TY  - BOOK
AU  - Vasy, András
AU  - Vasy, András
TI  - Partial differential equations:  an accessible route through theory and applications
T2  - Graduate studies in mathematics, volume 169
SN  - 9781470454746
U1  - 515.353 VAS 
PY  - 2015///
CY  - rovidence, Rhode Island 
PB  - : American Mathematical Society, 
KW  - Mathematics
KW  - Analysis
KW  - Differential equations, Partial -- Textbooks
KW  - Differential equations, Partial.
KW  - Partial differential equations -- Instructional exposition (textbooks, tutorial papers, )
KW  - Linear
KW  - Algebra
N1  - 	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
N2  - 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.
ER  -