A Beginner's Guide to Differential Forms - Brossura

Collier, Peter

Brossura

ISBN 10: 0957389477 ISBN 13: 9780957389472

Casa editrice: Incomprehensible Books, 2021

Riassunto

Differential forms eat tangent vectors, spit out numbers and do this in an alternating multilinear fashion. These properties make differential forms an essential tool for doing calculus on manifolds and thus of great interest to mathematicians and physicists. This book is aimed at the general reader who is interested in tackling a relaxed but wide-ranging introduction to this fascinating subject. The only prerequisite is a reasonable foundation in advanced, school-level mathematics. The text includes numerous worked problems. Topics covered include:

• An introduction to basic concepts.
• How differential forms eat tangent vectors and spit out numbers.
• Manipulating differential forms, including the wedge product, differentiation and integration.
• How differential forms provide an alternative means of understanding three-dimensional vector calculus.
• The generalised Stoke's theorem, which applies to manifolds of any dimension.
• Maxwell's equations in the language of differential forms.
• Using differential forms to prove three nice topological theorems, including the famous hairy ball theorem.

By the author of A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (ISBN 9780957389465) and Movement of the Spheres: Basic Astronomical Calculations Explained With 29 Spreadsheets (ISBN 9780957389489).

Dettagli dell'edizione

• Editore: Incomprehensible Books
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 0957389477
• ISBN 13: 9780957389472
• Rilegatura: Copertina flessibile
• Numero di pagine: 146
• Contatto del produttore: Manufactured by Amazon on behalf of the author; https://www.amazon.it/hz/contact-us; ; c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy; Luxembourg; L-1855; Lussemburgo