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Field name	Details
Dewey Class	516.36
Title	Differential Forms and Applications ([EBook]) / by Manfredo P. do Carmo.
Author	Carmo, Manfredo Perdigao do
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer Berlin Heidelberg , 1994
Physical Details	X, 118 p. : online resource.
Series	Universitext 0172-5939
ISBN	9783642579516
Summary Note	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 of a 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.:
Contents note	1. Differential Forms in Rn -- 2. Line Integrals -- 3. Differentiable Manifolds -- 4. Integration on Manifolds; Stokes Theorem and Poincaré’s Lemma -- 1. Integration of Differential Forms -- 2. Stokes Theorem -- 3. Poincaré’s Lemma -- 5. Differential Geometry of Surfaces -- 1. The Structure Equations of Rn -- 2. Surfaces in R3 -- 3. Intrinsic Geometry of Surfaces -- 6. The Theorem of Gauss-Bonnet and the Theorem of Morse -- 1. The Theorem of Gauss-Bonnet -- 2. The Theorem of Morse -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-57951-6
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Differential Geometry . Mathematical analysis . Mathematical Methods in Physics . Mathematics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Carmo, Manfredo Perdigao do . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 516.36 .

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Differential Forms and Applications

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