Partial Differential Equations in Action: From Modelling to Theory, 3rd Edition

Authors: Sandro Salsa



Addresses the interplay between theory and modeling in problems arising in the applied sciences

Focuses on ideas and connections to concrete applications, in order to promote readers’ intuition and feel for the subject

Offers a variety of examples from different perspectives in applied sciences

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.The third edition contains a few text and formulas revisions and new exercises.

Table of contents

Front Matter
Pages i-xviii

Introduction
Pages 1-16

Diffusion
Pages 17-114

The Laplace Equation
Pages 115-178

Scalar Conservation Laws and First Order Equations
Pages 179-257

Waves and Vibrations
Pages 259-346

Elements of Functional Analysis
Pages 347-426

Distributions and Sobolev Spaces
Pages 427-504

Variational Formulation of Elliptic Problems
Pages 505-550

Further Applications
Pages 551-580

Weak Formulation of Evolution Problems
Pages 581-614

Systems of Conservation Laws
Pages 615-656

Back Matter
Pages 657-686