The Geometry of Differential Forms

Tevian Dray

This manuscript expands on class notes developed for a 10-week course on differential forms, which leads into a second course on general relativity. It is intended either as a textbook for a mathematics topics course, and/or for reference. The manuscript emphasizes the use of differential forms, rather than tensors, which are barely mentioned. Applications to curves and surfaces are included, but Euclidean signature is not assumed. The material should be suitable for both advanced undergraduates and beginning graduate students in both mathematics and physics. The subject is treated as advanced vector calculus, rather than analysis; the only prerequisites are vector calculus, linear algebra, and a modicum of mathematical sophistication.

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