Analysis, manifolds, and physics
Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, and Margaret Dillard-Bleick.
Amsterdam : North Holland, 1977.
xvii, 544 págs. : ilustraciones ; 25 cm.
ISBN: 0720404940
Véase también: Analysis, manifolds, and physics. Part II: 92 applications.
Bibliografía: p. 521-526.
Reseña: MathSciNet, 57 #7631
Contenido
- 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).