Hodge dual, Levi Civita pseudo tensor, differential forms

With differential forms, we often use the so-called Hodge dual. This important operator allows constructing a N-p form starting from a p form embedded in an N-dimensional space.

In the recently published course on differential forms, we investigate these concepts intuitively and show how differential forms help constitute a natural extension of the fundamental theorem of calculus, the divergence theorem, Stokes’ theorem.

We will also see how to rewrite Maxwell equations in a compact and neat way with the help of differential forms. The concept of the Hodge dual will be essential to digging deeper into Maxwell equations.

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