دانلود کتاب Calculus on Normed Vector Spaces

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Preface
Contents
Chapter
1 Normed Vector Spaces
1.1 First Notions
1.2 Limits and Continuity
1.3 Open and Closed Sets
1.4 Compactness
1.5 Banach Spaces
1.6 Linear and Polynomial Mappings
1.7 Normed Algebras
1.8 The Exponential Mapping
Appendix: The Fundamental Theorem of Algebra
Chapter
2 Differentiation
2.1 Directional Derivatives
2.2 The Differential
2.3 Differentials of Compositions
2.4 Mappings of Class C1
2.5 Extrema
2.6 Differentiability of the Norm
Appendix: Gâteaux Differentiability
Chapter
3 Mean Value Theorems
3.1 Generalizing the Mean Value Theorem
3.2 Partial Differentials
3.3 Integration
3.4 Differentiation under the Integral Sign
Chapter
4 Higher Derivatives and Differentials
4.1 Schwarz\'s Theorem
4.2 Operations on Ck-Mappings
4.3 Multilinear Mappings
4.4 Higher Differentials
4.5 Higher Differentials and Higher Derivatives
4.6 Cartesian Product Image Spaces
4.7 Higher Partial Differentials
4.8 Generalizing Ck to Normed Vector Spaces
4.9 Leibniz\'s Rule
Chapter
5 Taylor Theorems and Applications
5.1 Taylor Formulas
5.2 Asymptotic Developments
5.3 Extrema: Second-Order Conditions
Appendix: Homogeneous Polynomials
Chapter
6 Hilbert Spaces
6.1 Basic Notions
6.2 Projections
6.3 The Distance Mapping
6.4 The Riesz Representation Theorem
Chapter
7 Convex Functions
7.1 Preliminary Results
7.2 Continuity of Convex Functions
7.3 Differentiable Convex Functions
7.4 Extrema of Convex Functions
Appendix: Convex Polyhedra
Chapter
8 The Inverse and Implicit Mapping Theorems
8.1 The Inverse Mapping Theorem
8.2 The Implicit Mapping Theorem
8.3 The Rank Theorem
8.4 Constrained Extrema
Appendix 1: Bijective Continuous Linear Mappings
Appendix 2: Contractions
Chapter
9 Vector Fields
9.1 Existence of Integral Curves
9.2 Initial Conditions
9.3 Geometrical Properties of Integral Curves
9.4 Complete Vector Fields
Appendix: A Useful Result on Smooth Functions
Chapter
10 The Flow of a Vector Field
10.1 Continuity of the Flow
10.2 Differentiability of the Flow
10.3 Higher Differentiability of the Flow
10.4 The Reduced Flow
10.5 One-Parameter Subgroups
Chapter
11 The Calculus of Variations: An Introduction
11.1 The Space C1(I,E)
11.2 Lagrangian Mappings
11.3 Fixed Endpoint Problems
11.4 Euler–Lagrange Equations
11.5 Convexity
11.6 The Class of an Extremal
References
Index