This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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.
@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
Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.
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
- No. of pages:
- © Academic Press 1996
- 6th August 1996
- Academic Press
- eBook ISBN:
- Paperback ISBN:
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.
Lehigh University, Bethlehem, PA, USA