an accessible route through theory and applications Vasy, András creator Vasy, András text rovidence, Rhode Island : American Mathematical Society ©2015 monographic eng

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x, 281 pages ; 27 cm. his text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material. 1. Introduction -- 2. Where do PDE come from? -- 3. First order scalar semilinear equations -- 4. First order scalar quasilinear equations -- 5. Distributions and weak derivatives -- 6. Second order constant coefficient PDE: types and d'Alembert's solution of the wave equation -- 7. Properties of solutions of second order PDE: propagation, energy estimates and the maximum principle -- 8. The Fourier transform: basic properties, the inversion formula and the heat equation -- 9. The Fourier transform: tempered distributions, the wave equation and Laplace's equation -- 10. PDE and boundaries -- 11. Duhamel's principle -- 12. Separation of variables -- 13. Inner product spaces, symmetric operators, orthogonality -- 14. Convergence of the Fourier series and the Poisson formula on disks -- 15. Bessel functions -- 16. The method of stationary phase -- 17. Solvability via duality -- 18. Variational problems. / András Vasy Mathematics Analysis Differential equations, Partial -- Textbooks Differential equations, Partial Partial differential equations -- Instructional exposition (textbooks, tutorial papers, ) Linear Algebra 515.353 VAS 9781470454746 191022 20191022145427.0