Differential Forms
Integration on Manifolds and Stokes's Theorem
- 1st Edition - December 17, 1992
- Author: Steven H. Weintraub
- Language: English
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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… Read more
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Description
Description
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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.
Key features
Key features
@bul:* 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
Readership
Readership
Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.
Table of contents
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
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
Product details
Product details
- Edition: 1
- Published: August 6, 1996
- Language: English
About the author
About the author
SW
Steven H. Weintraub
Steven H. Weintraub is a Professor of Mathematics at Lehigh University. He received his Ph.D. from Princeton University, spent many years at Louisiana State University, and has been at Lehigh since 2001. He has visited UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover. Professor Weintraub is a member of the American Mathematical Society and currently serves as an Associate Secretary of the AMS. He has written more than 50 research papers on a wide variety of mathematical subjects, and ten other books.
Affiliations and expertise
Lehigh University, Bethlehem, PA, USA