Introduction to Partial Differential Equations
Published on 12. January 2017
XVI, 283 pages
978-3-319-48936-0 (ISBN)
Description
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:
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?
Reviews / Votes
"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)More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Product notice
Reflowable
Illustrations
XVI, 283 p. 68 illus., 61 illus. in color.
File size
6,26 MB
ISBN-13
978-3-319-48936-0 (9783319489360)
DOI
10.1007/978-3-319-48936-0
Schweitzer Classification
Other editions
Additional editions
David Borthwick
Introduction to Partial Differential Equations
Book
01/2017
Springer
€58.84
Shipment within 10-15 days
Person
David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
Content
1. Introduction.- 2. Preliminaries.- 3. Conservation Equations and Characteristics.- 4. The Wave Equation.- 5. Separation of Variables.- 6. The Heat Equation.- 7. Function Spaces.- 8. Fourier Series.- 9. Maximum Principles.- 10. Weak Solutions.- 11. Variational Methods.- 12. Distributions.- 13. The Fourier Transform.- A. Appendix: Analysis Foundations.- References.- Notation Guide.- Index.
