Introduction to Partial Differential Equations

• Main Author: Borthwick, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Universitext,
• Subjects: Mathematics.; Partial differential equations.; Mathematical physics.; Partial Differential Equations.; Mathematical Applications in the Physical Sciences.

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...

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.