Differential Forms : A Complement to Vector Calculus
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 Until this text, multivariable calculus was taught mostly using the outdated notions of vector fields and related matters.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
- Hardback | 272 pages
- 152.4 x 226.06 x 20.32mm | 544.31g
- 21 Aug 1996
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
Back cover copy
This book has two audiences. Its primary audience is students in a third-semester (multivariable) calculus course, who are studying the material usually known as 'vector calculus'. Its secondary audience is more advanced students who are seeking a very concrete introduction to (or explanation of) differential forms.
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
About Steven H. Weintraub
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.