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.
