Indice: 1. The first ordinary differential equations 2. Variational problems and the calculus 3. The vibrating string and the partial differential calculus 4. Rational mechanics 5. The early theory of partial differential equations 6. Lagrange's general theory of partial differential equations 7. The calculus of variations 8. Monge and solutions to partial differential equations 9. Revision 10. The heat equation 11. Gauss and the hypergeometric equation 12. Existence theorems 13. Riemann and complex function theory 14. Riemann and the hypergeometric equation 15. Schwarz and the complex hypergeometric equation 16. Complex ordinary fifferential equations: Poincaré 17. More genral partial differential equations 18. Green's function and Dirichlet's principle 19. Attempts on Laplace's equation 20. Applied wave equations 21. Revision 22. Riemann's shockwave paper 23. The example of minimal surfaces 24. Partial differential equations and mechanics 25. Geometrical interpretations of mechanics 26. The calculus of variations in the nineteenth century 27. Poincaré and mathematical physics 28. Elliptic equations and regular variational problems 29. Initial value conditions for hyperbolic partial differential equations 30. Revision 31. Translations. Appendix A: Newton's Principia mathematica. Appendix B: Characteristics. Appendix C: The first-order non-linear partial differential equation. Appendix D: Green's theorem and heat conduction. Appendix E: Complex analysis. Appendix F: Möbius transformations. Appendix G: Lipschitz and Picard. Appendix H: The assessment. References. Index
