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Introduction to Partial Differential Equations

  • Textbook
  • © 2016

Overview

Authors:
  1. David Borthwick

    1. Computer Science, Emory University Dept. Mathematics &, Atlanta, USA

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  • Perfect book for a ?One-semester PDE course
  • Includes a thorough discussion of modeling process for each equation
  • Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction

    • David Borthwick
    Pages 1-7

  3. Preliminaries

    • David Borthwick
    Pages 9-24

  4. Conservation Equations and Characteristics

    • David Borthwick
    Pages 25-44

  5. The Wave Equation

    • David Borthwick
    Pages 45-73

  6. Separation of Variables

    • David Borthwick
    Pages 75-95

  7. The Heat Equation

    • David Borthwick
    Pages 97-110

  8. Function Spaces

    • David Borthwick
    Pages 111-130

  9. Fourier Series

    • David Borthwick
    Pages 131-153

  10. Maximum Principles

    • David Borthwick
    Pages 155-176

  11. Weak Solutions

    • David Borthwick
    Pages 177-204

  12. Variational Methods

    • David Borthwick
    Pages 205-238

  13. Distributions

    • David Borthwick
    Pages 239-260

  14. The Fourier Transform

    • David Borthwick
    Pages 261-275

  15. Erratum to: Introduction to Partial Differential Equations

    • David Borthwick
    Pages E1-E1

  16. Back Matter

    Pages 277-283
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Keywords

About this book

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. 


Within each section the author creates a narrative that answers the five questions: 

  1. What is the scientific problem we are trying to understand?
  2. How do we model that with PDE?
  3. What techniques can we use to analyze the PDE?
  4. How do those techniques apply to this equation?
  5. What information or insight did we obtain by developing and analyzing the PDE?

The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspirationfor the development of methods. 

Reviews

“The book under review is intended for an introductory course for students. The author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text.” (Dian K. Palagachev, zbMATH 1364.35001, 2017)

Authors and Affiliations

  • Computer Science, Emory University Dept. Mathematics &, Atlanta, USA

    David Borthwick

About the author

David Borthwick, Department of Mathematics and Computer Science, Emory University,  Atlanta, GA 30322

Bibliographic Information

  • Book Title: Introduction to Partial Differential Equations

  • Authors: David Borthwick

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-48936-0

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2016

  • Hardcover ISBN: 978-3-319-48934-6Published: 19 January 2017

  • Softcover ISBN: 978-3-319-84051-2Published: 13 July 2018

  • eBook ISBN: 978-3-319-48936-0Published: 12 January 2017

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XVI, 283

  • Number of Illustrations: 7 b/w illustrations, 61 illustrations in colour

  • Topics: Partial Differential Equations, Mathematical Applications in the Physical Sciences

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