Classical Electrodynamics

Maxwell's Equations, Electrostatics, and the Electric Field

Potential & Stokes Theorem

Gauss Law, Integral form of Gauss Law

Poisson's Law, Uniqueness of Potential pt 1

Holomorphic Functions & Theorems Necessary to Construct Louisville Theorem

Louisville Theorem, Harmonic Functions

Recap of Complex Analysis used to Prove Louisville Theorem for Harmonic Functions, Uniqueness of Potential pt 2

Electric Field of a Line Charge & Poisson's Equation

General Solutions to Laplace's Equation using Method of Spherical Harmonics

Properties of Spherical Harmonics

Example - Point Charge Centered at Origin

Example - Point Charge Some Finite Distance Away from an Infinite Conducting Plate using Method of Spherical Harmonics and Method of Images

Examples for Using Method of Images

Multipole Expansion and Corresponding Mathematical Buildup