The (Unfinished) PDE Coffee Table Book

Summary

THE (UNFINISHED) PDE COFFEE TABLE BOOK Lloyd N. Trefethen and Kristine Embree, editors Unpublished, 2001 During 2000-2001 a group project based in the Oxford University was begun to write this book. The vision was 100 2-page spreads, each one giving exactly the most useful possible starting information about a different partial differential equation, with beautiful color illustrations. Many people at Oxford and around the world contributed drafts, which were then extensively rewritten and edited to help bring about a uniform style and mathematical level. In the end, 34 of the pieces were brought into reasonably finished form. Many people have asked since then about the status of the PDE Coffee Table Book. Unfortunately, we have had to tell them that the project is stalled, with no plans at present to complete it. As people keep asking, it seems unreasonable not to make this easily available. Thus, with pride for what we finished and regret for what we didn't, here are the 34 finished pages. The numbers (which are not all distinct) give some idea of where each page might have ended up in the finished book. These may be used freely for educational purposes, but all publication rights are reserved. Copyright Lloyd N. Trefethen, 2011. 2. Laplace equation in 2D...harmonic functions from analytic functions 3. Heat equation...diffusion and smoothing 3. Backward heat equation...ill-posed problems and regularisation 3. Constant coefficient linear equations...Fourier analysis and boundedness 7. Laplace equation...the basis of potential theory 7. Biharmonic equation...solid mechanics and creeping flow 8. Minimal surface equation...mathematisation of a soap film 9. Capillary surface equation...where gases, liquids and solids meet 15. Wave equation...propagation of light and sound 15. Wave equation in 1D...left-going and right-going characteristics 17. Helmholtz equation...waveguides and scattering 19. One-way wave equations...pseudodifferential operators & absorbing boundaries ...