A Geometric Approach to Differential Forms

by David Bachman

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Genres: Mathematics, Geometry, Textbooks

172 pages, Kindle Edition

First published January 1, 2006

Reviews

[C. Hinsley · Rating 4 out of 5]

Just great. This was easily read despite not having had an introduction to differential geometry in any capacity beforehand; the exposition is clear and pacing is perfect. There was one error early on in the book that confused me for a while (I don't remember what it was now), but this only happened once and it did not affect understanding once I got past it.

[Kirk Peters · Rating 4 out of 5]

The version I completed had the small chapter from differential geometry ending with the Gauss-Bonnet theorem.
I thought this was a cool little book. I've finished advanced calc and differential geometry. I reviewed this book for computational practice. It was a bit of a challenge to figure out how to translate the bits of notation from what I learned in differential geometry from this book. Further the section on differential geometry really speaks about Riemannian geometry when you get to curvature.
I would recommend this, and have recommended it to others.

[Michael M. · Rating 4 out of 5]

Still some misprints in the second edition but a very good introduction to the topic.