Introduction to Partial Differential Equations

✍ Scribed by David Borthwick

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 291
• Series: Universitext
• Edition: 1st ed.
• Category: Library

✦ 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. 

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-7
Preliminaries....Pages 9-24
Conservation Equations and Characteristics....Pages 25-44
The Wave Equation....Pages 45-73
Separation of Variables....Pages 75-95
The Heat Equation....Pages 97-110
Function Spaces....Pages 111-130
Fourier Series....Pages 131-153
Maximum Principles....Pages 155-176
Weak Solutions....Pages 177-204
Variational Methods....Pages 205-238
Distributions....Pages 239-260
The Fourier Transform....Pages 261-275
Back Matter....Pages 277-285

✦ Subjects

Differential equations, Partial