# Surprises and Counterexamples in Real Function Theory

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

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

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.

- DOI https://doi.org/10.1007/978-93-86279-35-4
- Copyright Information Hindustan Book Agency (India) 2007
- Publisher Name Hindustan Book Agency, Gurgaon
- eBook Packages Mathematics and Statistics
- Print ISBN 978-81-85931-71-5
- Online ISBN 978-93-86279-35-4
- Buy this book on publisher's site