| Description |
1 online resource (viii, 290 pages) : illustrations |
| Series |
Texts and readings in mathematics ; 42 |
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Texts and readings in mathematics ; 42.
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| Contents |
Introduction to the real line R and some of its subsets -- Functions : pathological, peculiar, and extraordinary -- Famous everywhere continuous, nowhere differentiable functions : van der Waerden's and others -- Functions : continuous, periodic, locally recurrent, and others -- The derivative and higher derivatives -- Sequences, harmonic series, alternating series, and related results -- The infinite exponential and related results |
| Summary |
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis. Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II. This book will be useful for students and teachers alike |
| Bibliography |
Includes bibliographical references (pages 281-288) and index |
| Notes |
Print version record |
| Subject |
Functions of real variables.
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Mathematical analysis.
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Functions of real variables.
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Mathematical analysis.
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Gegenbeispiel
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Reelle Funktion
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| Form |
Electronic book
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| Author |
Bhandari, A. K. (Ashwani K.)
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| ISBN |
9789386279354 |
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9386279355 |
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8185931712 |
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9788185931715 |
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