Instructor: Gianfranco Vidali, 221 Physics Building, 3-9115, gvidali@syr.edu.

List of Topics

• Comments on Maxwell's equations. Review of mathematical methods: vector calculus.
• Electrostatics. Coulomb's and Poisson's laws. Electric field, path independence and the potential. Multipole expansions. Gauss's law. Green's identities. Energy in a electrostatic field.
• Solutions of boundary-value problems in electrostatics: uniqueness theorems, method of images and examples of its application, Poisson's equation, separation of variables. Review of mathematical methods: expansion in eigenfunctions. Legendre polynomials, spherical harmonics and Bessel functions and related generating functions. Application of method of expansion in eigenfunctions to electrostatics: Green's function method of solution of boundary-value problems in different boundary geometries (planar, cylindrical, spherical).
• Electrostatics in a dielectric medium. Susceptibility and molecular properties. Boundary-value problems in a dielectric medium. Applications. Energy in a dielectric medium.
• Magnetostatics. Biot-Savart law, B-field, the vector potential. Multiple expansion. Interaction of currents with external fields. Faraday's law. Boundary-value problems in magnetic media. Energy in magnetic fields.
• Time-varying fields and Maxwell's equations. Coulomb and Lorentz gauges. Energy, Poynting vector.
• Electromagnetic waves: propagation, generation and detection of waves. Polarization. Waves at boundaries. Propagation of waves and wave-packets in a dispersive medium.
• Additional topics, such as relativistic formulation of Maxwell's equations, optical fibers, magnetohydrodynamics etc., will be covered depending on time and interest.