includes index

1. The nature of differential equations ;
2. Families of curves ;
3. Orthogonal trajectories ;
4. Growth, decay, chemical reactions, and mixing ;
5. Falling bodies and other motion problems ;
6. The Brachistochrone ;
7. Fermat and the Bernoullis ;
8. First order equations ;
9. Homogeneous equations ;
10. Exact equations ;
11. Integrating factors ;
12. Linear equations ;
13. Reduction of order ;
14. The hanging chain ;
15. Pursuit curves ;
16. Simple electric circuits ;
17. Second order linear equations ;
18. Vibrations in mechanical and electrical systems ;
19. Newton's Law of Gravitation and the motion of the planets ;
20. Coupled harmonic oscillators ;
21. Qualitative properties of solutions ;
22. Oscillations and the Sturm Separation theorem ;
23. The Sturm Comparison theorem ;
24. Power series solutions and special functions ;
25. Gauss's hypergeometric equation ;
26. The point at infinity ;
27. Hermite polynomials and quantum mechanics ;
28. Chebyshev polynomials and the minimax property ;
29. Riemann's equation ;
30. Fourier series and orthogonal functions ;
31. Partial differential equations and boundary value problems ;
32. Eigenvalues, eigenfunctions, and the vibrating string ;
33. The heat equation ;
34. The Dirichlet problem for a circle ;
35. Poisson's integral ;
36. Sturm-Liouville problems ;
37. Some special functions of mathematical physics ;
38. Legendre polynomials ;
39. Bessel functions ;
40. Laplace transforms ;
41. Systems of first order equations ;
42. Linear systems ;
43. Linear equations ;
44. Liapunov ;
45. Poincccaré-Bendixson theorem ;
46. Proof of Liénard's theorem ;
47. The calculus of variations ;
48. The existence and uniqueness of solutions ;
49. Successive approximations ;
50. Picard ;
51. Numerical methods ;
52. Euler.