Analysis on Manifolds

ISBN-10: 0201315963

ISBN-13: 9780201315967

Edition: 1991 (Revised)

Authors: James R. Munkres
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Book details

List price: $88.00
Copyright year: 1991
Publisher: Westview Press
Publication date: 7/7/1997
Binding: Paperback
Pages: 380
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.518
Language: English

Preface
The Algebra and Topology of R[superscript n]
Review of Linear Algebra
Matrix Inversion and Determinants
Review of Topology in R[superscript n]
Compact Subspaces and Connected Subspaces of R[superscript n]
Differentiation
The Derivative
Continuously Differentiable Functions
The Chain Rule
The Inverse Function Theorem
The Implicit Function Theorem
Integration
The Integral over a Rectangle
Existence of the Integral
Evaluation of the Integral
The Integral over a Bounded Set
Rectifiable Sets
Improper Integrals
Change of Variables
Partitions of Unity
The Change of Variables Theorem
Diffeomorphisms in R[superscript n]
Proof of the Change of Variables Theorem
Applications of Change of Variables
Manifolds
The Volume of a Parallelopiped
The Volume of a Parametrized-Manifold
Manifolds in R[superscript n]
The Boundary of a Manifold
Integrating a Scalar Function over a Manifold
Differential Forms
Multilinear Algebra
Alternating Tensors
The Wedge Product
Tangent Vectors and Differential Forms
The Differential Operator
Application to Vector and Scalar Fields
The Action of a Differentiable Map
Stokes' Theorem
Integrating Forms over Parametrized-Manifolds
Orientable Manifolds
Integrating Forms over Oriented Manifolds
A Geometric Interpretation of Forms and Integrals
The Generalized Stokes' Theorem
Applications to Vector Analysis
Closed Forms and Exact Forms
The Poincare Lemma
The deRham Groups of Punctured Euclidean Space
Epilogue--Life Outside R[superscript n]
Differentiable Manifolds and Riemannian Manifolds
Bibliography
Index
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