Differential equations are vital to science, engineering and mathematics, and this book enables the reader to develop the required skills needed to understand them thoroughly. The authors focus on constructing solutions analytically and interpreting their meaning and use MATLAB extensively to illustrate the material along with many examples based on interesting and unusual real world problems. A large selection of exercises is also provided.

Part One: Linear Equations 1. Variable Coefficient, Second Order, Linear, Ordinary Differential Equations 2. Legendre Functions 3. Bessel Fuctions 4. Boundary Value Problems, Green's Fuctions 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 Two: 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. Groups 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

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