實分析（英文） [Real Analysis] epub pdf mobi txt 電子書 下載 2024

實分析（英文） [Real Analysis] epub pdf mobi txt 電子書 下載 2024

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實分析（英文） [Real Analysis] epub pdf mobi txt 電子書 下載 2024

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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☆☆☆☆☆

原版的 不錯

評分☆☆☆☆☆

大師的著作 我本科應該讀一下的

評分☆☆☆☆☆

和復分析是一套經典教材。。很不錯。

評分☆☆☆☆☆

英文版的書比較好，有些中文版的翻譯不行，這本書總體來說還是比較不錯的。

評分☆☆☆☆☆

一次買瞭4本，618有活動！太良心價瞭，非常滿意，謝謝京東！京東自營的書，質量有保證！

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棒棒棒棒棒棒棒棒棒棒棒棒棒棒棒棒

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優秀的書

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送到傢方便

評分☆☆☆☆☆

這本書後麵印刷有很大問題，懷疑不是正版

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