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A Primer on PDEs

Models, Methods, Simulations

  • Textbook
  • © 2013

Overview

Authors:
  1. Sandro Salsa

    1. Department of Mathematics, Politecnico di Milano, Italy

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  2. Federico M. G. Vegni

    1. Department of Mathematics, Politecnico di Milano, Italy

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  3. Anna Zaretti

    1. Department of Mathematics, Politecnico di Milano, Italy

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  4. Paolo Zunino

    1. MOX — Department of Mathematics, Politecnico di Milano, Italy
      Department of Mechanical Engineering and Materials Science, University of Pittsburgh, USA

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  • This minimal knowledge on numerical approximation schemes represents an useful tool for training on model applications
  • Numerical simulations help to put into action and visualize the theoretical properties of the models that will be analysed
  • Each chapter ends with a brief introduction to numerical approximation techniques for the specific problem at hand
  • Includes supplementary material: sn.pub/extras

Part of the book series: UNITEXT (UNITEXT)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Introduction

    1. Introduction

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

  3. Differential Models

    1. Front Matter

      Pages 15-15
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    2. Scalar Conservation Laws

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 17-58

    3. Diffusion

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 59-108

    4. The Laplace Equation

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 109-138

    5. Reaction-diffusion models

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 139-188

    6. Waves and vibrations

      • 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
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    2. Elements of Functional Analysis

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 243-305

    3. Variational formulation of elliptic problems

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 307-357

    4. Weak formulation of evolution problems

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 359-386

  5. Solutions

    1. Front Matter

      Pages 387-387
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    2. Solutions of selected exercises

      • Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino
      Pages 389-446

  6. Back Matter

    Pages 447-489
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Department of Mathematics, Politecnico di Milano, Italy

    Sandro Salsa, Federico M. G. Vegni, Anna Zaretti

  • MOX — Department of Mathematics, Politecnico di Milano, Italy

    Paolo Zunino

  • Department of Mechanical Engineering and Materials Science, University of Pittsburgh, USA

    Paolo Zunino

Bibliographic Information

  • Book Title: A Primer on PDEs

  • Book Subtitle: Models, Methods, Simulations

  • Authors: Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino

  • Series Title: UNITEXT

  • DOI: https://doi.org/10.1007/978-88-470-2862-3

  • Publisher: Springer Milano

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Milan 2013

  • Softcover ISBN: 978-88-470-2861-6Published: 22 January 2013

  • eBook ISBN: 978-88-470-2862-3Published: 13 May 2013

  • Series ISSN: 2038-5714

  • Series E-ISSN: 2532-3318

  • Edition Number: 1

  • Number of Pages: XIV, 489

  • Topics: Mathematics, general, Partial Differential Equations, Analysis

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