For the use of exterior form in daily physics, an introduction without coordinate frame

TL;DR

This paper introduces the exterior form formalism in physics, emphasizing coordinate-free definitions and proofs to enhance understanding of physical concepts, especially for students.

Contribution

It presents a coordinate-free approach to exterior forms in physics, focusing on intuitive understanding without relying on coordinate frames.

Findings

Coordinate-free exterior form formalism aids comprehension.

Approach emphasizes physical meaning over mathematical complexity.

Method recovers classical physics equations at the end.

Abstract

This is a short introduction of the exterior form formalism focus on its applications in physics and then mostly aimed to physics students. As a rule of a game played here we never use a coordinate frame neither in the definitions nor in the proofs but only at the end in order to recover the classical physics equations. This approach is unusual but we think is helpful for the understanding and very valuable to grab the physical meanings of the mathematical object.