Differential Forms and Applications.

Do Carmo, Manfredo P.:

ISBN 10: 3540576185 / ISBN 13: 9783540576181

Published by Berlin/New York, Springer (Universitext), 1994

About this Item

Formateinband: Paperback / kartonierte Ausgabe VIII, 118 S. 1st Edition; Preiskleber am Vorderdeckel; sonst sehr gut erhalten. Sprache: Englisch Gewicht in Gramm: 400 [Stichwörter: Differential Forms in Rn, Line Integrals, Differentiable Manifolds, Integration on Manifolds, Stokes Theorem and Poincaré Lemma, Differential Geometry of Surfaces, The Theorem of Gauss-Bonnet and the Theorem of Morse].

Seller Inventory # 73610

Bibliographic Details

• Title: Differential Forms and Applications.
• Publisher: Berlin/New York, Springer (Universitext)
• Publication Date: 1994
• Language: English
• ISBN 10: 3540576185
• ISBN 13: 9783540576181
• Binding: Soft cover
• Edition: 1st Edition
• Condition: Gut
• Weight: 400 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

This is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome­ try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a complete hyperbolic plane in euclidean 3-space (Hilbert's theorem). For the present edition, we introduced a chapter on line integrals. In Chapter 1 we introduce the differential forms in Rn. We only assume an elementary knowledge of calculus, and the chapter can be used as a basis for a course on differential forms for "users" of Mathematics. In Chapter 2 we start integrating differential forms of degree one along curves in Rn. This already allows some applications of the ideas of Chapter 1. This material is not used in the rest of the book. In Chapter 3 we present the basic notions of differentiable manifolds. It is useful (but not essential) that the reader be familiar with the notion ofa regular surface in R3. In Chapter 4 we introduce the notion of manifold with boundary and prove Stokes theorem and Poincare's lemma. Starting from this basic material, we could follow any of the possi­ ble routes for applications: Topology, Differential Geometry, Mechanics, Lie Groups, etc. We have chosen Differential Geometry. For simplicity, we re­ stricted ourselves to surfaces.

Language Notes

Text: English (translation)
Original Language: Portugese