Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

A Visual Introduction to Differential Forms and Calculus on Manifolds

  • Textbook
  • © 2018

Overview

Authors:
  1. Jon Pierre Fortney

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  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
    Download chapter PDF
Back to top

Keywords

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.

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

Publish with us

Policies and ethics

Back to top

Search

Navigation