Differential Forms with Applications to the Physical Sciences

by Harley Flanders

A graduate-level text introducing the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Directed primarily to graduate-level engineers and physical scientists, it has also been used successfully to introduce modern differential geometry to graduate students in mathematics. Includes 45 illustrations. Index.

Genres: Mathematics, Physics, Geometry

205 pages, Paperback

First published December 1, 1989

Reviews

[Brian Powell · Rating 5 out of 5]

Everybody's talking about differential forms these days. I can't go to the supermarket without somebody chatting me up in line about exterior derivatives and p-forms. It's nuts.

There are many options when it comes to learning about differential forms. Books with various permutations of the words "physics", "topology", "geometry", "gravity", and "gauge fields" in their titles will tell you about differential forms, and generally these discussion are passable (the best of these by far is Baez and Muniain's "Gauge Fields, Knots, and Gravity"). But if want the straight dope, you've got to pick up a copy of Flanders. It's a slim Dover volume so it costs like 10 cents. The first 30 or so pages introduce differential forms compactly and clearly (but not tersely), and the rest of the book explores their applications.

The book makes for a quick study: you'll be improvising jokes about the star operator and impressing friends in no time.

[David · Rating 3 out of 5]

Good reference book (though quite thin) only after you've taken a course in diff geometry. For the physics-minded (for which the title is misleading), this is a condensed set of ideas that will only begin to make sense after seeing enough applications in general relativity, topological insulators, fluid mechanics etc.

But to be fair, this is a topic that is quite difficult to motivate when there are ways to work around inconveniences with vectors & matrix representations in the above mentioned physical applications. Only those who dig really deep into these fields will appreciate the style in which the book is written.

This book has chapters on applications and, returning to it after a course in GR and one in advanced quantum mechanics, I found it much easier to follow by reading Ch 8 (applications in diff geometry) first, then through Ch 3 - 5. But to understand Ch 8 (I think) you need to know some GR, and many GR books begin with an informal introduction to differential forms anyway. Maybe I picked up things in a weird order, but by the time I started going through Ch 3 and onwards, there was very few new things left to learn.

I still keep the book as a reference because it has the clearest proofs for the important theorems, but wouldn't recommend this for courses.

[Cliff · Rating 4 out of 5]

Glad I read this book. Nice accessible treatment of differential forms. The applications provide insights into other areas of mathematics and physics.

[Lulu]

Geometry and topology for physicists