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Surprises and counterexamples in real function theory

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 transcendenta...

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Detalles Bibliográficos
Autores principales: Rajwade, A R, Bhandari, A K
Lenguaje:eng
Publicado: Springer 2007
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-93-86279-35-4
http://cds.cern.ch/record/2272788
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author Rajwade, A R
Bhandari, A K
author_facet Rajwade, A R
Bhandari, A K
author_sort Rajwade, A R
collection CERN
description 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.
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spelling cern-22727882021-04-21T19:09:23Zdoi:10.1007/978-93-86279-35-4http://cds.cern.ch/record/2272788engRajwade, A RBhandari, A KSurprises and counterexamples in real function theoryMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:22727882007
spellingShingle Mathematical Physics and Mathematics
Rajwade, A R
Bhandari, A K
Surprises and counterexamples in real function theory
title Surprises and counterexamples in real function theory
title_full Surprises and counterexamples in real function theory
title_fullStr Surprises and counterexamples in real function theory
title_full_unstemmed Surprises and counterexamples in real function theory
title_short Surprises and counterexamples in real function theory
title_sort surprises and counterexamples in real function theory
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-93-86279-35-4
http://cds.cern.ch/record/2272788
work_keys_str_mv AT rajwadear surprisesandcounterexamplesinrealfunctiontheory
AT bhandariak surprisesandcounterexamplesinrealfunctiontheory