內容簡介
《實分析(英文)》在Princeton大學使用,同時在其它學校,比如UCLA等名校也在本科生教學中得到使用。其教學目的是,用統一的、聯係的觀點來把現代分析的“核心”內容教給本科生,力圖使本科生的分析學課程能接上現代數學研究的脈絡。
內頁插圖
目錄
Foreword
Introduction
1 Fourier series: completion
2 Limits of continuous functions
3 Length of curves
4 Differentiation and integration
5 The problem of measure
Chapter 1. Measure Theory
1 Prelhninaries
2 The exterior measure
3 Measurable sets and the Lebesgue measure
4 Measurable functions
4.1 Definition and basic properties
4.2 Approximation by simple functions or step functions
4.3 Littlewood's three principles
5 The Brunn-Minkowski inequality
6 Exercises
7 Problems
Chapter 2. Integration Theory
1 The Lebesgue integral: basic properties and convergence theorems
2 The space L1 ofintegrable functions
3 Fubini's theorem
3.1 Statement and proof of the theorem
3.2 Applications of Fubini's theorem
4* A Fourier inversion formula
5 Exercises
6 Problems
Chapter 3. Differentiation and Integration
1 Differentiation of the integral
1.1 The Hardy-Littlewood maximal function
1.2 The Lebesgue differentiation theorem
2 Good kernels and approximations to the identity
3 Differentiability of functions
3.1 Functions of bounded variation
3.2 Absolutely continuous functions
3.3 Differentiability ofjump functions
4 Rectifiable curves and the isoperimetric inequality
4.1 Minkowski content of a curve
4.2 Isoperimetric inequality
5 Exercises
6 Problems
Chapter 4. Hilbert Spaces: An Introduction
1 The Hilbert space L2
2 Hilbert spaces
2.1 Orthogonality
2.2 Unitary mappings
2.3 Pre-Hilbert spaces
3 Fourier series and Fatou's theorem
3.1 Fatou's theorem
4 Closed subspaces and orthogonal projections
5 Linear transformations
5.1 Linear functionals and the Riesz representation theorem
5.2 Adjoints
5.3 Examples
6 Compact operators
7 Exercises
8 Problems
Chapter 5. Hilbert Spaces: Several Examples
1 The Fourier transform on L2
2 The Hardy space of the upper half-plane
3 Constant coefficient partial differential equations
3.1 Weaak solutions
3.2 The main theorem and key estimate
4 The Dirichlet principle
4.1 Harmonic functions
4.2 The boundary value problem and Dirichlet's principle
5 Exercises
6 Problems
Chapter 6. Abstract Measure and Integration Theory
Chapter 7. Hausdorff Measure and Fractals
Notes and References
Bibliography
Symbol Glossary
Index
前言/序言
實分析(英文) [Real Analysis] epub pdf mobi txt 電子書 下載 2024
實分析(英文) [Real Analysis] 下載 epub mobi pdf txt 電子書
評分
☆☆☆☆☆
大師之作,值得一讀,尤其數學係的學生更應該認真學學
評分
☆☆☆☆☆
商品非常好,物流速度非常快,派送服務非常好,非常滿意,值得信賴
評分
☆☆☆☆☆
大師之作,值得一讀,尤其數學係的學生更應該認真學學
評分
☆☆☆☆☆
好書,好書,好書,函數。好書。
評分
☆☆☆☆☆
《實分析(英文)》在Princeton大學使用,同時在其它學校,比如UCLA等名校也在本科生教學中得到使用。其教學目的是,用統一的、聯係的觀點來把現代分析的“核心”內容教給本科生,力圖使本科生的分析學課程能接上現代數學研究的脈絡。
評分
☆☆☆☆☆
經典教材之一瞭,用統一的、聯係的觀點來把現代分析的“核心”內容使本科生的分析學課程能接上現代數學研究的脈絡。
評分
☆☆☆☆☆
不錯的一本書,值得推薦購買
評分
☆☆☆☆☆
《實分析(英文)》在Princeton大學使用,同時在其它學校,比如UCLA等名校也在本科生教學中得到使用。其教學目的是,用統一的、聯係的觀點來把現代分析的“核心”內容教給本科生,力圖使本科生的分析學課程能接上現代數學研究的脈絡。
評分
☆☆☆☆☆
stein大師的實分析當然是灰常吼的呀!