A Geometric Approach to Differential Forms

Authors: Bachman, David

  • The second edition includes two additional chapters, focusing on the more advanced topics of the book
  • Presents differential forms from a geometric perspective accessible at the sophomore undergraduate level
  • Each new concept is presented with a natural picture that students can easily grasp; algebraic properties then follow
  • Designed to support three distinct, classroom tested, course tracks
  • Contains excellent motivation, numerous illustrations and solutions to selected problems
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eBook $34.99
price for USA (gross)
  • ISBN 978-0-8176-8304-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.95
price for USA
  • ISBN 978-0-8176-8303-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level.  The author approaches the subject 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. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions.

The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry. 

Reviews

From the reviews of the second edition:

“This book is a good complement to existing textbooks on vector calculus and shows a different view on classic material. It should be helpful to both physicists and mathematicians as an introduction to first concepts of the basic tools of modern theoretical physics, differential geometry, and topology.” (Vladislav Nikolaevich Dumachev, zbMATH, Vol. 1266, 2013)

Table of contents (8 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-0-8176-8304-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.95
price for USA
  • ISBN 978-0-8176-8303-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Geometric Approach to Differential Forms
Authors
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-8304-7
DOI
10.1007/978-0-8176-8304-7
Hardcover ISBN
978-0-8176-8303-0
Edition Number
2
Number of Pages
XVI, 156
Number of Illustrations and Tables
43 b/w illustrations
Topics