A pictorial introduction to differential geometry (2017)
Recorded: May 31, 2026, 7 a.m.
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[1709.08492] A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures
Skip to main content Learn about arXiv becoming an independent nonprofit. We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. > math > arXiv:1709.08492 Help | Advanced Search All fields Search GO quick links Login Mathematics > Differential Geometry arXiv:1709.08492 (math) [Submitted on 21 Sep 2017] 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. Subjects: Differential Geometry (math.DG); Classical Physics (physics.class-ph) Cite as: Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jonathan Gratus [view email] [v1]
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The article presents a pictorial introduction to the foundation of differential geometry, positioning it as a crucial tool applicable across various fields of physics, including general relativity and special relativity, as well as mechanics, thermodynamics, and the solution of differential equations. The central goal of the work is to utilize these concepts visually, presenting the mathematical foundations as pictures rather than equations, which allows the material to be accessible to pre-university students interested in physics, mathematics, and geometry. Furthermore, the presentation is designed to significantly enhance the intuition for undergraduate and master's students studying general relativity and related courses. The primary focus of the text is on establishing the necessary geometric tools required to comprehend Maxwell's equations, with the overarching objective of demonstrating these equations in three distinct visual representations. |