A Visual Introduction to Differential Forms and Calculus on Manifolds

Description

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. Front Matter ....Pages i-xii Background Material (Jon Pierre Fortney)....Pages 1-30 An Introduction to Differential Forms (Jon Pierre Fortney)....Pages 31-67 The Wedgeproduct (Jon Pierre Fortney)....Pages 69-105 Exterior Differentiation (Jon Pierre Fortney)....Pages 107-149 Visualizing One-, Two-, and Three-Forms (Jon Pierre Fortney)....Pages 151-188 Push-Forwards and Pull-Backs (Jon Pierre Fortney)....Pages 189-228 Changes of Variables and Integration of Forms (Jon Pierre Fortney)....Pages 229-257 Poincaré Lemma (Jon Pierre Fortney)....Pages 259-275 Vector Calculus and Differential Forms (Jon Pierre Fortney)....Pages 277-308 Manifolds and Forms on Manifolds (Jon Pierre Fortney)....Pages 309-335 Generalized Stokes’ Theorem (Jon Pierre Fortney)....Pages 337-367 An Example: Electromagnetism (Jon Pierre Fortney)....Pages 369-393 Back Matter ....Pages 395-468