Introduction to Partial Differential Equations

by David Borthwick

Overview

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?

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

Product Details

ISBN-13:	9783319840512
Publisher:	Springer International Publishing
Publication date:	07/12/2018
Series:	Universitext
Edition description:	Softcover reprint of the original 1st ed. 2016
Pages:	283
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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

Table of Contents

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.

Editorial 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)

From the Publisher