《賦范向量空間上的微積分》是2016年世界圖書出版公司出版的著作，作者是Rodney、Coleman。
基本介紹
- 中文名：《賦范向量空間上的微積分》
- 作者：Rodney、Coleman
- 出版時間：2016年01月01日
- 出版社：世界圖書出版公司
內容簡介,目錄,
內容簡介
《賦范向量空間上的微積分（英文版）》適合高年級本科生或低迎拔霉年級研究生學習賦范向量空間上的微積分。書中不僅有成熟的數學模型，還有基礎的微積分和線性代數。在必要處對重要拓悼微定撲學和泛函分析也作了介紹。您海婚刪
為了講述賦范向量空間上的微積分在多變數函式基礎微積分上的套用，《賦乃疊應范向量空間上的微積分（英文版）》是為數不多的幾本能夠連線初級文本和高級文本道擊的汗趨槳戀教科書。書中穿插的該理論非平凡解的套用以及有趣的練習為讀者學習賦范向量空間上的微積分提供了動力。
目錄
Preface
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．詢蘭嬸7 Normed Algebras
1．8 The Exponential Mapping
Appendix： The Fundamental Theorem of Algebra
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： Gateaux Differentiability
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
4 Higher Derivatives and Differentials
4．1 Schwarz's Theorem
4．2 Operationson 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
5 Taylor Theorems and Applicahons
5．1 Taylor Formulas
5．2 Asymptotic Developments
5．3 Extrema： Second-Order Conditions
Appendix： Homogeneous Polynomials
6 Hilbert Spaces
6．1 Basic Notions
6．2 Projections
6．3 The Distance Mapping
6．4 The Riesz Representation Theorem
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
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
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
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
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-LagrangeEquations
11．5 Convexity
11．6 The Class of an Extremal
References
Index
4．6 Cartesian Product Image Spaces
4．7 Higher Partial Differentials
4．8 Generalizing Ck to Normed Vector Spaces
4．9 Leibniz's Rule
5 Taylor Theorems and Applicahons
5．1 Taylor Formulas
5．2 Asymptotic Developments
5．3 Extrema： Second-Order Conditions
Appendix： Homogeneous Polynomials
6 Hilbert Spaces
6．1 Basic Notions
6．2 Projections
6．3 The Distance Mapping
6．4 The Riesz Representation Theorem
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
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
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
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
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-LagrangeEquations
11．5 Convexity
11．6 The Class of an Extremal
References
Index
