- 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
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- About this Textbook
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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:- What is the scientific problem we are trying to understand?
- How do we model that with PDE?
- What techniques can we use to analyze the PDE?
- How do those techniques apply to this equation?
- What information or insight did we obtain by developing and analyzing the PDE?
- What is the scientific problem we are trying to understand?
- About the authors
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David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
- Reviews
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“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)
- Table of contents (14 chapters)
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Introduction
Pages 1-7
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Preliminaries
Pages 9-24
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Conservation Equations and Characteristics
Pages 25-44
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The Wave Equation
Pages 45-73
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Separation of Variables
Pages 75-95
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Table of contents (14 chapters)
- Download Preface 1 PDF (39.7 KB)
- Download Sample pages 2 PDF (211.5 KB)
- Download Table of contents PDF (145.8 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Introduction to Partial Differential Equations
- Authors
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- David Borthwick
- Series Title
- Universitext
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-48936-0
- DOI
- 10.1007/978-3-319-48936-0
- Hardcover ISBN
- 978-3-319-48934-6
- Softcover ISBN
- 978-3-319-84051-2
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XVI, 283
- Number of Illustrations
- 7 b/w illustrations, 61 illustrations in colour
- Topics
