A Visual Introduction to Differential Forms and Calculus on Manifolds

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.

Table of Contents

1 Background Material

2 An Introduction to Differential Forms

3 The Wedgeproduct

4 Exterior Differentiation

5 Visualizing One-, Two-, and Three-Forms

6 Push-Forwards and Pull-Backs

7 Changes of Variables and Integration of Forms

8 Poincare Lemma

9 Vector Calculus and Different ial Forms

10 Manifolds and Forms on Manifolds

11 Generalized Stokes’ Theorem

12 An Example: Electromagnetism

A Introduction to Tensors

B Some Applications of Differential Forms

About the Author

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