Book description
Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, Second Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice.- Provides a solid theoretical basis of how to develop and apply differential forms to real research problems
- Includes computational methods to enable the reader to effectively use differential forms
- Introduces theoretical concepts in an accessible manner
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- 1: Differential Forms in , I
- 2: Differential Forms in , II
- 3: Push-forwards and Pull-backs in
-
4: Smooth Manifolds
- 4.1 The notion of a smooth manifold
- 4.2 Tangent vectors and differential forms
- 4.3 Further constructions
- 4.4 Orientations of manifolds—intuitive discussion
- 4.5 Orientations of manifolds—careful development
- 4.6 Partitions of unity
- 4.7 Smooth homotopies and the Converse of Poincaré’s Lemma in general
- 4.8 Exercises
- 5: Vector Bundles and the Global Point of View
- 6: Integration of Differential Forms
- 7: The Generalized Stokes’s Theorem
- 8: de Rham Cohomology
- Index
Product information
- Title: Differential Forms, 2nd Edition
- Author(s):
- Release date: February 2014
- Publisher(s): Academic Press
- ISBN: 9780123946171
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