• Feb 2, 2026 Basic Partial Differential Equations Bleecker ts satisfy: \[ B^2 - AC < 0 \] Examples - Laplace equation: \[ \nabla^2 u = u_{xx} + u_{yy} = 0 \] - Poisson equation: \[ \nabla^2 u = f(x,y) \] Characteristics - Solutions are generally smooth and unique. - Boundary value problems are commo BY Ms. Jean Bernhard