Syllabus: Electricity & Magnetism

1. Introduction
2. Vector Calculus
   1. Vector Algebra
   2. Vector Differential Operators
   3. Integral Theorems
      1. Gauss's Law
      2. Stokes's Theorem
      3. Vector Calculus in Fluid Mechanics
   4. Curvilinear Coordinates
   5. The Helmholtz Theorem
3. Basic Principles of Electrostatics
   1. Coulomb's Law
   2. Electric Fields
   3. Curl and Divergence of E
   4. Integral form of Gauss's law
   5. Green's Functions & The Dirac Delta Function
   6. Electric Potential
   7. Energy of the Electric Field
   8. The Multipole Expansion
4. Electrostatics and Conductors
   1. Static properties of conductors
   2. Problems with Rectangular Symmetry
      1. Method of Images
   3. Spherical Symmetry
   4. Problems with Cylindrical Symmetry
5. General Methods for Laplace's Equation
   1. Separation of Varibles in Cartesian Coordinates
   2. Separation of Varibles in Sperical Coordinates
      1. Legendre Polynomials
   3. Separation of Varibles in Cylindrical Coordinates
6. Electrostatics and Dielectrics
   1. Atomic and Molecular Electric Dipoles
   2. The Electric Polarization: P & Bound Charge: ρ_b
   3. The Displacement Field: D
   4. Linear Isotropic Dielectrics
   5. Dielectrics and Boundary Value Problems
   6. Capacitor Design
7. Electric Currents
   1. Current I, Surface Current K & Current Density J
   2. The Continuity Equation
   3. Current & Resistance
8. Magnetostatics
   1. Magnetic Forces & Magnetic Fields
      1. Magnetic Forces on Moving Charges
      2. Magnetic Forces on Currents
   2. The Biot-Savart Law
   3. Ampère's Law
   4. The Vector Potential: A
   5. Magnetic Dipoles
9. Magnetic Field & Matter
   1. Magnetic Dipoles
   2. Magnetization
   3. Ampère's Law
10. Electromagnetic Induction
11. Maxwell's Equations
    1. ∇ ⋅ B = 0
    2. ∇ ⋅ E = ρ/ε₀
    3. ∇×E = -∂B/∂t
    4. ∇×B = μ₀J + μ₀ε₀ ∂E/∂ t