A differential geometric view on Maxwell's equations

This thesis explores the mathematical reformulation of classical electromagnetism through the framework of differential geometry. By employing the formalism of differential forms, the study demonstrates how Maxwell's equations can be elegantly expressed in R^4. The analysis focuses on the exterior derivative, the wedge product, the Hodge star and the flat operators to provide a description of the electromagnetic field. Furthermore, the thesis examines the transition from the traditional vector calculus approach to this geometric perspective, establishing the foundational structures required to generalize electromagnetic theory within a covariant framework.