A visual introduction to differential geometry and Maxwell's equations through pictures
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[Submitted on 21 Sep 2017]
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Summary
This article presents a pictorial introduction to differential geometry, aimed at making the mathematical foundation accessible to pre-university students while also aiding undergraduate and master's students learning general relativity. The content covers differential geometry concepts without using equations, relying entirely on visual representations. The ultimate goal is to present Maxwell's equations as three pictures, demonstrating how differential geometry serves as a crucial tool for multiple areas of physics including special/general relativity, mechanics, thermodynamics, and solving differential equations.
Key quotes
· 5 pulledIn 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.
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