Analysis, manifolds, and physics - Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile; Dillard-Bleick, Margaret; Choquet-Bruhat, Yvonne (Amsterdam : North Holland, 1977)
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).
Bibliografía: p. 521-526.
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Véase también: Analysis, manifolds, and physics. Part II: 92 applications.
Keywords: Manifolds (Mathematics); Mathematical physics