Basic Electromagnetism: Course Outline

• Vector algebra.
• Vector operations.
• Vector algebra.
• Component form.
• Triple products.
• Position.
• Displacement and separation vectors.
• How vector transform.
• Differential calculus. 
• Ordinary derivatives.
• Gradient. 
• The operator.
• The divergence.
• Product rules.
• Second derivatives.
• Integral calculus.
• Line, surface and volume integrals.
• The fundamental theorem of calculus.
• The fundamental theorem for divergences.
• The fundamental theorem for curls.
• Integration by parts.
• Curvilinear coordinates.
• Spherical polar coordinates.
• Cylindrical coordinates.
• The Dirac delta function.
• The divergence of r/r^2.
• The one dimensional Dirac delta function.
• The three dimensional delta function.
• The Theory of vector fields:
• The Helmholtz theorem.
• Potentials.
• Electrostatics.
• The electric field.
• Introduction, Coulomb’s law.
• The electric field.
• Continuous charged distributions.
• Divergence and curl of electrostatic fields.
• Field lines.
• Flux and Gauss’s law.
• The divergence of E.
• Application of Gauss’s law.
• The curl of E.
• Electric potential.
• Introduction to potential.
• Comments on potential.
• Poisson’s and Laplace’s equations.
• The potential of a localized charged distribution.
• Electrostatic boundary conditions.
• Work and energy in electrostatics. 
• The work done to move a charge.
• The energy of a point charge distribution.
• Comments on electrostatic energy.
• Conductors: Basic properties.
• induced charges.
• Surface charge and force on a conductor.
• Capacitors.

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• Special techniques.
• Laplace’s equation in one dimension.
• in two dimensions.
• and in three dimensions.
• Boundary conditions and Uniqueness theorems.
• Conductors and seconds uniqueness theorem.
• The methods of image.
• The classic Image problem.
• Induced surface charge.
• Force and energy.
• Other image problems.
• Separations of variables.
• Cartesian coordinates.
• Spherical coordinates.
• Multipole expansion.
• Approximate potential at large distance.
• The monopole and dipole terms.
• Origin of coordinates in multipole expansions.
• The electric field of a dipole.
• Electric Fields in Matter.
• Polarization.
• Dielectric.
• Induced dipoles.
• Alignment of polar molecules.
• Polarization.
• The field of a polarized object.
• Bound charges.
• Physical interpretation of bound charges.
• The field inside a dielectric.
• The electric displacement.
• Gauss’s law in the presence of dielectrics.
• A deceptive parallel.
• Boundary conditions.
• Linear dielectrics.
• Susceptibility.
• Permittivity.
• Dielectric constant.
• Boundary value problems with linear dielectrics.
• Energy in dielectric systems.
• Forces on dielectrics.
• Magnetostatics.
• Lorentz force law.
• Magnetic fields.
• Magnetic forces.
• Currents.
• Biot-Savart law.
• Steady current.
• The magnetic field of a steady current.
• The divergence and curl of B.
• Straight-line currents.
• Applications of Amplere’s law.
• Comparison of magnetostatics and electrostatics.
• Magnetic vector potential.
• The vector potential.
• Magnetostatic boundary conditions.
• Multipole expansion of the vector potential.