Differential Forms

Steven Weintraub

ISBN 0127425101
Pages 272

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This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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

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