Differential Forms: Integration on Manifolds and Stokes's Theorem / Edition 1

Differential Forms: Integration on Manifolds and Stokes's Theorem / Edition 1

by Steven H. Weintraub
     
 

ISBN-10: 0127425101

ISBN-13: 9780127425108

Pub. Date: 08/01/1996

Publisher: Elsevier Science

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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

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Overview

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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

• Treats vector calculus using differential forms
• Presents a very concrete introduction to differential forms
• Develops Stokess theorem in an easily understandable way
• Gives well-supported, carefully stated, and thoroughly explained definitions and theorems.
• Provides glimpses of further topics to entice the interested student

Product Details

ISBN-13:
9780127425108
Publisher:
Elsevier Science
Publication date:
08/01/1996
Pages:
272
Product dimensions:
0.75(w) x 6.00(h) x 9.00(d)

Table of 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

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