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Author : Wiesława J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 55,5 Mb
Release : 2000
Category : MATHEMATICS
ISBN : 9780821820506
Solutions for all the problems are provided."--BOOK JACKET.
Author : Biler
Publisher : Routledge
Page : 232 pages
File Size : 44,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351421454
Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen
Author : Wieslawa J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 53,8 Mb
Release : 2000
Category : Mathematical analysis
ISBN : 0821884433
Author : Keith Hirst
Publisher : Elsevier
Page : 208 pages
File Size : 51,8 Mb
Release : 1994-12-08
Category : Mathematics
ISBN : 9780080928586
Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.
Author : Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 48,7 Mb
Release : 2009-05-29
Category : Mathematics
ISBN : 9780387773780
Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
Author : Derek G. Ball
Publisher : Elsevier
Page : 324 pages
File Size : 53,8 Mb
Release : 2014-05-17
Category : Mathematics
ISBN : 9781483158969
An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.
Author : Asuman G. Aksoy,Mohamed A. Khamsi
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 45,8 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9781441912961
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
Author : Tomasz Radożycki
Publisher : Springer Nature
Page : 375 pages
File Size : 42,5 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9783030358440
This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
Author : R. P. Burn
Publisher : Cambridge University Press
Page : 384 pages
File Size : 44,7 Mb
Release : 2000-08-28
Category : Mathematics
ISBN : 0521788366
This work should aid students in the transition from studying calculus in schools to studying mathematical analysis at university. It helps them tackle a sequence of problems to concepts, definitions and proofs of classical real analysis.
Author : Wiesława J. Kaczor,Maria T. Nowak
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 54,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821884478
This is the sequel to Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (Volume 4 in the AMS series, the Student Mathematical Library). As in the first volume, this book is divided into two parts. The first is a collection of exercises and problems, and the second contains their solutions. The book mainly deals with real functions of one real variable. Topics include: properties of continuous functions, intermediate value property, uniform continuity, meanvalue theorems, Taylor's formula, convex functions, sequences and series of functions.The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of material is designed to help student comprehension, to encourage them to ask their own questions, and to start research.The collection of problems in the book will alsohelp teachers who wish to incorporate problems into their lectures. Solutions for most problems are provided.
Author : Asuman Güven Aksoy,Mohamed A. Khamsi
Publisher : Unknown
Page : 268 pages
File Size : 42,6 Mb
Release : 2010-11
Category : Mathematical analysis
ISBN : 1441913114
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis. Prerequisites for the reader are a robust understanding of calculus and linear algebra.
Author : John F. Randolph
Publisher : Elsevier
Page : 526 pages
File Size : 54,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483272757
Basic Real and Abstract Analysis focuses on the processes, methodologies, and approaches involved in the process of abstraction of mathematical problems. The book first offers information on orientation and sets and spaces, including equivalent and infinite sets, metric spaces, cardinals, distance and relative properties, real numbers, and absolute value and inequalities. The text then takes a look at sequences and series and measure and integration. Topics include rings and additivity, Lebesgue integration, outer measures and measurability, extended real number system, sequences in metric spaces, and series of real numbers. The publication ponders on measure theory, continuity, derivatives, and Stieltjes integrals. Discussions focus on integrators of bounded variation, Lebesgue integral relations, exponents and logarithms, bounded variation, mean values, trigonometry, and Fourier series. The manuscript is a valuable reference for mathematicians and researchers interested in the process of abstraction of mathematical equations.
Author : Charles H.C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer
Page : 476 pages
File Size : 46,8 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9781493926510
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
Author : Charles Chapman Pugh
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 47,8 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9780387216843
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 47,8 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9780387721767
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.