Partial Differential Equations: An Introduction

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs).  The second edition of Partial Differential Equations provides an introduction to the basic properties of  PDEs and the ideas and techniques that have proven useful in analyzing them.  It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations.  

In this book mathematical jargon is minimized.  Our focus is on the three most classical PDEs: the wave, heat and Laplace equations.  Advanced concepts are introduced frequently but with the least possible technicalities.  The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics. 

Chapter 1: Where PDEs Come From 

Chapter 2: Waves and Diffusions

Chapter 3: Reflections and Sources

Chapter 4: Boundary Problems

Chapter 5: Fourier Series

Chapter 6: Harmonic Functions

Chapter 7: Green’s Identities and Green’s Functions

Chapter 8: Computation of Solutions

Chapter 9: Waves in Space

Chapter 10: Boundaries in the Plane and in Space

Chapter 11: General Eigenvalue Problems

Chapter 12: Distributions and Transforms

Chapter 13: PDE Problems for Physics

Chapter 14: Nonlinear PDEs

Appendix

 A.1 Continuous and Differentiable Functions

 A.2 Infinite Sets of Functions

 A.3 Differentiation and Integration

 A.4 Differential Equations

 A.5 The Gamma Function