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Introduction to Partial Differential Equations

  • David¬†Borthwick

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David Borthwick
    Pages 1-7
  3. David Borthwick
    Pages 9-24
  4. David Borthwick
    Pages 25-44
  5. David Borthwick
    Pages 45-73
  6. David Borthwick
    Pages 75-95
  7. David Borthwick
    Pages 97-110
  8. David Borthwick
    Pages 111-130
  9. David Borthwick
    Pages 131-153
  10. David Borthwick
    Pages 155-176
  11. David Borthwick
    Pages 177-204
  12. David Borthwick
    Pages 205-238
  13. David Borthwick
    Pages 239-260
  14. David Borthwick
    Pages 261-275
  15. Back Matter
    Pages 277-283

About this book

Introduction

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 inspiration for the development of methods.

Keywords

linear equations partial differential equations Laplace equation mathematical analysis wave equation heat equation

Authors and affiliations

  • David¬†Borthwick
    • 1
  1. 1.Computer ScienceEmory University Dept. Mathematics &AtlantaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-48936-0
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-48934-6
  • Online ISBN 978-3-319-48936-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site