Partial Differential Equations: An Introduction [Hardcover]

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

1.1* What is a Partial Differential Equation? 1

1.2* First-Order Linear Equations 6

1.3* Flows, Vibrations, and Diffusions 10

1.4* Initial and Boundary Conditions 20

1.5 Well-Posed Problems 25

1.6 Types of Second-Order Equations 28

Chapter 2/Waves and Diffusions

2.1* The Wave Equation 33

2.2* Causality and Energy 39

2.3* The Diffusion Equation 42

2.4* Diffusion on the Whole Line 46

2.5* Comparison of Waves and Diffusions 54

Chapter 3/Reflections and Sources

3.1 Diffusion on the Half-Line 57

3.2 Reflections of Waves 61

3.3 Diffusion with a Source 67

3.4 Waves with a Source 71

3.5 Diffusion Revisited 80&llƒ3