A Visual Introduction to Differential Forms and Calculus on Manifolds

• Main Author: Fortney, Jon Pierre (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Subjects: Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Global analysis (Mathematics).; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).; Global Analysis and Analysis 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,...

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
• Vector Calculus and Differential Forms
• Manifolds and Forms on Manifolds
• Generalized Stokes' Theorem
• An Example: Electromagnetism.