Introduction to the Hodge Star Operator - 1

The Hodge star operator is a central concept in differential geometry and mathematical physics, particularly in the study of manifolds and exterior calculus. It provides a way to relate different forms on a manifold and is crucial in formulating theories such as electromagnetism in a coordinate-free manner. In this introduction, we will explore the definition, properties alongside some detailed examples to illustrate its usage.

Note: At 10:00 the formula should read 𝜔∧𝜂 = ⟨⋆𝜔, 𝜂⟩ 𝑣𝑜𝑙_𝑀.

Note: At 19:58 the Levi-Civita symbol should read 𝜀^1234 = +1 and 𝜀^3412 = +1.

Note: At 11:51 the letter g was meant to be a k. So the1-form η should read:
η = fdx + kdy + hdz.