Orbits and Limit Sets
Applications in Biology
Applications in Circuit Theory
Applications in Mechanics
The Lorenz System
Discrete Dynamical Systems
Homoclinic Phenomena
Existence and Uniqueness Revisited