Differential Equations

'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

• 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.