Contents

• • Syllabus and Course Rules
    • Contact Information
    • Useful Texts and Web References
    • Course Description
    • Basis of Grade
      • Percentages
      • Research Project:
    • Course Rules
    • The Interplay of Physics and Mathematics
  
  
• Mathematical Physics
  • Mathematical Prelude
  • Vector Calculus: Integration by Parts
  • Numbers
    • Real Numbers
    • Complex Numbers
    • Contour Integration
    • Geometric Algebra
  • Partial Differential Equations
    • The Laplace Equation
    • The Helmholtz Equation
    • The Wave Equation
  • Tensors
    • The Dyad and $N$-adic Forms
    • Coordinate Transformations
  • Group Theory
    • Definition of a Group
    • Groups of Transformation
  • Math References
  
  
• Non-Relativistic Electrodynamics
  • Plane Waves
    • The Free Space Wave Equation
      • Maxwell's Equations
      • The Wave Equation
      • Plane Waves
      • Polarization of Plane Waves
    • Reflection and Refraction at a Plane Interface
      • Kinematics and Snell's Law
      • Dynamics and Reflection/Refraction
    • Dispersion
      • Static Case
      • Dynamic Case
      • Things to Note
      • Anomalous Dispersion, and Resonant Absorption
      • Attenuation by a complex $\epsilon$
      • Low Frequency Behavior
      • High Frequency Limit; Plasma Frequency
    • Penetration of Waves Into a Conductor - Skin Depth
      • Wave Attenuation in Two Limits
    • Kramers-Kronig Relations
    • Plane Waves Assignment
  • Wave Guides
    • Boundary Conditions at a Conducting Surface: Skin Depth
    • Mutilated Maxwell's Equations (MMEs)
    • TEM Waves
    • TE and TM Waves
      • TM Waves
      • Summary of TE/TM waves
    • Rectangular Waveguides
    • Resonant Cavities
    • Wave Guides Assignment
  • Radiation
    • Maxwell's Equations, Yet Again
      • Quickie Review of Chapter 6
    • Green's Functions for the Wave Equation
      • Poisson Equation
      • Green's Function for the Helmholtz Equation
      • Green's Function for the Wave Equation
    • Simple Radiating Systems
      • The Zones
      • The Near Zone
      • The Far Zone
    • The Homogeneous Helmholtz Equation
      • Properties of Spherical Bessel Functions
      • $J_L({\bf r})$, $N_L({\bf r})$, and $H_L^\pm ({\bf r}$)
      • General Solutions to the HHE
      • Green's Functions and Free Spherical Waves
    • Electric Dipole Radiation
      • Radiation outside the source
      • Dipole Radiation
    • Magnetic Dipole and Electric Quadrupole Radiation Fields
      • Magnetic Dipole Radiation
      • Electric Quadrupole Radiation
    • Radiation Assignment
  • Vector Multipoles
    • Angular momentum and spherical harmonics
    • Magnetic and Electric Multipoles Revisited
    • Vector Spherical Harmonics and Multipoles
  • The Hansen Multipoles
    • The Hansen Multipoles
      • The Basic Solutions
      • Their Significant Properties
      • Explicit Forms
    • Green's Functions for the Vector Helmholtz Equation
    • Multipolar Radiation, revisited
    • A Linear Center-Fed Half-Wave Antenna
    • Connection to Old (Approximate) Multipole Moments
    • Angular Momentum Flux
    • Concluding Remarks About Multipoles
    • Table of Properties of Vector Harmonics
  • Optical Scattering
    • Radiation Reaction of a Polarizable Medium
    • Scattering from a Small Dielectric Sphere
    • Scattering from a Small Conducting Sphere
    • Many Scatterers
  
  
• Relativistic Electrodynamics
  • Special Relativity
    • Einstein's Postulates
    • The Elementary Lorentz Transformation
    • 4-Vectors
    • Proper Time and Time Dilation
    • Addition of Velocities
    • Relativistic Energy and Momentum
  • The Lorentz Group
    • The Geometry of Space-Time
    • Tensors in 4 Dimensions
    • The Metric Tensor
    • Generators of the Lorentz Group
      • Infinitesimal Transformations
    • Thomas Precession
    • Covariant Formulation of Electrodynamics
    • The Transformation of Electromagnetic Fields
  • Relativistic Dynamics
    • Covariant Field Theory
      • The Brute Force Way
      • The Elegant Way
    • Motion of a Point Charge in a Static Magnetic Field
    • Building a Relativistic Field Theory
    • The Symmetric Stress Tensor
    • Covariant Green's Functions
  • Radiation from Point Charges
    • Larmor's Formula
    • Thomson Scattering of Radiation
  • Radiation Reaction
    • The Death of Classical Physics
    • Radiation Reaction and Energy Conservation
    • Integrodifferential Equations of Motion
    • Radiation Damping of an Oscillating Charge
    • Dirac's Derivation of Radiation Reaction
    • Wheeler and Feynman's Derivation of Radiation Reaction
    • My Own Field-Free Derivation of Radiation Reaction