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Partial Differential Equations in Action

From Modelling to Theory

  • Textbook
  • © 2015

Overview

Authors:
  1. Sandro Salsa

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: UNITEXT (UNITEXT, volume 86)

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

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  2. Introduction

    • Sandro Salsa
    Pages 1-16

  3. Diffusion

    • Sandro Salsa
    Pages 17-114

  4. The Laplace Equation

    • Sandro Salsa
    Pages 115-178

  5. Scalar Conservation Laws and First Order Equations

    • Sandro Salsa
    Pages 179-256

  6. Waves and Vibrations

    • Sandro Salsa
    Pages 257-343

  7. Elements of Functional Analysis

    • Sandro Salsa
    Pages 345-424

  8. Distributions and Sobolev Spaces

    • Sandro Salsa
    Pages 425-501

  9. Variational Formulation of Elliptic Problems

    • Sandro Salsa
    Pages 503-548

  10. Further Applications

    • Sandro Salsa
    Pages 549-578

  11. Weak Formulation of Evolution Problems

    • Sandro Salsa
    Pages 579-616

  12. Systems of Conservation Laws

    • Sandro Salsa
    Pages 617-658

  13. Erratum

    • Sandro Salsa
    Pages 701-701

  14. Erratum to: Elements of Functional Analysis

    • Sandro Salsa
    Pages 698-698

  15. Erratum to: Diffusion

    • Sandro Salsa
    Pages 698-698

  16. Erratum to: Scalar Conservation Laws and First Order Equations

    • Sandro Salsa
    Pages 698-698

  17. Erratum to: The Laplace Equation

    • Sandro Salsa
    Pages 698-698

  18. Erratum to: Variational Formulation of Elliptic Problems

    • Sandro Salsa
    Pages 699-699

  19. Erratum to: Weak Formulation of Evolution Problems

    • Sandro Salsa
    Pages 699-700

  20. Erratum to: Distributions and Sobolev Spaces

    • Sandro Salsa
    Pages 699-699
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Keywords

About this book

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.

Reviews

“This book, presented at the advanced undergraduate or first year graduate level, presents a very interesting mix of physical applications and abstract theory supporting rigorous existence and regularity results for PDEs. … Rigorous approaches, including Sobolev spaces, dual spaces, distribution theory, and weak solutions, are introduced in a transparent, well-motivated fashion, achieving a level that allows one to make contact with the professional literature.” (Peter Bernard Weichman, Mathematical Reviews, May, 2016)

“In this advanced textbook, Salsa (Politecnico di Milano, Italy) provides a well-written book blending abstract theory with examples. … The author explains theory and models clearly, using techniques such as well-thought-out examples, theorems and proofs, and reader-posed questions with answers and exercises at the end of each chapter. … Summing Up: Recommended. Graduate students and researchers/faculty.” (S. L. Sullivan, Choice, Vol. 53 (4), December, 2015)

Authors and Affiliations

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Sandro Salsa

About the author

Prof. Sandro Salsa, Dipartimento di Matematica, Politecnico di Milano, Italy.

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