Continuous Nowhere Differentiable Functions
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Continuous Nowhere Differentiable Functions
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Author : Marek Jarnicki
language : en
Publisher: Springer
Release Date : 2018-03-31
Continuous Nowhere Differentiable Functions written by Marek Jarnicki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-31 with Mathematics categories.
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function. For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of symbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.
Surprises And Counterexamples In Real Function Theory
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Author : A. R. Rajwade
language : en
Publisher: Springer
Release Date : 2007-01-15
Surprises And Counterexamples In Real Function Theory written by A. R. Rajwade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-15 with Mathematics categories.
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.
Continuous Nowhere Differentiable Functions
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Author : Marek Jarnicki
language : en
Publisher: Springer
Release Date : 2015-12-30
Continuous Nowhere Differentiable Functions written by Marek Jarnicki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-30 with Mathematics categories.
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function. For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of symbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.
Classics On Fractals
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Author : Gerald A. Edgar
language : en
Publisher: CRC Press
Release Date : 2019-03-08
Classics On Fractals written by Gerald A. Edgar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-08 with Science categories.
Read the masters! Experience has shown that this is good advice for the serious mathematics student. This book contains a selection of the classical mathematical papers related to fractal geometry. For the convenience of the student or scholar wishing to learn about fractal geometry, nineteen of these papers are collected here in one place. Twelve of the nineteen have been translated into English from German, French, or Russian. In many branches of science, the work of previous generations is of interest only for historical reasons. This is much less so in mathematics.1 Modern-day mathematicians can learn (and even find good ideas) by reading the best of the papers of bygone years. In preparing this volume, I was surprised by many of the ideas that come up.
Counterexamples In Analysis
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Author : Bernard R. Gelbaum
language : en
Publisher: Courier Corporation
Release Date : 2003-06-04
Counterexamples In Analysis written by Bernard R. Gelbaum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-04 with Mathematics categories.
These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
A Second Course On Real Functions
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Author : A. C. M. van Rooij
language : en
Publisher: Cambridge University Press
Release Date : 1982-03-25
A Second Course On Real Functions written by A. C. M. van Rooij and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-25 with Mathematics categories.
When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
Continuous Nowhere Differentiable Functions
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Author : Elaina Loréal Blanks
language : en
Publisher:
Release Date : 2000
Continuous Nowhere Differentiable Functions written by Elaina Loréal Blanks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Continuous Nowhere Differentiable Functions
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Author :
language : en
Publisher:
Release Date : 2003
Continuous Nowhere Differentiable Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Strange Functions In Real Analysis Second Edition
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Author : A.B. Kharazishvili
language : en
Publisher: CRC Press
Release Date : 2000-01-31
Strange Functions In Real Analysis Second Edition written by A.B. Kharazishvili and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-31 with Mathematics categories.
This volume aims to explicate extraordinary functions in real analysis and their applications. It examines the Baire category method, the Zermelo-Fraenkel set, the Axiom of Dependent Choices, Cantor and Peano type functions, the Continuum Hypothesis, everywhere differentiable nowhere monotone functions, and Jarnik's nowhere approximately differentiable functions.
Separately Analytic Functions
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Author : Marek Jarnicki
language : en
Publisher: JP Medical Ltd
Release Date : 2011
Separately Analytic Functions written by Marek Jarnicki and has been published by JP Medical Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The story of separately holomorphic functions began about 100 years ago. During the second half of the 19th century, it became known that a separately continuous function is not necessarily continuous as a function of all variables. At the beginning of the 20th century, the study of separately holomorphic functions started due to the fundamental work of Osgood and Hartogs. This book provides the first self-contained and complete presentation of the study of separately holomorphic functions, from its beginnings to current research. Most of the results presented have never been published before in book form. The text is divided into two parts. The first part deals with separately holomorphic functions, ``without singularities''. The second part addresses the situation of existing singularities. A discussion of the classical results related to separately holomorphic functions leads to the most fundamental result, the classical cross theorem as well as various extensions and generalizations, to more complicated ``crosses''. Additionally, several applications for other classes of ``separately regular'' functions are given. A solid background in basic complex analysis is a prerequisite. To make the book self contained, all the results are collected in special introductory chapters and referred to at the beginning of each section. This book is addressed to students and researchers in several complex variables as well as mathematicians and theoretical physicists interested in this area of mathematics.