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

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1997 Hardcover First Edition New with No dust jacket as issued 0127425101. This specific hardback book is in new condition with a hard board cover that has sharp edges and ... corners and has a tight binding. The pages are clean, crisp, unmarked and uncreased. We package all books in custom cardboard book boxes for shipment and ship daily with tracking numbers.; "This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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 Stoke Read more Show Less

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Overview

Differential forms are a powerful computational tool used in advanced mathematics. Until this text, multivariable calculus was taught mostly using the outdated notions of vector fields and related matters. Theuse of differential forms unifies the subject and makes it more understandable, so students learning the subject from this book should emerge with a better conceptual understanding of it.

* 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

Audience: Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.

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Editorial Reviews

Booknews
Primarily addressed to students in a third-semester, multivariable calculus course who are studying vector calculus, but also of interest to more advanced students who want a concrete introduction to differential forms. Differential forms are explained from the mathematical perspective rather than from that of physics or engineering, as is usually the case. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780127425108
  • Publisher: Elsevier Science
  • Publication date: 8/1/1996
  • Edition number: 1
  • Pages: 272
  • Product dimensions: 0.75 (w) x 6.00 (h) x 9.00 (d)

Meet the Author

Steven H. Weintraub is a Professor of Mathematics at Louisiana State University. He received his Ph.D. from Princeton University, and has been at LSU since that time, with temporary leaves to UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover (Germany).Professor Weintraub is a member of the American Mathematical Society and a former member of the Council of the AMS. He has written more than 40 research papers and two other books: a graduate algebra book and a reserach monograph.
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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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