Differential Forms - 2nd Edition - ISBN: 9780123944030, 9780123946171

Differential Forms

2nd Edition

Theory and Practice

eBook ISBN: 9780123946171
Hardcover ISBN: 9780123944030
Imprint: Academic Press
Published Date: 24th February 2014
Page Count: 408
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


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, 2nd 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.

Key Features

  • 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


Pure and applied mathematicians, physicists, and engineers; Graduate students and advanced undergraduates in these fields

Table of Contents

  • Dedication
  • Preface
  • 1: Differential Forms in , I
    • 1.0 Euclidean spaces, tangent spaces, and tangent vector fields
    • 1.1 The algebra of differential forms
    • 1.2 Exterior differentiation
    • 1.3 The fundamental correspondence
    • 1.4 The Converse of Poincaré’s Lemma, I
    • 1.5 Exercises

  • 2: Differential Forms in , II
    • 2.1 -forms
    • 2.2 -Forms
    • 2.3 Orientation and signed volume
    • 2.4 The converse of Poincaré’s Lemma, II
    • 2.5 Exercises

  • 3: Push-forwards and Pull-backs in
    • 3.1 Tangent vectors
    • 3.2 Points, tangent vectors, and push-forwards
    • 3.3 Differential forms and pull-backs
    • 3.4 Pull-backs, products, and exterior derivatives
    • 3.5 Smooth homotopies and the Converse of Poincaré’s Lemma, III
    • 3.6 Exercises

  • 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
    • 5.1 The definition of a vector bundle
    • 5.2 The dual bundle, and related bundles
    • 5.3 The tangent bundle of a smooth manifold, and related bundles
    • 5.4 Exercises

  • 6: Integration of Differential Forms
    • 6.1 Definite integrals in
    • 6.2 Definition of the integral in general
    • 6.3 The integral of a -form over a point
    • 6.4 The integral of a -form over a curve
    • 6.5 The integral of a -form over a surface
    • 6.6 The integral of a -form over a solid body
    • 6.7


No. of pages:
© Academic Press 2014
Academic Press
eBook ISBN:
Hardcover ISBN:


"…a very nice book…covers things at a more leisurely pace, with many examples...would go a long way toward making the subject more popular and accessible."--SIAM Review, Differential Forms, Second Edition
Second Edition

"This is a rigorous and well-written treatment of differential forms with a careful and detailed progression from very basic notions."--MAA.org, 24-Sep-14

Ratings and Reviews