Partial Differential Equations: Basics

This lecture introduces Partial Differential Equations (PDEs) and their applications in various fields. It covers the concept of well-posed PDEs, including regular PDEs, constitutive equations, boundary conditions, and initial conditions. The lecture also explains typical PDE operators like Gradient, Divergence, Rotation, and Laplacian. Moreover, it discusses the scalar coefficient form of PDEs, linear and nonlinear PDEs, and the classification of physical PDEs into elliptic, parabolic, and hyperbolic types. Examples of elliptic PDEs, such as the Laplace equation for static solid deformation and heat conduction, are presented to illustrate the theory.