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Partial Differential Equations: An Accessible Route through Theory and Applications
About this Title
András Vasy, Stanford University, Stanford, CA
Publication: Graduate Studies in Mathematics
Publication Year:
2015; Volume 169
ISBNs: 978-1-4704-1881-6 (print); 978-1-4704-2785-6 (online)
DOI: https://doi.org/10.1090/gsm/169
MathSciNet review: MR3410751
MSC: Primary 35-01
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
- Chapter 2. Where do PDE come from?
- Chapter 3. First order scalar semilinear equations
- Chapter 4. First order scalar quasilinear equations
- Chapter 5. Distributions and weak derivatives
- Chapter 6. Second order constant coefficient PDE: Types and d’Alembert’s solution of the wave equation
- Chapter 7. Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle
- Chapter 8. The Fourier transform: Basic properties, the inversion formula and the heat equation
- Chapter 9. The Fourier transform: Tempered distributions, the wave equation and Laplace’s equation
- Chapter 10. PDE and boundaries
- Chapter 11. Duhamel’s principle
- Chapter 12. Separation of variables
- Chapter 13. Inner product spaces, symmetric operators, orthogonality
- Chapter 14. Convergence of the Fourier series and the Poisson formula on disks
- Chapter 15. Bessel functions
- Chapter 16. The method of stationary phase
- Chapter 17. Solvability via duality
- Chapter 18. Variational problems
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