Introduction to Partial Differential Equations (Universitext) - Softcover

Borthwick, David

Softcover

ISBN 10: 3319840517 ISBN 13: 9783319840512

Publisher: Springer, 2018

Synopsis

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. 

About this title

About the Author

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

Review

“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)

Edition details

• Publisher: Springer
• Publication date: 2018
• ISBN 10: 3319840517
• ISBN 13: 9783319840512
• Binding: Paperback
• Language: English
• Number of pages: 299