Differential Forms
Integration on Manifolds and Stokes's Theorem
By- Steven Weintraub, Louisiana State University, Baton Rouge
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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.
Hardbound, 272 Pages
Published: August 1996
Imprint: Academic Press
ISBN: 978-0-12-742510-8
Contents
- Differential FormsThe Algrebra of Differential FormsExterior DifferentiationThe Fundamental Correspondence Oriented ManifoldsThe Notion Of A Manifold (With Boundary)Orientation Differential Forms Revisitedl-FormsK-FormsPush-Forwards And Pull-Backs Integration Of Differential Forms Over Oriented ManifoldsThe 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' TheoremStatement Of The TheoremThe Fundamental Theorem Of Calculus And Its Analog For Line IntegralsGreen's And Stokes' TheoremsGauss's TheoremProof of the GST For The Advanced ReaderDifferential Forms In IRN And Poincare's LemmaManifolds, Tangent Vectors, And OrientationsThe Basics of De Rham Cohomology AppendixAnswers To ExercisesSubject Index
