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This course aims to give a concise, complete and mathematically intuitive description of the fundamental laws of electromagnetism, namely: Maxwell's equations, Lorentz force, electromagnetic energy momentum tensor, etc.
The following concepts are used extensively: tensors, Minkowski metric, lagrangian mechanics, which were introduced by the instructor in the course "Mathematical intuition behind Special and General Relativity".
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is clearly invariant under Lorentz transformations, in the formalism of special relativity (therefore using inertial coordinate systems). These expressions simply prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, as well as provide a way to treat the fields and forces in different reference frames.
We will derive Maxwell's equations in vacuum, where they can be written as two tensor equations (instead of 4 vector equations).
We will also see how to derive the electromagnetic tensor, starting from an intuitive Lagrangian approach, and also calculate the energy-momentum-tensor related to electromagnetic fields, by recalling some expressions derived in the course on General Relativity ("Mathematical Intuition behind Special and General Relativity").