Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers

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Dominic Jordan (University of Keele) Peter Smith (University of Keele)

Nonlinear Ordinary Differential Equations

An Introduction for Scientists and Engineers

Dominic Jordan (University of Keele), Peter Smith (University of Keele)

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English

Oxford University Press
01 August 2007

Mathematics & Sciences; Differential calculus & equations; Maths for scientists; Maths for engineers

Series: Oxford Texts in Applied and Engineering Mathematics

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book.

Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents.

Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).

Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

By: Dominic Jordan (University of Keele), Peter Smith (University of Keele)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 4th Revised edition
Volume: No. 10
Dimensions: Height: 250mm, Width: 170mm, Spine: 30mm
Weight: 1g
ISBN: 9780199208258
ISBN 10: 0199208255
Series: Oxford Texts in Applied and Engineering Mathematics
Pages: 544
Publication Date: 01 August 2007
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Preface 1: Second-order differential equations in the phase plane 2: Plane autonomous systems and linearization 3: Geometrical aspects of plane autonomous systems 4: Periodic solutions; averaging methods 5: Perturbation methods 6: Singular perturbation methods 7: Forced oscillations: harmonic and subharmonic response, stability, and entrainment 8: Stability 9: Stability by solution perturbation: Mathieu's equation 10: Liapurnov methods for determining stability of the zero solution 11: The existence of periodic solutions 12: Bifurcations and manifolds 13: Poincaré sequences, homoclinic bifurcation, and chaos Answers to the exercises Appendices A: Existence and uniqueness theorems B: Topographic systems C: Norms for vectors and matrices D: A contour integral E: Useful identities References and further reading Index

Prior to his retirement, Dominic Jordan was a professor in the Mathematics Department at Keele University. His research interests include applications of applied mathematics to elasticity, asymptotic theory, wave and diffusion problems, as well as research on the development of applied mathematics in its close association with late 19th century engineering technologies. Peter Smith is a professor in the Mathematics Department of Keele University. He has taught courses in mathematical methods, applied analysis, dynamics, stochastic processes, and nonlinear differential equations, and his research interests include fluid dynamics and applied analysis.

Reviews for Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers

`Review from previous edition ...classic book...The book succeeds as an exceptionally well written test for its intended audience...No doubt one of its strongest features is over 500 problems...throughout the entire book only important physical processes are described... The new edition is greatly enhanced...I strongly recommend that you take a look. The presentation is exquisitely straightforward with numerous physically interesting examples, and it is carefully and well written ' SIAM