天元基金影印數(shù)學(xué)叢書：實(shí)數(shù)學(xué)分析簡介，目錄書摘
2019-10-18 14:16
來源：京東
作者：京東
天元基金影印數(shù)學(xué)叢書：實(shí)數(shù)學(xué)分析
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內(nèi)容簡介: 作者Pugh在伯克利大學(xué)講授數(shù)學(xué)分析課程30多年之久的基礎(chǔ)上編寫而成，書中語言表述生動(dòng)活潑、通俗易懂，引用了很多有價(jià)值的例子以及來自Dieudonne，Littlewood和Osserman等幾位數(shù)學(xué)家的評(píng)論，還精心挑選了500多個(gè)精彩的練習(xí)題?！秾?shí)數(shù)學(xué)分析（影印版）》內(nèi)容包括實(shí)數(shù)、拓?fù)渲R(shí)初步、實(shí)變函數(shù)、函數(shù)空間、多元微積分、Lebesgue積分理論等，其中多元微積分的講法較為接近當(dāng)前數(shù)學(xué)界常用的語言，將會(huì)對(duì)我國數(shù)學(xué)分析的教學(xué)產(chǎn)生積極的影響。
作者簡介:
目錄:1 Real Numbers
1 Preliminaries
2 Cuts
3 Euclidean Space
4 Cardinality
5* Comparing Cardinalities
6* The Skeleton of Calculus
Exercises
2 A Taste of Topology
1 Metric Space Concepts
2 Compactness
3 Connectedness
4 Coverings
5 Cantor Sets
6* Cantor Set Lore
7* Completion
Exercises
3 Functions of a Real Variable
1 Differentiation
2 Riemann Integration
3 Series
Exercises
4 Function Spaces
1 Uniform Convergence and C0[a, b]
2 Power Series
3 Compactness and Equicontinuity in CO
4 Uniform Approximation in Co
5 Contractions and ODEs
6* Analytic Functions
7* Nowhere Differentiable Continuous Functions
8* Spaces of Unbounded Functions
Exercises
5 Multivariable Calculus
1 Linear Algebra
2 Derivatives
3 Higher derivatives
4 Smoothness Classes
5 Implicit and Inverse Functions
6* The Rank Theorem
7* Lagrange Multipliers
8 Multiple Integrals
9 Differential Forms
10 The General Stokes Formula
11* The Brouwer Fixed Point Theorem
Appendix A: Perorations of Dieudonne
Appendix B: The History of Cavalieris Principle
Appendix C: A Short Excursion into
the Complex Field
Appendix D: Polar Form
Appendix E: Determinants
Exercises
6 Lebesgue Theory
1 Outer measure
2 Measurability
3 Regularity
4 Lebesgue integrals
5 Lebesgue integrals as limits
6 Italian Measure Theory
7 Vitali coverings and density points
8 Lebesgues Fundamental Theorem of Calculus
9 Lebesgues Last Theorem
Appendix A: Translations and Nonmeasurable sets
Appendix B: The Banach-Tarski Paradox
Appendix C: Riemann integrals as undergraphs
Appendix D: Littlewoods Three Principles
Appendix E: Roundness
Appendix F: Money
Suggested Reading
Bibliography
Exercises
Index
1 Preliminaries
2 Cuts
3 Euclidean Space
4 Cardinality
5* Comparing Cardinalities
6* The Skeleton of Calculus
Exercises
2 A Taste of Topology
1 Metric Space Concepts
2 Compactness
3 Connectedness
4 Coverings
5 Cantor Sets
6* Cantor Set Lore
7* Completion
Exercises
3 Functions of a Real Variable
1 Differentiation
2 Riemann Integration
3 Series
Exercises
4 Function Spaces
1 Uniform Convergence and C0[a, b]
2 Power Series
3 Compactness and Equicontinuity in CO
4 Uniform Approximation in Co
5 Contractions and ODEs
6* Analytic Functions
7* Nowhere Differentiable Continuous Functions
8* Spaces of Unbounded Functions
Exercises
5 Multivariable Calculus
1 Linear Algebra
2 Derivatives
3 Higher derivatives
4 Smoothness Classes
5 Implicit and Inverse Functions
6* The Rank Theorem
7* Lagrange Multipliers
8 Multiple Integrals
9 Differential Forms
10 The General Stokes Formula
11* The Brouwer Fixed Point Theorem
Appendix A: Perorations of Dieudonne
Appendix B: The History of Cavalieris Principle
Appendix C: A Short Excursion into
the Complex Field
Appendix D: Polar Form
Appendix E: Determinants
Exercises
6 Lebesgue Theory
1 Outer measure
2 Measurability
3 Regularity
4 Lebesgue integrals
5 Lebesgue integrals as limits
6 Italian Measure Theory
7 Vitali coverings and density points
8 Lebesgues Fundamental Theorem of Calculus
9 Lebesgues Last Theorem
Appendix A: Translations and Nonmeasurable sets
Appendix B: The Banach-Tarski Paradox
Appendix C: Riemann integrals as undergraphs
Appendix D: Littlewoods Three Principles
Appendix E: Roundness
Appendix F: Money
Suggested Reading
Bibliography
Exercises
Index
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