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Differential Forms: Theory and Practice

Steven H. Weintraub
Publisher: 
Academic Press
Publication Date: 
2014
Number of Pages: 
395
Format: 
Hardcover
Price: 
119.95
ISBN: 
9780123944030
Category: 
Textbook
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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

Dummy View - NOT TO BE DELETED