Nonlinear Ordinary Differential Equations

• Emphasizes the practical and application side of the subject
• Ideal for lecturers and students in science and engineering
• Highly illustrated
• Worked examples and exercises are included throughout the text, with answers to the exercises included at the end of the book
• Over 500 end-of-chapter problems are provided
• Fully worked solutions to the end-of-chapter problems may be found in a companion volume, Nonlinear Ordinary Differential Equations: Problems and Solutions (OUP, 2007)

New to this edition

• Extended sections on Mathieu's equation
• New section on Liapunov exponents added
• Exercises added throughout the text
• Appendices extended to include trigonometric identities

Readership: An ideal resource for students and lecturers in engineering, mathematics and the sciences.

Dominic Jordan, University of Keele, and Peter Smith, University of Keele

Review(s) 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

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