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An Introduction to Analysis

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Author(s): Robert C. Gunning
Publisher: Princeton University Press
Year: 2018

Language: English

Contents
Preface
1 Algebraic Fundamentals
1.1 Sets and Numbers
1.2 Groups, Rings, and Fields
1.3 Vector Spaces
2 Topological Fundamentals
2.1 Normed Spaces
2.2 Metric Spaces
2.3 Topological Spaces
2.4 Compact Sets
3 Mappings
3.1 Continuous Mappings
3.2 Differentiable Mappings
3.3 Analytic Mappings
4 Linear Mappings
4.1 Endomorphisms
4.2 Inner Product Spaces
5 Geometry of Mappings
5.1 Inverse Mapping Theorem
5.2 Implicit Function Theorem
5.3 Rank Theorem
6 Integration
6.1 Riemann Integral
6.2 Calculation of Integrals
7 Differential Forms
7.1 Line Integrals
7.2 Differential Forms
7.3 Integrals of Differential Forms
Index
Index of Notation