A Visual Introduction to Differential Forms and Calculus on Manifolds

Jon Pierre Fortney (Autor)

Buch | Hardcover

XII, 468 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-96991-6 (ISBN)

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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.

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

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.

"The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book." (Hirokazu Nishimura, zbMath 1419.58001, 2019)

“The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)

Erscheinungsdatum	17.11.2018
Zusatzinfo	XII, 468 p. 258 illus., 243 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	210 x 279 mm
Gewicht	1486 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	calculus on manifolds • cotangent bundle • differential forms • electromagnetism • exterior differentiation • integration of differential forms • Manifolds • pull-backs of differential forms • Stokes' theorem • Stokes’ Theorem • tangent bundle • Vector calculus • visualization of differential forms • wedgeproduct
ISBN-10	3-319-96991-9 / 3319969919
ISBN-13	978-3-319-96991-6 / 9783319969916
Zustand	Neuware