# Exploring 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

- Introduction
- First-order scalar linear ODEs
- First-order scalar nonlinear ODEs
- Second-order equations and damped oscillations
- Boundary-value problems
- Eigenvalues of linear BVPs
- Variable coefficients and adjoints
- Resonance
- Second-order equations in the phase plane
- Systems of equations
- The fundamental existence theorem
- Random functions and random ODEs
- Chaos
- Linear systems and linearization
- Stable and unstable fixed points
- Multiple solutions of nonlinear BVPs
- Bifurcation
- Continuation and path-following
- Periodic ODEs
- Boundary and interior layers
- Into the complex plane
- Time-dependent PDEs
- Appendix A: Chebfun and its ODE algorithms
- Appendix B: 100 more examples