#differential-equations
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...
34. Ordinary Differential Equations
This volume studies differential equations involving functions of a single variable. It develops existence theory, qualitative behavior, and analytical and numerical methods. Part I. First-Order Equations Chapter 1. Basic Concepts 1.1 Definitions and examples 1.2 Solutions and integral curves 1.3 Initial value problems 1.4 Direction fields 1.5 Modeling examples Chapter 2. Separable and Exact Equations 2.1 Separable equations 2.2 Exact equations 2.3 Integrating factors 2.4 Applications 2.5 Examples Chapter 3....