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1. Introduction, 1
2. First-order scalar linear ODEs, 11
3. First-order scalar nonlinear ODEs, 25
4. Second-order ODEs and damped oscillations, 39
5. Boundary-value problems, 51
6. Eigenvalues of linear BVPs, 63
7. Variable coefficients and adjoints, 77
8. Resonance, 91
9. Second-order equations in the phase plane, 103
10. Systems of equations, 115
11. The fundamental existence theorem, 129
12. Random functions and random ODEs, 141
13. Chaos, 155
14. Linear systems and linearization, 171
15. Stable and unstable fixed points, 185
16. Multiple solutions of nonlinear BVPs, 195
17. Bifurcation, 209
18. Continuation and path-following, 225
19. Periodic ODEs, 237
20. Boundary and interior layers, 253
21. Into the complex plane, 267
22. Time-dependent PDEs, 281
Appendix A: Chebfun and its ODE algorithms, 297
Appendix B: 100 more examples, 309
Index, 329
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