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Introduction to Partial Differential Equations

  • Textbook
  • © 2016


  • 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:

Part of the book series: Universitext (UTX)

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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. 

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Table of contents (14 chapters)


“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:

  • 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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