UID:
almafu_9958067085002883
Umfang:
1 online resource (347 p.)
ISBN:
1-281-76650-X
,
9786611766504
,
0-08-087407-X
Serie:
Pure and applied mathematics ; 91
Inhalt:
Introduction to global analysis
Anmerkung:
Description based upon print version of record.
,
Front Cover; Introduction to Global Analysis; Copyright Page; Contents; Preface; Introduction; Chapter 1. Manifolds and Their Maps; Differentiable Manifolds and Their Maps; The Case of Euclidean Spaces; Power Series; Functions with Prescribed Properties; Norms; Germs and Jets; Problems and Projects; Chapter 2. Embeddings and Immersions of Manifolds; Some Important Examples; The Tangent Space; Existence of Embeddings and Immersions; Approximation of Smooth Mappings; Problems and Projects; Chapter 3. Critical Values, Sard's Theorem, and Transversality; Critical Points and Values
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Sard's Theorem Applications; Thom's Transversality Lemma; Problems and Projects; Chapter 4. Tangent Bundles, Vector Bundles, and Classification; Groups Acting on Spaces; The Tangent Bundle; Vector Bundles; Constructions with Vector Bundles; The Classification of Vector Bundles; Examples of Classifications; Problems and Projects; Chapter 5. Differentiation and Integration on Manifolds; Integration in Several Variables; Exterior Algebra and Forms; Integration on Manifolds; The Poincarè Lemma; Stokes' Theorem; Problems and Projects; Chapter 6. Differential Operators on Manifolds
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Differential Operators on Smooth BundlesRiemann Metrics and the Laplacian; Characterization of Linear Differential Operators; The Symbol; Ellipticity; Problems and Projects; Chapter 7. Infinite-Dimensional Manifolds; Topological Vector Spaces; Elements of Infinite-Dimensional Manifolds; Hilbert Manifolds; Partition of Unity; Function Spaces; The Unitary Group; Problems and Projects; Chapter 8. Morse Theory and Its Applications; Nondegenerate Critical Points; Homology and Morse Inequalities; Cell Decompositions from a Morse Function; Applications to Geodesics; Problems and Projects
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Chapter 9. Lie GroupsBasic Theory of Lie Groups; The Idea of Lie Algebras; The Exponential Map; Closed Subgroups of Lie Groups; Invariant Forms and Integration; Representations of Lie Groups; Lie Groups Acting on Manifolds; Problems and Projects; Chapter 10. Dynamical Systems; Transformation Groups; Invariant and Minimal Sets; Linear Differential Equations in Euclidean Space; Planar Flows: The Poincaè-Bendixson Theorem; Families of Subspaces; The Frobenius Theorem; Problems and Projects; Chapter 11. A Description of Singularities and Catastrophes; Singularities of Smooth Maps; Stability
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Finite Determination and CodimensionUnfoldings of Singularities; Elementary Catastrophes; Bibliography; Index
,
English
Weitere Ausg.:
ISBN 0-12-394050-8
Sprache:
Englisch
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