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Synopsis
Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.
Contents: 1. Introduction; 2. First-order scalar linear ODEs; 3. First-order scalar nonlinear ODEs; 4. Second-order equations and damped oscillations; 5. Boundary-value problems; 6. Eigenvalues of linear BVPs; 7. Variable coefficients and adjoints; 8. Resonance; 9. Second-order equations in the phase plane; 10. Systems of equations 11. The fundamental existence theorem; 12. Random functions and random ODEs; 13. Chaos; 14. Linear systems and linearization; 15. Stable and unstable fixed points; 16. Multiple solutions of nonlinear BVPs; 17. Bifurcation; 18. Continuation and path-following; 19. Periodic ODEs; 20. Boundary and interior layers; 21. Into the complex plane; 22. Time-dependent PDEs; Appendix A: Chebfun and its ODE algorithms; Appendix B: 100 more examples.
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About the Author
Nick Trefethen is Professor of Numerical Analysis at the University of Oxford and Global Distinguished Professor of Mathematics and Computer Science at New York University.
Ásgeir Birkisson completed his DPhil at Oxford in 2014 and is currently a Quantitative Researcher at Squarepoint Capital in London.
Toby Driscoll is a Professor in the Department of Mathematical Sciences at the University of Delaware.
"About this title" may belong to another edition of this title.
- PublisherSIAM-Society for Industrial and Applied Mathematics
- Publication date2017
- ISBN 10 1611975158
- ISBN 13 9781611975154
- BindingHardcover
- LanguageEnglish
- Number of pages343
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Exploring ODEs
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ISBN 13: 9781611975154
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