Nonlinear Ordinary Differential Equations An Introduction to Dynamical Systems

ISBN-10: 0198565623
ISBN-13: 9780198565628
Edition: 3rd 1999 (Revised)
List price: $64.95
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Description: Nonlinear ordinary differential equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical  More...

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Book details

List price: $64.95
Edition: 3rd
Copyright year: 1999
Publisher: Oxford University Press, Incorporated
Publication date: 10/21/1999
Binding: Paperback
Pages: 560
Size: 6.50" wide x 9.50" long x 1.25" tall
Weight: 1.760
Language: English

Nonlinear ordinary differential equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical systems in mathematics or mathematics-related subjects. The text of this third edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. The book is directed towards practical applications of the theory, with several hundred examples and problems covering a wide variety of applications. Prerequisites are kept to a minimum, with appendices containing the necessary mathematical theory new to this edition. From reviews of the first edition: The book can profitably be used in a senior undergraduate course. It is well written, well motivated and contains some recent developments of interest which have not been readily accessible before at this level. V. Lakshmikantham in Mathematical Reviews From reviews of the second edition: The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance. The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style. P. K. Kythe in Applied Mechanics Reviews

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Second-order differential equations in the phase plane
Plane autonomous systems and linearization
Geometrical aspects of plane autonomous systems
Periodic solutions averaging methods
Perturbation methods
Singular perturbation methods
Forced oscillations: harmonic and subharmonic response, stability, and entrainment
Stability
Determination of stability by solution perturbation
Liapunov methods for determining stability of the zero solution
The existence of periodic solutions
Bifurcations and manifolds
Poincare sequences, homoclinic bifurcation, and chaos
Hints and answers to the problems
Existence and uniqueness theorems
Topographic systems
Norms for vectors and matrices
A contour integral
References and further reading
Index

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