Sandro Salsa 
Partial Differential Equations in Action 
From Modelling to Theory

This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines. The main purpose is on the one hand to train students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods. At the end of each chapter, a number of exercises at different level of complexity is included

Содержание

Diffusion.- The Laplace Equation.- Scalar Conservation Laws and First Order Equations.- Waves and Vibrations.- Elements of Functional Analysis.- Distributions and Sobolev Spaces.- Variational Formulation of Elliptic Problems.- Weak Formulation of Evolution Problems.