Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 First-order equations
- 3 Second-order linear equations in two indenpendent variables
- 4 The one-dimensional wave equation
- 5 The method of separation of variables
- 6 Sturm–Liouville problems and eigenfunction expansions
- 7 Elliptic equations
- 8 Green's functions and integral representations
- 9 Equations in high dimensions
- 10 Variational methods
- 11 Numerical methods
- 12 Solutions of odd-numbered problems
- References
- Index
Preface
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 First-order equations
- 3 Second-order linear equations in two indenpendent variables
- 4 The one-dimensional wave equation
- 5 The method of separation of variables
- 6 Sturm–Liouville problems and eigenfunction expansions
- 7 Elliptic equations
- 8 Green's functions and integral representations
- 9 Equations in high dimensions
- 10 Variational methods
- 11 Numerical methods
- 12 Solutions of odd-numbered problems
- References
- Index
Summary
This book presents an introduction to the theory and applications of partial differential equations (PDEs). The book is suitable for all types of basic courses on PDEs, including courses for undergraduate engineering, sciences and mathematics students, and for first-year graduate courses as well.
Having taught courses on PDEs for many years to varied groups of students from engineering, science and mathematics departments, we felt the need for a textbook that is concise, clear, motivated by real examples and mathematically rigorous. We therefore wrote a book that covers the foundations of the theory of PDEs. This theory has been developed over the last 250 years to solve the most fundamental problems in engineering, physics and other sciences. Therefore we think that one should not treat PDEs as an abstract mathematical discipline; rather it is a field that is closely related to real-world problems. For this reason we strongly emphasize throughout the book the relevance of every bit of theory and every practical tool to some specific application. At the same time, we think that the modern engineer or scientist should understand the basics of PDE theory when attempting to solve specific problems that arise in applications. Therefore we took great care to create a balanced exposition of the theoretical and applied facets of PDEs.
The book is flexible enough to serve as a textbook or a self-study book for a large class of readers.
- Type
- Chapter
- Information
- An Introduction to Partial Differential Equations , pp. xi - xiiPublisher: Cambridge University PressPrint publication year: 2005