The Mathematization of the Physical Sciences - Differential Equations of Nature
نویسنده
چکیده
1. Everything is number 2. Ancient Astronomy 3. Optics and statics 4. The middle ages and the renaissance 5. Mechanics of motion 6. Newtonian mechanics 7. Early differential equations 8. The Brachistochrone 9. Early methods of solutionLinear differential equations 10 Newton’s second law as a differential equationThe method of perturbations 11. The vibrating stringPartial differential equations 12. The vibrating stringTrigonometric series 13. Potential theoryLaplace’s equation 14. The parsimonious universeCalculus of variations 15. The Hamilton formalism 16. ElectrostaticsPoisson’s equation 17. Fourier on heat conduction and Fourier series 18. Orthogonal functions and curvilinear coordinates 19. Sturm-Liouville theoryThe qualitative theory 20. Continuum mechanicsElasticity 21. HydrodynamicsThe Navier-Stokes equation 22. ElectromagnetismMaxwell’s equations 23. Relativity 24. Quantum mechanicsThe Schrödinger equation 25. DistributionsGeneralized solutions of differential equations 26. Concluding remarks Glossary Bibliography Biographical Sketch
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