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| DIFFERENTIAL FORMS
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A Complement to Vector Calculus
To order this title, and for more information, click here
By
Steven Weintraub, Louisiana State University, Baton Rouge
Description
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.
Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable.
Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in
this book should come away with a better conceptual understanding of it than those who learn using conventional methods.
Audience
Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.
Contents
Differential Forms
The Algrebra of Differential Forms
Exterior Differentiation
The Fundamental Correspondence
Oriented Manifolds
The
Notion Of A Manifold (With Boundary)
Orientation
Differential Forms Revisited
l-Forms
K-Forms
Push-Forwards And Pull-Backs
Integration
Of Differential Forms Over Oriented Manifolds
The Integral Of A 0-Form Over A Point (Evaluation)
The Integral Of A 1-Form Over A Curve
(Line Integrals)
The Integral Of A2-Form Over A Surface (Flux Integrals)
The Integral Of A 3-Form Over A Solid Body (Volume Integrals)
Integration Via Pull-Backs
The Generalized Stokes' Theorem
Statement Of The Theorem
The Fundamental Theorem Of Calculus And Its Analog
For Line Integrals
Green's And Stokes' Theorems
Gauss's Theorem
Proof of the GST
For The Advanced Reader
Differential Forms In IRN
And Poincare's Lemma
Manifolds, Tangent Vectors, And Orientations
The Basics of De Rham Cohomology
Appendix
Answers To Exercises
Subject
Index
| Bibliographic details |
Hardbound, 272 pages, publication date: AUG-1996
ISBN-13: 978-0-12-742510-8
ISBN-10: 0-12-742510-1
Imprint: ACADEMIC PRESS
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| Price and Ordering |
Price:
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USD 114
GBP 72
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Last update: 4 Sep 2009
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