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Counterexamples on uniform convergence : sequences, series, functions, and integrals

Author: Andrei Bourchtein; Ludmila Bourchtein
Publisher: Hoboken, New Jersey : John Wiley & Sons, Inc., [2017]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents counterexamples to false statements typically found within the study of mathematical analysis, real analysis, and calculus, all of which are related to infinite sequences, series of functions, and functions and integrals depending on a parameter. --
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Genre/Form: Electronic books
Problems and exercises
Problems, exercises, etc
Additional Physical Format: Print version:
Bourchtein, Andrei.
Counterexamples on uniform convergence.
Hoboken, New Jersey : John Wiley & Sons, Inc., ©2017
(DLC) 2016038687
(OCoLC)957414461
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andrei Bourchtein; Ludmila Bourchtein
ISBN: 9781119303404 1119303400
OCLC Number: 969434882
Description: 1 online resource (xlix, 220 pages) : illustrations
Contents: Title Page ; Copyright Page ; Contents; Preface; List of Examples; List of Figures; About the CompanionWebsite; Introduction; I.1 Comments; I.1.1 On the Structure of This Book; I.1.2 OnMathematical Language and Notation; I.2 Background (Elements of Theory); I.2.1 Sequences of Functions; I.2.2 Series of Functions; I.2.3 Families of Functions; Chapter1 Conditions of Uniform Convergence; 1.1 Pointwise, Absolute, and Uniform Convergence. Convergence on a Set and Subset ; 1.2 Uniform Convergence of Sequences and Series of Squares and Products ; 1.3 Dirichlet's and Abel's Theorems; Exercises. Further ReadingChapter 2 Properties of the Limit Function: Boundedness, Limits, Continuity ; 2.1 Convergence and Boundedness; 2.2 Limits and Continuity of Limit Functions; 2.3 Conditions of Uniform Convergence. Dini's Theorem ; 2.4 Convergence and Uniform Continuity; Exercises; Further Reading; Chapter3 Properties of the Limit Function: Differentiability and Integrability ; 3.1 Differentiability of the Limit Function; 3.2 Integrability of the Limit Function; Exercises; Further Reading; Chapter 4 Integrals Depending on a Parameter; 4.1 Existence of the Limit and Continuity. 4.2 Differentiability4.3 Integrability; Exercises; Further Reading; Chapter 5 Improper Integrals Depending on a Parameter ; 5.1 Pointwise, Absolute, and Uniform Convergence; 5.2 Convergence of the Sum and Product; 5.3 Dirichlet's and Abel's Theorems; 5.4 Existence of the Limit and Continuity; 5.5 Differentiability; 5.6 Integrability; Exercises; Further Reading; Bibliography; Index.
Responsibility: Andrei Bourchtein, Ludmila Bourchtein.

Abstract:

This book presents counter examples to false statements typically found within the study of mathematical analysis, real analysis, and calculus, all of which are related to infinite sequences, series  Read more...

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"The features of the book include An overview of important concepts and theorems on uniform convergence, Well-organized coverage of the majority of the topics on uniform convergence studied in Read more...

 
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