Unit: Gauss's Law

Flux (20-50 minutes)

Gauss's Law (120 minutes)

Divergence (40 min)

Divergence Theorem (20 min)

  • Reading: GVC § Divergence Theorem
  • Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.

Differential Form of Gauss's Law (10 min)

Unit: Current, Magnetic Vector Potential, and Magnetic Field


Vector Potentials (Optional)

Magnetic Fields

Unit: Ampère's Law

Ampère's Law


Stokes' Theorem

Differential Form of Ampère's Law

  • Stokes' Theorem (lecture) (Math 3.12: Stokes' Theorem)
  • Differential Form of Ampère's Law: Maxwell Eq. 2 & 4 $\Vec{\nabla } \times \Vec{E} = 0$, $\Vec{\nabla } \times \Vec{B} = \mu_0 \Vec{J}$(lecture) (Physics 41: Differential Form of Ampère's Law)

Unit: Conductors

Step & Delta Functions (1 hr)

Conductors (1 hr)

Boundary Conditions

Unit: Conservative Fields

Conservative Fields

Second Derivatives

Unit: Energy

Product Rules

Energy for Continuous Distributions

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