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.Read more
- Class-tested with special attention given to areas students find hard
- Extensive exercises, with solutions available to instructors from firstname.lastname@example.org
- Many examples taken from real-world problems
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"An eloquent applied differential equations textbook, with its own identity." SIAM Review
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- Date Published: June 2003
- format: Paperback
- isbn: 9780521016872
- length: 556 pages
- dimensions: 248 x 175 x 26 mm
- weight: 1.093kg
- contains: 169 b/w illus. 173 exercises
- availability: Available
Table of Contents
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
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