Exploring ODEs

A different kind of introduction to ODEs.

• Buy from the SIAM bookstore. Members of SIAM, including student members, get a 30% discount.
• Download the PDF for free.

Written by Nick Trefethen, Asgeir Birkisson, and myself, Exploring ODEs takes a look at ordinary differential equations unlike any other text. Rather than focusing on the mechanics of finding solutions in a limited number of special problems, we use Chebfun to illustrate the wide range of behavior of those solutions for a variety of linear, nonlinear, and multidimensional problems, including initial-value, boundary-value, and eigenvalue problems. Each short chapter includes a detailed application and a favorite reference. The text is accessible as an accompaniment or follow-up to a standard first undergraduate text on ODEs. All of the MATLAB codes generating the examples and figures are available for download, as is the full text in PDF, from the book’s website.

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
23. Appendix A: Chebfun and its ODE algorithms
24. Appendix B: 100 more examples