For students taking second courses; the subject is central and required at second year and above.
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.
Inhaltsverzeichnis
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.
