《實分析引論（英文版）（原書第2版）》是2008年3月機械工業出版社出版的圖書，作者是（美）Manfred、Stoll。
基本介紹
- 中文名：實分析引論（英文版）（原書第2版）
- 作者：（美）Manfred、Stoll
- ISBN：7111147472
- 定價：55元
- 出版社：機械工業出版社
- 出版時間：2008年3月
- 裝幀：平裝
- 開本：16開
內容簡介,圖書目錄,
內容簡介
《實分析引論（英文版）（原書第2版）》內容豐富，既包括了數學分析和實變函式的基本內容，又有近代數學中最基礎的概念和方法。但又具有很強的可讀性，對於概念的講述注意從簡單到複雜，從一般到特殊，基礎內容和較深入的研究性問題兼顧。
圖書目錄
出版說明
序
PREFACE
T0 THE STUDENT
1 The Real Number System
1．1 Sets and Operations on Sets
1．2 Functions
1．3 MathematicaIInduction
1．4 The Least Upper Bound Property
1．5 Consequences of the Least upper Bound Propety
1．6 Binary and rernarv Expansions
1．7 Countable and Uncountable Sets
Notes
Miscellaneous Exercises
Supplemental Reading
2 Sequences of Real Numbers
2．1 Convergent Sequences
2．2 Limit Theorems
2．3 Monotone Sequences
2．4 Subsequences and the Bolzano-Weierstrass Theorem
2．5 Limit Superior and fnferior of a Sequence
2．6 Cauchy Sequences
2．7 Series of ReaI Numbers
Notes
Miscellaneous Exercises
Supplemental Reading
3 Structure of Point Sets
3．1 Open and Closed Sets
3．2 Compact Sets
3．3 The Cantor Set
Notes
Miscellaneous Exercises
Supplemental Reading
4 Limits and Continuity
4．1 Limit of a Function
4．2 Continuous Functions
4．3 Uniform Continuity
4．4 Monotone Functions and Discontjnuities
Notes
Miscellaneous Exercises
Supplemental Reading
5 Differentiation
5．1 The Derivative
5．2 The Mean Value Theorem
5．3 L#Hospital#s Rule
5．4 Newton#s Method
Notes
Miscellaneous Exercises
Supplemental Reading
6 The Riemann and Riemann—Stieltjes Integral
6．1 The Riemann Integral
6．2 Properties of the Riemann IntegraI
6．3 Fundamental Theorem of Calculus
6．4 Improper Riemann Integrals
6．5 The Riemann-Stieltjes Integral
6．6 Numerical Methods
6．7 Proof of Lebesque#s Theorem
Notes
Miscellaneous Exercises
Supplemental Reading
7 Series of Real Numbers
7．1 Convergence Tests
7．2 The Dirichlet Test
7．3 Absolute and Conditional Convergence
7．4 Square Summable Sequences
Notes
Miscellaneous Exercises
Supplemental Reading
8 Sequences and Series of Functions
8．1 Pointwise Convergence and Interchange of Limits
8．2 Uniform Convergence
8．3 Uniform Convergence and Continuity
8．4 Uniform Convergence and Integration
8．5 Uniform Convergence and Differentiation
8．6 The Weierstrass Approximation Theorem
8．7 Power Series Expansions
8．8 The Gamma Function
Notes
Miscellaneous Exercises
Supplemental Reading
9 Orthogonal Functions and Fourier Series
9．1 Orthogonal Functions
9．2 Completeness and Parseval#s Equality
9．3 Trigonometric and Fourier Series 394
9．4 Convergence in the Mean of Fourier Series
9．5 Pointwise Convergence of Fourier Series
Notes
Miscellaneous Exercises
Supplemental Reading
10 Lebesgue Measure and Integration
10．1 Introduction to Measure
10．2 Measure of Open Sets:Compact Sets
10．3 Inner and Outer Measure:Measurable Sets
10．4 Properties of Measurable Sets
10．5 Measurable Functions
10．6 The Lebesgue Integral of a Bounded Function
10．7 The General Lebesgue Integral
10．8 Square Integrable Functions
Notes
Miscellaneous Exercises
Supplemental Reading
APPENDIX：Logic and Proofs
A．1 Propositions and Connectives
A．2 Rules of Inference
A．3 Mathematical Proofs
A．4 Use of Quantifiers
Supplemental Reading
Bibliography
Hints and Solutions to Selected Exercises
Notation Index
Index
教輔材料申請表
