Real Functions
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Rational Approximation Of Real Functions
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Author : P. P. Petrushev
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-03
Rational Approximation Of Real Functions written by P. P. Petrushev 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 2011-03-03 with Mathematics categories.
This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
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.
Functions Of A Real Variable
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Functions Of A Real Variable written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
Differentiation Of Real Functions
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Author : A. M. Bruckner
language : en
Publisher: Springer
Release Date : 2006-11-15
Differentiation Of Real Functions written by A. M. Bruckner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Scenes From The History Of Real Functions
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Author : F.A. Medvedev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Scenes From The History Of Real Functions written by F.A. Medvedev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.
Real Functions
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Author : Brian S. Thomson
language : en
Publisher: Springer
Release Date : 2006-11-14
Real Functions written by Brian S. Thomson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Real Analysis
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Author : Miklós Laczkovich
language : en
Publisher: Springer
Release Date : 2015-10-08
Real Analysis written by Miklós Laczkovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
Symmetric Properties Of Real Functions
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Author : Brian thomson
language : en
Publisher: CRC Press
Release Date : 2020-08-25
Symmetric Properties Of Real Functions written by Brian thomson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-25 with Mathematics categories.
This work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.
Introduction To The Theory Of Analytic Functions
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Author : James Harkness
language : en
Publisher:
Release Date : 1898
Introduction To The Theory Of Analytic Functions written by James Harkness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1898 with Analytic functions categories.
The Calculus Of Complex Functions
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Author : William Johnston
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-01
The Calculus Of Complex Functions written by William Johnston and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.