E2 · Potentials & boundary-value problems
A 19-module path through e2 · potentials & boundary-value problems, in study order from foundations to the frontier.
Modules
- Laplace's Equation
- Poisson's Equation
- Harmonic Functions and the Mean-Value Theorem
- Boundary Conditions for the Potential
- Uniqueness Theorems for the Potential
- Method of Images
- Image Charge for a Grounded Plane
- Image Charges for a Conducting Sphere
- Separation of Variables in Cartesian Coordinates
- Separation of Variables in Spherical Coordinates
- Separation of Variables in Cylindrical Coordinates
- Legendre Polynomials
- Associated Legendre Functions
- Spherical Harmonics
- Multipole Expansion of the Potential
- Monopole Moment
- Electric Dipole Moment
- Electric Quadrupole Moment
- Origin Dependence of Multipole Moments