This 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 during the last decade at the Politecnico of Milan. 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 background for numerical methods, such as finite differences and finite elements.
Author(s): Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino (auth.)
Series: UNITEXT
Edition: 1
Publisher: Springer-Verlag Mailand
Year: 2013
Language: English
Pages: 489
Tags: Mathematics, general; Partial Differential Equations; Analysis
Front Matter....Pages I-XIV
Introduction....Pages 1-13
Front Matter....Pages 15-15
Scalar Conservation Laws....Pages 17-58
Diffusion....Pages 59-108
The Laplace Equation....Pages 109-138
Reaction-diffusion models....Pages 139-188
Waves and vibrations....Pages 189-240
Front Matter....Pages 241-241
Elements of Functional Analysis....Pages 243-305
Variational formulation of elliptic problems....Pages 307-357
Weak formulation of evolution problems....Pages 359-386
Front Matter....Pages 387-387
Solutions of selected exercises....Pages 389-446
Back Matter....Pages 447-489
