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A Guide to Real Variables

Author: Steven G Krantz
Publisher: Cambridge : Cambridge University Press, 2012.
Series: Dolciani mathematical expositions.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Krantz, Steven G.
Guide to Real Variables.
Washington : Mathematical Association of America, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Steven G Krantz
ISBN: 9780883859162 0883859165
OCLC Number: 775428962
Notes: Title from publishers bibliographic system (viewed on 30 Jan 2012).
Description: 1 online resource.
Contents: ""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""; ""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""
Series Title: Dolciani mathematical expositions.
Responsibility: Steven G. Krantz.

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