Salsa S. Partial Differential Equations in Action: From Modelling to Theory

3rd Edition. — Springer International Publishing, Switzerland, 2016. — 699 p. — (UNITEXT – La Matematica per il 3+2. 99) — ISBN: 9783319312378This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations (PDEs) during the last few years at the Politecnico di Milano.
The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods, such as finite elements.Diffusion
The Laplace Equation
Scalar Conservation Laws and First Order Equations
WavesandVibrations
Elements of Functional Analysis
Distributions and Sobolev Spaces
Variational Formulation of Elliptic Problems
Further Applications
Weak Formulation of Evolution Problems
Systems of Conservation Laws
Appendix:
Fourier Series
Measures and Integrals
Identities and Formulas