Differential Equations Linear, Nonlinear, Ordinary, Partial

 Content: Part one: 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 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. 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. Introduction to chaotic systems.
 Abstract:             The authors focus on constructing solutions analytically, and interpreting their meaning; MATLAB is used extensively to illustrate the material. The many worked examples, based on interesting real world problems, the large selection of exercises, including several lengthier projects, the broad coverage, and clear and concise presentation will appeal to undergraduates