Introduction
This, the second semester of the PHYS 3320/3330 Electricity and Magnetism
sequence, is primarily concerned with the methods of solving Maxwell's
Equations

divD = ρ

divB = 0

curlE =  ∂B/∂t

curlH = J + ∂D/∂t
There are two cases to consider

Electrostatic and magnetostatic solutions; time independent equations,
for which the electric and magnetic fields are independent of one another
and can be solved separately

Electromagnetism; time dependent equations, for which the electric and
magnetic fields are inherently linked, in which case Maxwell's equations
must be solved as a set of simultaneous equations
We shall make some simplifying assumptions in order to extract solutions

that the free charge and current densities (ρ and J) are
both zero

that the natural of materials is restricted to those which are linear,
isotropic, and homogeneous. Solutions in which the material is nonlinear
(e.g. frequency doubling crystals) or anisotropic (birefringence) are covered
in the class PHYS 4900 Modern Optics and Lasers.

Required mathematics
Solutions of Maxwell's Equations relies on knowledge of the appropriate
mathematics, all of which we covered in PHYS 3010 Mathematical Physics
I. I will review as appropriate, but it is also to your advantage to review
the following ahead of time

for static solutions

partial differential equations, especially the method of separation of
variable

Special functions, especially the Legendre equation and Legendre polynomials

for time dependent solutions

vector calculus

complex numbers, and the representation of a wave in complex form.

relativity

matrices, and matrix multiplication
Assignments
