Buch, Englisch, 272 Seiten
Integration on Manifolds and Stokes's Theorem
Buch, Englisch, 272 Seiten
ISBN: 978-1-4933-0212-3
Verlag: Elsevier Science
Zielgruppe
Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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