A Visual Introduction to Differential Forms and Calculus on Manifolds

1. Auflage 2018
ISBN: 978-3-319-96991-6
Verlag: Springer International Publishing

Buch, Englisch, 468 Seiten, Format (B × H): 215 mm x 285 mm, Gewicht: 1413 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Fortney, Jon Pierre

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

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