Charges, fields, circuits and light: the math behind Maxwell's equations.
Electric charge and Coulomb's law, the electric field of point charges and dipoles, fields of continuous charge from integrals and how charges move through fields.
Electric flux, Gauss's law and the symmetric charges it solves in one line, conductors and shielding, and the differential form ∇·E = ρ/ε₀.
Potential energy and voltage, the field as the downhill slope of the potential, capacitors and the energy they store, and Poisson's and Laplace's equations as boundary value problems.
Current as moving charge, Ohm's law from the microscopic picture, Kirchhoff's laws as linear systems, and the RC circuit's first-order differential equation.
How magnetic fields push on moving charges and currents, and how currents make magnetic fields: the Lorentz force, motors, the Biot–Savart law and Ampère's law.
How changing magnetic flux drives currents: Faraday's and Lenz's laws, motional EMF, generators, self-inductance, RL circuits and the LC and RLC circuits that oscillate like springs.
Alternating current with complex numbers: phasors and impedance, rms values and real power, then the resonance and filtering that tune radios and clean up signals.
The displacement current completes Ampère's law, and Maxwell's four equations then predict light: waves of E and B that move at c = 1/√(μ₀ε₀) and carry energy and momentum.