Ebook: Partial Differential Equations

Cover; Title Page; Copyright Page; Preface; Contents; Chapter 1: Where PDEs Come From; What is a Partial Differential Equation?; First-Order Linear Equations; Flows, Vibrations, and Diffusions; Initial and Boundary Conditions; Well-Posed Problems; Types of Second-Order Equations; Chapter 2: Waves and Diffusions; The Wave Equation; Causality and Energy; The Diffusion Equation; Diffusion on the Whole Line; Comparison of Waves and Diffusions; Chapter 3: Reflections and Sources; Diffusion on the Half-Line; Reflections of Waves; Diffusion with a Source; Waves with a Source; Diffusion Revisited