Maxwells Equations in Differential Forms

This is an honors project for physics II at CCD. I will be releasing a video soon covering through this material, the hodge star, a more in depth look at the exterior derivative in minkowski spacetime, and the other equation d*F=4piJ, the continuity equation and then integrating all through the generalized stokes theorem and further interpretation on what this all means. Some important clarifications: -The flat and sharp maps are said to move between V and V*, formally these are maps between the tangent bundle TM and the cotangent bundle T*M, but in R3 and Minkowski spacetime, the tangent space at all points is isomorphic to the whole space. -Lengths(distances) and angles do depends on coordinates, but the geometry of the space between two points does not -The claim is not that all of electromagnetism is derived from pure mathematics. The point is narrower: once the field-strength 2-form is written as F=dA the identity d^2=0 gives dF=0. In vector language, this is the homogeneous half of Maxwell’s equations. The sourced equations, involving charge and current, require additional physical input. - The equation F=dA is always valid locally in ordinary electromagnetism, but global topology can complicate the existence of a single potential A everywhere. I have a summary pdf on my github https://github.com/unreasonablyEffective42/Differential-Forms-Presentation/blob/main/emformssummary.pdf If you want to see where the potential A comes from, Richard Behiel has an excellent video https://www.youtube.com/watch?v=Sj_GSBaUE1o&t=4650s Michael Penn has a playlist on differential forms https://www.youtube.com/playlist?list=PL22w63XsKjqzQZtDZO_9s2HEMRJnaOTX7