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© 2013

A Primer on PDEs

Models, Methods, Simulations

Textbook

Part of the UNITEXT book series (UNITEXT)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Introduction

    1. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 1-13
  3. Differential Models

    1. Front Matter
      Pages 15-15
    2. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 17-58
    3. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 59-108
    4. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 109-138
    5. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 139-188
    6. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 189-240
  4. Functional Analysis Techniques for Differential Problems

    1. Front Matter
      Pages 241-241
    2. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 243-305
    3. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 307-357
    4. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 359-386
  5. Solutions

    1. Front Matter
      Pages 387-387
    2. Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 389-446
  6. Back Matter
    Pages 447-489

About this book

Introduction

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.

Keywords

Analysis Partial Differential Equations

Authors and affiliations

  1. 1.Department of MathematicsPolitecnico di MilanoItaly
  2. 2.MOX — Department of MathematicsPolitecnico di MilanoItaly
  3. 3.Department of Mechanical Engineering and Materials ScienceUniversity of PittsburghUSA

Bibliographic information

Reviews

From the book reviews:

“This book, presented at the advanced undergraduate or first year graduate level, takes a very interesting mixed approach to partial differential equations, shining a modern light on a classic subject. In addition to the usual analytic solution methods, the presentation includes both numerical approaches and mathematical techniques for proving rigorous existence and regularity results. … Each chapter concludes with an informative set of exercises, and solutions to many of them are provided at the end of the book.” (Peter Bernard Weichman, Mathematical Reviews, May, 2014)

“The present text is suitable for a two semester introduction to partial differential equations. … The text is well-written and can be particularly recommended for students who are interested in the interplay between modeling, theory, and numerics.” (G. Teschl, Monatshefte für Mathematik, 2013)

“Part I (Chapters 2–6) of this book … is entitled Differential models. … Part II (Chapters 7–9) is entitled Functional analysis techniques for differential problems and it is devoted to Hilbert space methods for the variational formulation and the analysis of linear boundary and initial-boundary value problems. … at the end of each chapter the authors include a brief account of numerical methods, with a discussion of some particular case study. … recommend this book to students in engineering, applied mathematics and physics.” (Vicenţiu D. Rădulescu, zbMATH, Vol. 1270, 2013)