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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 Part II. Nonlinear Equations and Advanced Techniques: 7. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations 8. Nonlinear ordinary differential equations 9. Group theoretical methods 10. Asymptotic methods: basic ideas 11. Asymptotic methods: differential equations 12. Stability, instability and bifurcations 13. Time-optimal control in the phase plane 14. 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. A short introduction to MATLAB Bibliography Index.