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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