Differential Forms: A Complement to Vector Calculus

by Steven H. Weintraub

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.

* Treats vector calculus using differential forms
* Presents a very concrete introduction to differential forms
* Develops Stokess theorem in an easily understandable way
* Gives well-supported, carefully stated, and thoroughly explained definitions and theorems.
* Provides glimpses of further topics to entice the interested student

Genres: Mathematics, Calculus

268 pages, Hardcover

First published August 1, 1996

Reviews

[Erickson · Rating 5 out of 5]

Nice book on differential forms, with very intuitive explanations and diagrams which allow proper understanding of forms for first time readers before going for more advanced texts. It is illustrative enough to enable understanding of Generalized Stokes' Theorems and pull-backs and pushforwards, which are extremely useful in reinterpreting the whole integration of forms over the manifolds.

The section for Advanced Readers would need more background such as topology to access properly. However, apart from that the first 5 chapters can be read fully. Will come back to the last 40 pages after I have knowledge on basic topology.