Exploring ODEs

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.