A Visual Introduction to Differential Forms and Calculus on Manifolds

Capa
Springer, 3 de nov. de 2018 - 468 páginas
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.
 

Conteúdo

1 Background Material
1
2 An Introduction to Differential Forms
31
3 The Wedgeproduct
69
4 Exterior Differentiation
107
5 Visualizing One Two and ThreeForms
151
6 PushForwards and PullBacks
189
7 Changes of Variables and Integration of Forms
229
8 Poincaré Lemma
258
10 Manifolds and Forms on Manifolds
309
11 Generalized Stokes Theorem
337
Electromagnetism
369
A Introduction to Tensors
394
B Some Applications of Differential Forms
435
References
463
Index
465
Direitos autorais

9 Vector Calculus and Differential Forms
277

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Termos e frases comuns

Sobre o autor (2018)

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

Informações bibliográficas