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About this book
About this book
Focuses on the business of constructing solutions to differential equations analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. Topics range from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory.
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.
541 pages, 169 figs
'This is a useful book, providing an excellent introduction to postgraduate studies in applied mathematics. It is very well produced and one is grateful to the publishers for having produced a useful book which, at its paperback price, is reasonable these days ! I have no hesitation in giving this book my full recommendation.' The Mathematical Gazette '! an eloquent applied differential equations textbook ! I'd be delighted if each new graduate student coming to our department knew and was inspired by the contents of this attractive new textbook.' Robert E. O'Malley, Jr., University of Washington 'I can highly recommend this book for a first introduction to differential equations to both students and teachers.' Monatshefte fur Mathematik 'The book is well-organized, theoretical material, illustrative examples, exercises and projects are carefully selected ! The textbook provides a well-balanced exposition of theoretical results and applied techniques and is a welcome contribution to the existing literature on differential equations.' Zentralblatt MATH 'This is an eloquent applied differential equations textbook, with its own identity ! There's no doubt, however, that I'd be delighted if each new graduate student coming to our department knew and was inspired by the contents of this attractive new textbook.' Society for Industrial and Applied Mathematics 'There are not many books like this about. The real benefit is that it is well within reach of a competent physics student and it should satisfy the most inquisitive minds. Secondly, it contains material on nonlinear differential equations, a topic that is usually left out. The text introduces clever techniques that will help the student develop useful skills rapidly.' Contemporary Physics