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Multidimensional Real Analysis I Differentiation 1st Edition by JJ Duistermaat, JAC Kolk, JP van Braam Houckgeest ISBN 0511195583 9780521551144

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Multidimensional Real Analysis I Differentiation 1st Edition J.J. Duistermaat Digital Instant Download

Author(s): J.J. Duistermaat, J.A.C. Kolk; J.P. van Braam Houckgeest (Translator from Dutch)
ISBN(s): 9780521551144, 0511195583
Edition: 1
File Details: PDF, 5.50 MB
Year: 2004
Language: english
SKU: EB-2042564 Category: Tags: , ,

Multidimensional Real Analysis I Differentiation 1st Edition by JJ Duistermaat, JAC Kolk, JP van Braam Houckgeest – Ebook PDF Instant Download/Delivery: 0511195583, 9780521551144
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Product details:

ISBN 10: 0511195583 
ISBN 13: 9780521551144
Author: JJ Duistermaat, JAC Kolk, JP van Braam Houckgeest

Part one of the authors’ comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Multidimensional Real Analysis I Differentiation 1st Table of contents:

Chapter 1 Continuity
1.1 Inner product and norm
1.2 Open and closed sets
1.3 Limits and continuous mappings
1.4 Composition of mappings
1.5 Homeomorphisms
1.6 Completeness
1.7 Contractions
1.8 Compactness and uniform continuity
1.9 Connectedness
Chapter 2 Differentiation
2.1 Linear mappings
2.2 Differentiable mappings
2.3 Directional and partial derivatives
2.4 Chain rule
2.5 Mean Value Theorem
2.6 Gradient
2.7 Higher-order derivatives
2.8 Taylor?s formula
2.9 Critical points
2.10 Commuting limit operations
Chapter 3 Inverse Function and Implicit Function Theorems
3.1 Diffeomorphisms
3.2 Inverse Function Theorems
3.3 Applications of Inverse Function Theorems
3.4 Implicitly defined mappings
(A) The problem
(B) An idea about the solution
(C) Formula for the derivative of the solution
(D) The conditions are necessary
3.5 Implicit Function Theorem
3.6 Applications of the Implicit Function Theorem
3.7 Implicit and Inverse Function Theorems on C
Chapter 4 Manifolds
4.1 Introductory remarks
4.2 Manifolds
4.3 Immersion Theorem
4.4 Examples of immersions
4.5 Submersion Theorem
4.6 Examples of submersions
4.7 Equivalent definitions of manifold
4.8 Morse?s Lemma
Chapter 5 Tangent Spaces
5.1 Definition of tangent space
5.2 Tangent mapping
5.3 Examples of tangent spaces
5.4 Method of Lagrange multipliers
5.5 Applications of the method of multipliers
5.6 Closer investigation of critical points
5.7 Gaussian curvature of surface
5.8 Curvature and torsion of curve in R3
5.9 One-parameter groups and infinitesimal generators
5.10 Linear Lie groups and their Lie algebras
5.11 Transversality

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Tags: JJ Duistermaat, JAC Kolk, JP van Braam Houckgeest, Multidimensional Real Analysis