04636nam 22007095 450 991048071580332120200706022631.03-642-57951-510.1007/978-3-642-57951-6(CKB)3400000000104358(SSID)ssj0000805847(PQKBManifestationID)11458114(PQKBTitleCode)TC0000805847(PQKBWorkID)10841528(PQKB)11774836(DE-He213)978-3-642-57951-6(MiAaPQ)EBC3089646(PPN)23791946X(EXLCZ)99340000000010435820121227d1994 u| 0engurnn|008mamaatxtccrDifferential Forms and Applications[electronic resource] /by Manfredo P. Do Carmo1st ed. 1994.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1994.1 online resource (X, 118 p.) Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph3-540-57618-5 Includes bibliographical references (page 115) and index.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.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.Universitext,0172-5939Differential geometryMathematical analysisAnalysis (Mathematics)Mathematical physicsPhysicsDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Theoretical, Mathematical and Computational Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19005Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Numerical and Computational Physics, Simulationhttps://scigraph.springernature.com/ontologies/product-market-codes/P19021Differential geometry.Mathematical analysis.Analysis (Mathematics).Mathematical physics.Physics.Differential Geometry.Analysis.Theoretical, Mathematical and Computational Physics.Mathematical Methods in Physics.Numerical and Computational Physics, Simulation.515/.37Do Carmo Manfredo Pauthttp://id.loc.gov/vocabulary/relators/aut912565BOOK9910480715803321Differential Forms and Applications2043853UNINA