#pde

35. Partial Differential Equations

This volume studies equations involving partial derivatives of functions in several variables. It develops theory, methods, and applications across analysis, physics, and geometry. Part I. Foundations Chapter 1. Introduction to PDEs 1.1 Definitions and examples 1.2 Classification: elliptic, parabolic, hyperbolic 1.3 Linear vs nonlinear equations 1.4 Initial and boundary conditions 1.5 Modeling contexts Chapter 2. First-Order PDEs 2.1 Linear equations 2.2 Method of characteristics 2.3 Nonlinear first-order equations 2.4 Hamilton–Jacobi...