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Exploring ODEs

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by Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll


2018 / viii + 335 pages / Hardcover / ISBN 978-1-611975-15-4 / List Price $64.00 / SIAM Member Price $44.80 / Order Code: OT157

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

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.

About the Authors
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.


ISBN 9781611975154

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