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Fortney J.P. A Visual Introduction to Differential Forms and Calculus on Manifolds

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Fortney J.P. A Visual Introduction to Differential Forms and Calculus on Manifolds
Springer, 2018. — 470 p. — ISBN 978-3-319-96991-6.
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
Background Material
An Introduction to Differential Forms
The Wedgeproduct
Exterior Differentiation
Visualizing One-, Two-, and Three-Forms
Push-Forwards and Pull-Backs
Changes of Variables and Integration of Forms
Poincaré Lemma
Vector Calculus and Differential Forms
Manifolds and Forms on Manifolds
Generalized Stokes’ Theorem
An Example: Electromagnetism
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