Syllabus
* Vector analysis and partial differential equations.
Scalar, vector and tensor fields. Physical fields. Differential operators. Integral theorems. Symmetries. Curvilinear coordinates.
Linear field equations with elliptic, parabolic and hyperbolic character. Boundary and initial value conditions. Green's function.
* Static, stationary, quasistationary and wave-like solutions of Maxwell's equations.
Maxwell's equations. Material relations. Lorentz's force. Conservation laws (for charge, energy, momentum and angular momentum). Special relativistic formulation of equations.
Laplace's and Poisson's equations for electrostatic potential. Boundary conditions. Uniqueness of the solution. Multipole expansion.
Magnetostatic filed. Magnetic field in stationary and quasistationary approximation. Biot-Savart's law. Skin effect.
Electromagnetic potential. Gauge transformations. Hertz's vector. Retarded and advanced potentials.
Waves and electromagnetic radiation. Plane wave in a vacuum, dielectric and conductive media and their interface. Hertzian dipole. Waveguide and electromagnetic cavity resonator.
Annotation
Maxwell's equations. Methods of solution. Static, stationary, and quasistationary approximation. Conservation laws.
Relativistic formulation. Dynamical theory and electromagnetic radiation.