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Electromagnetism

Maxwell's equations, plus the boundary value problems you spend most of a course actually solving.

  1. 01Electrostatics and the Laplace EquationGuessing a solution is a legitimate method. The uniqueness theorem is what makes it one.
  2. 02Magnetostatics in MediaFields in matter, worked from the absence of magnetic charge.
  3. 03Electromagnetic WavesAdd the displacement current and a wave equation appears. Light was sitting in Maxwell's equations all along.
  4. 04The Multipole ExpansionFar from a charge distribution the details stop mattering. Only the first surviving term does.
  5. 05Potentials and Gauge FreedomSix field components traded for four potentials. The redundancy left over is the gauge freedom.