Problems In Mathematical Analysis Real Numbers Sequences And Series

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Problems In Mathematical Analysis Real Numbers Sequences And Series

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Author : Wiesława J. Kaczor
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Problems In Mathematical Analysis Real Numbers Sequences And Series written by Wiesława J. Kaczor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Solutions for all the problems are provided."--BOOK JACKET.

Problems In Mathematical Analysis

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Author : Wieslawa J. Kaczor
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Problems In Mathematical Analysis written by Wieslawa J. Kaczor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematical analysis categories.

A Problem Book In Real Analysis

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Author : Asuman G. Aksoy
language : en
Publisher: Springer
Release Date : 2016-08-23

A Problem Book In Real Analysis written by Asuman G. Aksoy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-23 with Mathematics categories.

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.

Problems In Real Analysis

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Author : Teodora-Liliana Radulescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12

Problems In Real Analysis written by Teodora-Liliana Radulescu 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 2009-06-12 with Mathematics categories.

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.

Real Mathematical Analysis

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Author : Charles Chapman Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19

Real Mathematical Analysis written by Charles Chapman Pugh 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 2013-03-19 with Mathematics categories.

Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing 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 I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .

Basic Real Analysis

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Author : Houshang H. Sohrab
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27

Basic Real Analysis written by Houshang H. Sohrab 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 2011-06-27 with Mathematics categories.

One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. Basic Real Analysis is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. Key features include: * A broad view of mathematics throughout the book * Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter * Elegant proofs * Excellent choice of topics * Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter * Emphasis on monotone functions throughout * Good development of integration theory * Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis * Solid preparation for deeper study of functional analysis * Chapter on elementary probability * Comprehensive bibliography and index * Solutions manual available to instructors upon request By covering all the basics and developing rigor simultaneously, this introduction to real analysis is ideal for senior undergraduates and beginning graduate students, both as a classroom text or for self-study. With its wide range of topics and its view of real analysis in a larger context, the book will be appropriate for more advanced readers as well.

Problems And Solutions In Real Analysis

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Author : Masayoshi Hata
language : en
Publisher: World Scientific
Release Date : 2007

Problems And Solutions In Real Analysis written by Masayoshi Hata and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.

Real Analysis Via Sequences And Series

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Author : Charles H.C. Little
language : en
Publisher: Springer
Release Date : 2016-10-09

Real Analysis Via Sequences And Series written by Charles H.C. Little and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-09 with Mathematics categories.

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.

Introduction To Real Analysis

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Author : Michael J. Schramm
language : en
Publisher: Courier Corporation
Release Date : 2012-05-11

Introduction To Real Analysis written by Michael J. Schramm and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-11 with Mathematics categories.

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

Methods Of Solving Sequence And Series Problems

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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2016-12-09

Methods Of Solving Sequence And Series Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.

This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.