# Introduction to Partial Differential Equations

Part of the Universitext book series (UTX)

Part of the Universitext book series (UTX)

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?

(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.

linear equations partial differential equations Laplace equation mathematical analysis wave equation heat equation

- DOI https://doi.org/10.1007/978-3-319-48936-0
- Copyright Information Springer International Publishing AG 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-48934-6
- Online ISBN 978-3-319-48936-0
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
- About this book