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分析學引論:英文 版權(quán)信息
- ISBN：9787560391939
- 條形碼：9787560391939 ; 978-7-5603-9193-9
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>
分析學引論:英文 內(nèi)容簡介
本書是分析學的**門課程，全書共九章內(nèi)容，包含實數(shù)、微分法、積分法、函數(shù)序列、度量空間與歐幾里得空間、高維微分法、高維積分法、曲線與曲面、微分形式等內(nèi)容。本書試圖用一種從一個問題開始，并進行逐步分析的闡述形式，*終回答這個問題，并引入相關(guān)的定義、論據(jù)、猜想和例子。本書適合高等院校師生、研究人員及數(shù)學愛好者參考閱讀。
分析學引論:英文 目錄
Preface
1 The Real Numbers
1.1 Sets and Functions
1.2 The Real Numbers
1.3 Convergence
1.4 Series
1.5 Countable and Uncountable Sets
1.6 Open Sets and Closed Sets
1.7 Continuous Functions
1.8 Trigonometric Functions
2 Differentiation
2.1 Limits
2,2 The Derivative
2.3 The Sign of the Derivative
2.4 Critical Points
2.5 Some Applications
3 Integration
3.1 The Riemann Integral
3.2 The Fundamental Theorem of Calculus
3.3 The Logarithm and Exponential Functions
3.4 Improper Integrals
3.5 Sets of Measure Zero and Integrability
3.6 The Riemann-Stieltjes Integral
4 Sequences of Functions
4.1 Uniform Convergence
4.2 Power Series
5 Metric and Euclidean Spaces
5.1 Definitions and Examples
5.2 Sequences and Completeness
5.3 Open and Closed Sets
5.4 Continuity
5.5 Compactness
5.6 Connectedness
5.7 The Space of Continuous Functions
6 Differentiation in Higher Dimensions
6.1 Vector-valued Functions
6.2 Differentiable Functions, Part 1
6.3 0rthogonality
6.4 Linear Transformations
6.5 Differentiable Functions, Part 2
6.6 Critical Points
6.7 Tangent Planes
6.8 Inverse Function Theorem
6.9 Implicit Function Theorem
6.10 Lagrange Multipliers
7 Integration in Higher Dimensions
7.1 Integration of Vector-valued Functions
7.2 The Riemann Integral
7.3 Iterated Integration
7.4 Change of Variables
7.5 Differentiation under the Integral Sign
8 Curves and Surfaces
8.1 Curves
8.2 Green's Theorem
8.3 Surfaces
8.4 Integration on Surfaces
8.5 The Theorems of Gauss and Stokes
9 Differential Forms
9.1 Introduction
9.2 Change of Variables for Forms
9.3 Simplexes and Chains
9.4 Oriented Boundaries
9.5 Stokes's Theorem
9.6 Closed and Exact Forms
9.7 Denouement
Bibliography
Index of Terms
Index of Symbols
編輯手記
1 The Real Numbers
1.1 Sets and Functions
1.2 The Real Numbers
1.3 Convergence
1.4 Series
1.5 Countable and Uncountable Sets
1.6 Open Sets and Closed Sets
1.7 Continuous Functions
1.8 Trigonometric Functions
2 Differentiation
2.1 Limits
2,2 The Derivative
2.3 The Sign of the Derivative
2.4 Critical Points
2.5 Some Applications
3 Integration
3.1 The Riemann Integral
3.2 The Fundamental Theorem of Calculus
3.3 The Logarithm and Exponential Functions
3.4 Improper Integrals
3.5 Sets of Measure Zero and Integrability
3.6 The Riemann-Stieltjes Integral
4 Sequences of Functions
4.1 Uniform Convergence
4.2 Power Series
5 Metric and Euclidean Spaces
5.1 Definitions and Examples
5.2 Sequences and Completeness
5.3 Open and Closed Sets
5.4 Continuity
5.5 Compactness
5.6 Connectedness
5.7 The Space of Continuous Functions
6 Differentiation in Higher Dimensions
6.1 Vector-valued Functions
6.2 Differentiable Functions, Part 1
6.3 0rthogonality
6.4 Linear Transformations
6.5 Differentiable Functions, Part 2
6.6 Critical Points
6.7 Tangent Planes
6.8 Inverse Function Theorem
6.9 Implicit Function Theorem
6.10 Lagrange Multipliers
7 Integration in Higher Dimensions
7.1 Integration of Vector-valued Functions
7.2 The Riemann Integral
7.3 Iterated Integration
7.4 Change of Variables
7.5 Differentiation under the Integral Sign
8 Curves and Surfaces
8.1 Curves
8.2 Green's Theorem
8.3 Surfaces
8.4 Integration on Surfaces
8.5 The Theorems of Gauss and Stokes
9 Differential Forms
9.1 Introduction
9.2 Change of Variables for Forms
9.3 Simplexes and Chains
9.4 Oriented Boundaries
9.5 Stokes's Theorem
9.6 Closed and Exact Forms
9.7 Denouement
Bibliography
Index of Terms
Index of Symbols
編輯手記
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