Partial Differential Equations
A 21-module path through partial differential equations, in study order from foundations to the frontier.
Modules
- First-Order Linear PDEs and the Method of Characteristics
- Quasilinear PDEs and Characteristic Curves
- Shock Formation and Weak Solutions
- Classification of Second-Order Linear PDEs
- Boundary and Initial Conditions for PDEs
- The Heat Equation and the Diffusion Model
- Separation of Variables for the Heat Equation
- Fourier Series Solutions of Boundary Value Problems
- Convergence of Fourier Series Solutions
- The Wave Equation and Vibrating Strings
- d'Alembert's Solution of the Wave Equation
- Domains of Dependence and Influence
- Separation of Variables for the Wave Equation
- Laplace's Equation and Harmonic Functions
- The Maximum Principle for Parabolic and Elliptic Equations
- Sturm-Liouville Theory
- Eigenfunction Expansions
- Green's Functions for Boundary Value Problems
- Fourier Transform Methods for PDEs
- Laplace Transform Methods for PDEs
- Well-Posedness of PDE Problems