Skip to main content
  • Textbook
  • © 2018

A Visual Introduction to Differential Forms and Calculus on Manifolds

Birkhäuser
  • Explains and helps the reader to develop geometric intuition as it relates to differential forms

  • Over 250 figures aiding the reader to understand and visualize the concepts being discussed

  • Basic ideas and concepts are gradually build up

  • Aimed at second and third year undergraduate mathematics and physics students

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-96992-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 84.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
  2. Background Material

    • Jon Pierre Fortney
    Pages 1-30
  3. An Introduction to Differential Forms

    • Jon Pierre Fortney
    Pages 31-67
  4. The Wedgeproduct

    • Jon Pierre Fortney
    Pages 69-105
  5. Exterior Differentiation

    • Jon Pierre Fortney
    Pages 107-149
  6. Visualizing One-, Two-, and Three-Forms

    • Jon Pierre Fortney
    Pages 151-188
  7. Push-Forwards and Pull-Backs

    • Jon Pierre Fortney
    Pages 189-228
  8. Changes of Variables and Integration of Forms

    • Jon Pierre Fortney
    Pages 229-257
  9. Poincaré Lemma

    • Jon Pierre Fortney
    Pages 259-275
  10. Vector Calculus and Differential Forms

    • Jon Pierre Fortney
    Pages 277-308
  11. Manifolds and Forms on Manifolds

    • Jon Pierre Fortney
    Pages 309-335
  12. Generalized Stokes’ Theorem

    • Jon Pierre Fortney
    Pages 337-367
  13. An Example: Electromagnetism

    • Jon Pierre Fortney
    Pages 369-393
  14. Back Matter

    Pages 395-468

About this book

This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

Keywords

  • differential forms
  • wedgeproduct
  • visualization of differential forms
  • calculus on manifolds
  • integration of differential forms
  • exterior differentiation
  • tangent bundle
  • cotangent bundle
  • pull-backs of differential forms
  • manifolds
  • vector calculus
  • Stokes’ theorem
  • electromagnetism

Reviews

 “The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)  

Authors and Affiliations

  • Department of Mathematics and Statistics, Zayed University, Dubai, United Arab Emirates

    Jon Pierre Fortney

About the author

Jon Pierre Fortney, Zayed University, Dubai, United Arab Emirates.  

Bibliographic Information

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-96992-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 84.99
Price excludes VAT (USA)