A Second Course On Real Functions
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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.
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.
A Primer Of Real Functions
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Author : Ralph P. Boas
language : en
Publisher: Cambridge University Press
Release Date : 1996
A Primer Of Real Functions written by Ralph P. Boas 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 1996 with Mathematics categories.
This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.
An Introduction To The Theory Of Real Functions
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Author : Stanislaw Lojasiewicz
language : en
Publisher:
Release Date : 1988-08-18
An Introduction To The Theory Of Real Functions written by Stanislaw Lojasiewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08-18 with Mathematics categories.
A concise, classical approach to the theory of real functions, set in the topological context of metric spaces. Newly translated by G. H. Lawden of the Univ. of Sussex and expanded from the earlier Polish editions to include remarks on the extension of finitely many additive functions to a measure, construction of a continuous, non-differential function of a general type, the Banach-Vitali theorem, and Stepanov's theorem. Prerequisites are set theory, topology, and calculus.
A First Course In Real Analysis
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Author : M.H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Real Analysis written by M.H. Protter 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 2012-12-06 with Mathematics categories.
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
The Theory Of Functions Of Real Variables
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Author : Lawrence M Graves
language : en
Publisher: Courier Corporation
Release Date : 2012-01-27
The Theory Of Functions Of Real Variables written by Lawrence M Graves and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-27 with Mathematics categories.
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Calculus Deconstructed
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Author : Zbigniew H. Nitecki
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-11
Calculus Deconstructed written by Zbigniew H. Nitecki 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 2022-01-11 with Mathematics categories.
Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.
Real And Abstract Analysis
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Author : E. Hewitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Real And Abstract Analysis written by E. Hewitt 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 2012-12-06 with Mathematics categories.
This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with appro priate suggestions for skipping. We have given complete definitions, ex planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in TOM M. ApOSTOL'S Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], or WALTER RUDIN'S Principles of M athe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].
Symmetric Properties Of Real Functions
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Author : Brian thomson
language : en
Publisher: CRC Press
Release Date : 1994-06-10
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 1994-06-10 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.
A Second Course In Calculus
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Author : Harley Flanders
language : en
Publisher:
Release Date : 1974-01-01
A Second Course In Calculus written by Harley Flanders and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Calculus categories.
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.