000			02233nam a22002777a 4500
999			_c55803 _d55803
005			20191022145427.0
008			191022b ||||| |||| 00| 0 eng d
020			_a9781470454746
082			_a515.353 VAS
100			_aVasy, András
245			_aPartial differential equations _b an accessible route through theory and applications _c/ András Vasy
260			_arovidence, Rhode Island _b: American Mathematical Society, _c©2015
300			_ax, 281 pages _c ; 27 cm.
490			_aGraduate studies in mathematics, volume 169.
505			_a 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.
520			_ahis 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.
650			_aMathematics
650			_aAnalysis
650			_aDifferential equations, Partial -- Textbooks.
650			_aDifferential equations, Partial.
650			_aPartial differential equations -- Instructional exposition (textbooks, tutorial papers, )
650			_aLinear
650			_aAlgebra
700			_aVasy, András
942			_cMDL