Analysis, manifolds, and physics / Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, and Margaret Dillard-Bleick.
Editor: Amsterdam : North Holland, 1977Descripción: xvii, 544 p. : il. ; 25 cmISBN: 0720404940Tema(s): Manifolds (Mathematics) | Mathematical physicsOtra clasificación: 58-01 (35-01 46-01)I. Review of fundamental notions of analysis (A: Set theory, definitions; B: Algebraic structures, definitions; C: Topology; D: Integration; E: Key theorems in linear functional analysis)II. Differential calculus on Banach spaces (A: Foundations; B: Calculus of variations; C: Implicit function theorem; inverse function theorem; D: Differential equations)III. Differentiable manifolds, finite-dimensional case (A: Definitions; B: Vector fields; tensor fields; C: Groups of transformations; D: Lie groups)IV. Integration on manifolds (A: Exterior differential forms; B: Integration; C: Exterior differential systems)V. Riemannian manifolds (A: The Riemannian structure; B: Connections; C: Geodesics)VI. Distributions (A: Test functions; B: Distributions; C: Sobolev spaces and partial differential equations)VII. Differentiable manifolds, infinite-dimensional case (A: Infinite-dimensional manifolds; B: Theory of degree; Leray-Schauder theory; C: Morse theory; D: Cylindrical measures, Wiener integral).
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Bibliografía: p. 521-526.
MR, 57 #7631
I. Review of fundamental notions of analysis (A: Set theory, definitions; B: Algebraic structures, definitions; C: Topology; D: Integration; E: Key theorems in linear functional analysis) -- II. Differential calculus on Banach spaces (A: Foundations; B: Calculus of variations; C: Implicit function theorem; inverse function theorem; D: Differential equations) -- III. Differentiable manifolds, finite-dimensional case (A: Definitions; B: Vector fields; tensor fields; C: Groups of transformations; D: Lie groups) -- IV. Integration on manifolds (A: Exterior differential forms; B: Integration; C: Exterior differential systems) -- V. Riemannian manifolds (A: The Riemannian structure; B: Connections; C: Geodesics) -- VI. Distributions (A: Test functions; B: Distributions; C: Sobolev spaces and partial differential equations) -- VII. Differentiable manifolds, infinite-dimensional case (A: Infinite-dimensional manifolds; B: Theory of degree; Leray-Schauder theory; C: Morse theory; D: Cylindrical measures, Wiener integral).
Véase también: Analysis, manifolds, and physics. Part II: 92 applications.
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