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CONTENTS
# Introduction
* Intended audience
* Major sources
* Preface
* Outline of course
# Vectors
* Introduction
* Vector algebra
* Vector areas
* The scalar product
* The vector product
* Rotation
* The scalar triple product
* The vector triple product
* Vector calculus
* Line integrals
* Vector line integrals
* Surface integrals
* Vector surface integrals
* Volume integrals
* Gradient
* Divergence
* The Laplacian
* Curl
* Summary
# Time-independent Maxwell equations
* Introduction
* Coulomb’s law
* The electric scalar potential
* Gauss’ law
* Poisson’s equation
* Ampère’s experiments
* The Lorentz force
* Ampère’s law
* Magnetic monopoles?
* Ampère’s circuital law
* Helmholtz’s theorem
* The magnetic vector potential
* The Biot-Savart law
* Electrostatics and magnetostatics
# Time-dependent Maxwell’s equations
* Introduction
* Faraday’s law
* Electric scalar potential?
* Gauge transformations
* The displacement current
* Potential formulation
* Electromagnetic waves
* Green’s functions
* Retarded potentials
* Advanced potentials?
* Retarded fields
* Summary
# Electrostatics
* Introduction
* Electrostatic energy
* Ohm’s law
* Conductors
* Boundary conditions on the electric field
* Capacitors
* Poisson’s equation
* The uniqueness theorem
* One-dimensional solution of Poisson’s equation
* The method of images
* Complex analysis
* Separation of variables
# Dielectric and magnetic media
* Introduction
* Polarization
* Boundary conditions for ${\bf E}$ and ${\bf D}$
* Boundary value problems with dielectrics
* Energy density within a dielectric medium
* Magnetization
* Magnetic susceptibility and permeability
* Ferromagnetism
* Boundary conditions for ${\bf B}$ and ${\bf H}$
* Boundary value problems with ferromagnets
* Magnetic energy
# Magnetic induction
* Introduction
* Inductance
* Self-inductance
* Mutual inductance
* Magnetic energy
* Alternating current circuits
* Transmission lines
# Electromagnetic energy and momentum
* Introduction
* Energy conservation
* Electromagnetic momentum
* Momentum conservation
# Electromagnetic radiation
* Introduction
* The Hertzian dipole
* Electric dipole radiation
* Thompson scattering
* Rayleigh scattering
* Propagation in a dielectric medium
* Dielectric constant of a gaseous medium
* Dielectric constant of a plasma
* Faraday rotation
* Propagation in a conductor
* Dielectric constant of a collisional plasma
* Reflection at a dielectric boundary
* Wave-guides
# Relativity and electromagnetism
* Introduction
* The relativity principle
* The Lorentz transformation
* Transformation of velocities
* Tensors
* The physical significance of tensors
* Space-time
* Proper time
* 4-velocity and 4-acceleration
* The current density 4-vector
* The potential 4-vector
* Gauge invariance
* Retarded potentials
* Tensors and pseudo-tensors
* The electromagnetic field tensor
* The dual electromagnetic field tensor
* Transformation of fields
* Potential due to a moving charge
* Fields due to a moving charge
* Relativistic particle dynamics
* The force on a moving charge
* The electromagnetic energy tensor
* Accelerated charges
* The Larmor formula
* Radiation losses
* Angular distribution of radiation
* Synchrotron radiation
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