Includes Appendix and index

Introduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction–Diffusion Equations and Systems -- Hyperbolic Equations -- The Heat Equation, Semigroups, and Brownian Motion -- Relationships Between Different Partial Differential Equations -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)