主畫面 | 輔助說明 | 重新查詢 | English Mode 中研院圖書館首頁

```MARC 主機 00000nam a22004453i 4500
001    EBC3330367
003    MiAaPQ
005    20200713055353.0
006    m     o  d |
007    cr cnu||||||||
008    200713s2009    xx      o     ||||0 eng d
020    9780883859162|q(electronic bk.)
020    |z9780883853443
035    (MiAaPQ)EBC3330367
035    (Au-PeEL)EBL3330367
035    (CaPaEBR)ebr10728516
035    (OCoLC)929120456
040    MiAaPQ|beng|erda|epn|cMiAaPQ|dMiAaPQ
050  4 QA331.5 -- .K68 2009eb
082 0  515.8
100 1  Krantz, Steven G
245 10 Guide to Real Variables
264  1 Washington :|bAmerican Mathematical Society,|c2009
300    1 online resource (164 pages)
336    text|btxt|2rdacontent
337    computer|bc|2rdamedia
338    online resource|bcr|2rdacarrier
490 1  Dolciani Mathematical Expositions ;|vv.38
505 0  Intro -- Contents -- Preface -- 1  Basics -- 1.1 Sets --
1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations
on Functions -- 1.5 Number Systems -- 1.5.1 The Real
Numbers -- 1.6 Countable and Uncountable Sets -- 2
Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The
Definition and Convergence -- 2.1.2 The Cauchy Criterion -
- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle --
2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass
Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special
Sequences -- 3  Series -- 3.1 Introduction to Series --
3.1.1 The Definition and Convergence -- 3.1.2 Partial Sums
-- 3.2 Elementary Convergence Tests -- 3.2.1 The
Comparison Test -- 3.2.2 The Cauchy Condensation Test --
3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The
Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence --
3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts
-- 3.3.2 Abel's Test -- 3.3.3 Absolute and Conditional
Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some
Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other
Representations for e -- 3.4.3 Sums of Powers -- 3.5
Operations on Series -- 3.5.1 Sums and Scalar Products of
Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy
Product -- 4  The Topology of the Real Line -- 4.1 Open
and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets --
4.1.3 Characterization of Open and Closed Sets in Terms of
Sequences -- 4.1.4 Further Properties of Open and Closed
Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior
Points and Isolated Points -- 4.2.2 Accumulation Points --
4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction
-- 4.4.2 The Heine-Borel Theorem -- 4.4.3 The Topological
Characterization of Compactness -- 4.5 The Cantor Set --
4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity
-- 4.7 Perfect Sets -- 5  Limits and the Continuity of
Functions
505 8  5.1 Definitions and Basic Properties -- 5.1.1 Limits --
5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of
Limits -- 5.1.4 Properties of Limits -- 5.1.5
Characterization of Limits Using Sequences -- 5.2
Continuous Functions -- 5.2.1 Continuity at a Point --
5.2.2 The Topological Approach to Continuity -- 5.3
Topological Properties and Continuity -- 5.3.1 The Image
of a Function -- 5.3.2 Uniform Continuity -- 5.3.3
Continuity and Connectedness -- 5.3.4 The Intermediate
Value Property -- 5.4 Monotonicity and Classifying
Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2
Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6
The Derivative -- 6.1 The Concept of Derivative -- 6.1.1
The Definition -- 6.1.2 Properties of the Derivative --
6.1.3 The Weierstrass Nowhere Differentiable Function --
6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and
Applications -- 6.2.1 Local Maxima and Minima -- 6.2.2
Fermat's Test -- 6.2.3 Darboux's Theorem -- 6.2.4 The Mean
Value Theorem -- 6.2.5 Examples of the Mean Value Theorem
-- 6.3 Further Results on the Theory of Differentiation --
6.3.1 l'Hopital's Rule -- 6.3.2 Derivative of an Inverse
Function -- 6.3.3 Higher Derivatives -- 6.3.4 Continuous
Differentiability -- 7  The Integral -- 7.1 The Concept of
Integral -- 7.1.1 Partitions -- 7.1.2 Refinements of
Partitions -- 7.1.3 Existence of the Riemann Integral --
7.1.4 Integrability of Continuous Functions -- 7.2
Properties of the Riemann Integral -- 7.2.1 Existence
Theorems -- 7.2.2 Inequalities for Integrals -- 7.2.3
Preservation of Integrable Functions Under Composition --
7.2.4 The Fundamental Theorem of Calculus -- 7.2.5 Mean
Value Theorems -- 7.3 Further Results on the Riemann
Integral -- 7.3.1 The Riemann-Stieltjes Integral -- 7.3.2
Riemann's Lemma -- 7.4 Advanced Results on Integration
Theory
505 8  7.4.1 Existence for the Riemann-Stieltjes Integral --
7.4.2 Integration by Parts -- 7.4.3 Linearity Properties -
- 7.4.4 Bounded Variation -- 8  Sequences and Series of
Functions -- 8.1 Partial Sums and Pointwise Convergence --
8.1.1 Sequences of Functions -- 8.1.2 Uniform Convergence
-- 8.2 More on Uniform Convergence -- 8.2.1 Commutation of
Limits -- 8.2.2 The Uniform Cauchy Condition -- 8.2.3
Limits of Derivatives -- 8.3 Series of Functions -- 8.3.1
Series and Partial Sums -- 8.3.2 Uniform Convergence of a
Series -- 8.3.3 The Weierstrass M-Test -- 8.4 The
Weierstrass Approximation Theorem -- 8.4.1 Weierstrass's
Main Result -- 9  Advanced Topics -- 9.1 Metric Spaces --
9.1.1 The Concept of a Metric -- 9.1.2 Examples of Metric
Spaces -- 9.1.3 Convergence in a Metric Space -- 9.1.4 The
Cauchy Criterion -- 9.1.5 Completeness -- 9.1.6 Isolated
Points -- 9.2 Topology in a Metric Space -- 9.2.1 Balls in
a Metric Space -- 9.2.2 Accumulation Points -- 9.2.3
Compactness -- 9.3 The Baire Category Theorem -- 9.3.1
Density -- 9.3.2 Closure -- 9.3.3 Baire's Theorem -- 9.4
The Ascoli-Arzela Theorem -- 9.4.1 Equicontinuity -- 9.4.2
Equiboundedness -- 9.4.3 The Ascoli-Arzela Theorem --
Glossary of Terms from Real Variable Theory --
Bibliography -- Index -- About the Author
588    Description based on publisher supplied metadata and other
sources
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest
Ebook Central, 2020. Available via World Wide Web. Access
may be limited to ProQuest Ebook Central affiliated
libraries
650  0 Functions of real variables
655  4 Electronic books
776 08 |iPrint version:|aKrantz, Steven G.|tGuide to Real
Variables|dWashington : American Mathematical Society,
c2009|z9780883853443
830  0 Dolciani Mathematical Expositions
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
detail.action?docID=3330367|zClick to View
```

 主畫面 | 輔助說明 | English Mode