PDE

Elliptic Equations Laplace Equation Poisson Equation Fundamental Solutions Distributions and Weak Solutions Boundary Value Problems Poincare Inequality Sobolev Spaces and Energy Estimates Calculus of Variations Euler-Lagrange Equations Lagrange Multipliers Maximum Principles Heat Equation and Parabolic Equations Spectral Decay and Principal Eigenvalues Reaction-Diffusion-Advection Equations Wave Equation and Energy Methods Finite Speed of Propagation and Domain of Dependence Method of Characteristics Scalar Conservation Laws Entropy Solutions, Shocks, and Rarefactions