Preface
Introduction
List of Symbols
Part 3: Differentiation of Functions of Several Variables
1 Metric Spaces
2 Convergence and Continuity in Metric Spaces
3 More on Metric Spaces and Continuous Functions
4 Continuous Mappings Between Subsets of Euclidean Spaces
5 Partial Derivatives
6 The Differential of a Mapping
7 Curves in Rn
8 Surfaces in R3. A First Encounter
9 Taylor Formula and Local Extreme Values
10 Implicit Functions and the Inverse Mapping Theorem
11 Further Applications of the Derivatives
12 Curvilinear Coordinates
13 Convex Sets and Convex Functions in Rn
14 Spaces of Continuous Functions as Banach Spaces
15 Line Integrals
Part 4: Integration of Functions of Several Variables
16 Towards Volume Integrals in the Sense of Riemann
17 Parameter Dependent and Iterated Integrals
18 Volume Integrals on Hyper-Rectangles
19 Boundaries in Rn and Jordan Measurable Sets
20 Volume Integrals on Bounded Jordan Measurable Sets
21 The Transformation Theorem: Result and Applications
22 Improper Integrals and Parameter Dependent Integrals
Part 5: Vector Calculus
23 The Scope of Vector Calculus
24 The Area of a Surface in R3 and Surface Integrals
25 Gauss‘ Theorem in R3
26 Stokes’ Theorem in R2 and R3
27 Gauss’ Theorem for Rn
Appendices
Appendix I: Vector Spaces and Linear Mappings
Appendix II: Two Postponed Proofs of Part 3
Solutions to Problems of Part 3
Solutions to Problems of Part 4
Solutions to Problems of Part 5
References
Mathematicians Contributing to Analysis (Continued)
Subject Index
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