MP6 · Partial differential equations
A 20-module path through mp6 · partial differential equations, in study order from foundations to the frontier.
Modules
- Classification of Second-Order Linear PDEs
- The Wave Equation
- The Heat (Diffusion) Equation
- Laplace's and Poisson's Equations
- Boundary Conditions and Well-Posedness
- Separation of Variables in Cartesian Coordinates
- Separation of Variables in Cylindrical Coordinates
- Separation of Variables in Spherical Coordinates
- The Helmholtz Equation
- Sturm-Liouville Theory and Eigenfunction Expansions
- d'Alembert's Solution and Characteristics of the Wave Equation
- Method of Characteristics
- Fundamental Solutions and Green's Functions for PDEs
- Heat Kernel and the Fundamental Solution of the Diffusion Equation
- Retarded and Advanced Green's Functions for the Wave Equation
- Green's Functions via Eigenfunction Expansion and the Method of Images
- Integral Transform Methods for PDEs
- Maximum Principles and Uniqueness for Elliptic and Parabolic PDEs
- Energy Methods and A Priori Estimates
- Weak Solutions and Distributional Formulation of PDEs