The course aims at deepening the Mathematical-Physics of Electromagnetism, focusing on some aspects that usually are not discussed in the classes for undergraduate students in engineering. More specifically, the general target is to improve and extend the knowledge of electromagnetic theory, provide some epistemological elements, and foster the critical ability required for solving applied problems.
1) Historical introduction
2) Physical interpretation of the mathematical operators; generalized coordinates; decomposition theorem
3) Analysis of the local form of Maxwell’s equations; macroscopic view and validity of the model; integral version of the equations in the most general form; electromagnetic induction and “flux rule”; Galilean limits of electromagnetism
4) Electromagnetic potentials; gauge transformation; propagation of the electromagnetic potentials; features and validity of Coulomb and Lorenz gauges; other gauges
5) Boundary value problems in electromagnetism; Green’s theorem and application to Laplace/Poisson equations; vector analogue of Green’s theorem and direct integration of the field equations; direct integration in the time domain and Jefimenko’s equations; Kirchhoff’s formula in both frequency and time domains; examples of the numerical setting of the boundary value problems