Differential Forms book cover

Differential Forms

Integration on Manifolds and Stokes's Theorem

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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.

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

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