Differential equations : linear, nonlinear, ordinary, partial

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.