A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures

Gratus, Jonathan (2017) A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures. arxiv.org.

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Abstract

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in this article. As such this article may be read by pre-university students who enjoy physics, mathematics and geometry. However it will also greatly aid the intuition of an undergraduate and masters students, learning general relativity and similar courses. It concentrates on the tools needed to understand Maxwell's equations thus leading to the goal of presenting Maxwell's equations as 3 pictures.