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 編輯手記
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