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Surprises and Counterexamples in Real Function Theory

  • Book
  • © 2007

Overview

Authors:
  1. A. R. Rajwade

    1. Panjab University, Chandigarh, India

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    You can also search for this author in PubMed   Google Scholar

  2. A. K. Bhandari

    1. Panjab University, Chandigarh, India

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Texts and Readings in Mathematics (TRM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction to the real line ℝ and some of its subsets

    • A. R. Rajwade, A. K. Bhandari
    Pages 1-24

  3. Functions: pathological, peculiar and extraordinary

    • A. R. Rajwade, A. K. Bhandari
    Pages 25-55

  4. The famous everywhere continuous, nowhere differentiable functions: van der Waerden’s and others

    • A. R. Rajwade, A. K. Bhandari
    Pages 56-77

  5. Functions: continuous, periodic, locally recurrent and others

    • A. R. Rajwade, A. K. Bhandari
    Pages 78-110

  6. The Derivative and Higher Derivatives

    • A. R. Rajwade, A. K. Bhandari
    Pages 111-154

  7. Sequences, Harmonic Series, Alternating Series and Related Topics

    • A. R. Rajwade, A. K. Bhandari
    Pages 155-194

  8. The infinite exponential \({x^{{x^{{x^ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} }}}}}\) and Related Topics

    • A. R. Rajwade, A. K. Bhandari
    Pages 195-225

  9. Back Matter

    Pages 226-292
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About this book

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.

Authors and Affiliations

  • Panjab University, Chandigarh, India

    A. R. Rajwade, A. K. Bhandari

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