Differential Equations
Linear, Nonlinear, Ordinary, Partial

For students taking second courses; the subject is central and required at second year and above.

A. C. King (Author), J. Billingham (Author), S. R. Otto (Author)

9780521816588, Cambridge University Press

Hardback, published 8 May 2003

554 pages, 169 b/w illus. 173 exercises
24.4 x 17 x 3 cm, 1.247 kg

'… a very well written book that will be useful for researchers in ODE-s, PDE-s, classical Calculus, for the physicists, engineers, chemists, biologists and those applying differential equations. The book is warmly recommended also to students with basic knowledge in Analysis.' Acta Scientiarum Mathematicarum

Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies.

Preface
Part I. Linear Equations: 1. Variable coefficient, second order, linear, ordinary differential equations
2. Legendre functions
3. Bessel functions
4. Boundary value problems, Green's functions and Sturm–Liouville theory
5. Fourier series and the Fourier transform
6. Laplace transforms
7. Classification, properties and complex variable methods for second order partial differential equations
Part II. Nonlinear Equations and Advanced Techniques: 8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations
9. Nonlinear ordinary differential equations: phase plane methods
10. Group theoretical methods
11. Asymptotic methods: basic ideas
12. Asymptotic methods: differential equations
13. Stability, instability and bifurcations
14. Time-optimal control in the phase plane
15. An introduction to chaotic systems
Appendix 1. Linear algebra
Appendix 2. Continuity and differentiability
Appendix 3. Power series
Appendix 4. Sequences of functions
Appendix 5. Ordinary differential equations
Appendix 6. Complex variables
Appendix 7. A short introduction to MATLAB
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK]