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Basic Real Analysis
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Book Synopsis Basic Real Analysis by : Anthony W. Knapp
Download or read book Basic Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.
Book Synopsis Basic Real Analysis by : Houshang H. Sohrab
Download or read book Basic Real Analysis written by Houshang H. Sohrab and published by Springer. This book was released on 2014-11-15 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews
Book Synopsis Basic Real Analysis by : James Howland
Download or read book Basic Real Analysis written by James Howland and published by Jones & Bartlett Learning. This book was released on 2010 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for the one-semester undergraduate course, Basic Real Analysis is intended for students who have recently completed a traditional calculus course and proves the basic theorems of Single Variable Calculus in a simple and accessible manner. It gradually builds upon key material as to not overwhelm students beginning the course and becomes more rigorous as they progresses. Optional appendices on sets and functions, countable and uncountable sets, and point set topology are included for those instructors who wish include these topics in their course. The author includes hints throughout the text to help students solve challenging problems. An online instructor's solutions manual is also available.
Book Synopsis Basic Real and Abstract Analysis by : John F. Randolph
Download or read book Basic Real and Abstract Analysis written by John F. Randolph and published by Elsevier. This book was released on 2014-05-12 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Concise Introduction to Basic Real Analysis by : Hemen Dutta
Download or read book Concise Introduction to Basic Real Analysis written by Hemen Dutta and published by CRC Press. This book was released on 2019-08-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysis Adopts a reasonable approach to make the subject easier to learn Contains many solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spaces
Book Synopsis Advanced Real Analysis by : Anthony W. Knapp
Download or read book Advanced Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2008-07-11 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Book Synopsis A Basic Course in Real Analysis by : Ajit Kumar
Download or read book A Basic Course in Real Analysis written by Ajit Kumar and published by CRC Press. This book was released on 2014-01-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.
Book Synopsis Basic Elements of Real Analysis by : Murray H. Protter
Download or read book Basic Elements of Real Analysis written by Murray H. Protter and published by Springer Science & Business Media. This book was released on 1998-10-16 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.
Book Synopsis Basic Real Analysis by : Anthony W. Knapp
Download or read book Basic Real Analysis written by Anthony W. Knapp and published by Birkhäuser. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.
Author :Charalambos D. Aliprantis Publisher :Gulf Professional Publishing ISBN 13 :9780120502578 Total Pages :434 pages Book Rating :4.5/5 (25 download)
Book Synopsis Principles of Real Analysis by : Charalambos D. Aliprantis
Download or read book Principles of Real Analysis written by Charalambos D. Aliprantis and published by Gulf Professional Publishing. This book was released on 1998-08-26 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new, Third Edition of this successful text covers the basic theory of integration in a clear, well-organized manner. The authors present an imaginative and highly practical synthesis of the "Daniell method" and the measure theoretic approach. It is the ideal text for undergraduate and first-year graduate courses in real analysis. This edition offers a new chapter on Hilbert Spaces and integrates over 150 new exercises. New and varied examples are included for each chapter. Students will be challenged by the more than 600 exercises. Topics are treated rigorously, illustrated by examples, and offer a clear connection between real and functional analysis. This text can be used in combination with the authors' Problems in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text. Key Features: * Gives a unique presentation of integration theory * Over 150 new exercises integrated throughout the text * Presents a new chapter on Hilbert Spaces * Provides a rigorous introduction to measure theory * Illustrated with new and varied examples in each chapter * Introduces topological ideas in a friendly manner * Offers a clear connection between real analysis and functional analysis * Includes brief biographies of mathematicians "All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student." --J. Lorenz in Zentralblatt für Mathematik "...a clear and precise treatment of the subject. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use." --CASPAR GOFFMAN, Department of Mathematics, Purdue University
Book Synopsis Basic Real Analysis by : Anthony W. Knapp
Download or read book Basic Real Analysis written by Anthony W. Knapp and published by . This book was released on 2020-09-15 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Real Analysis: Along with a companion volume Advanced Real Analysis by Anthony W. KnappThis book and its companion volume Advanced Real Analysis systematicallydevelop concepts and tools in real analysis that are vital to every mathematician,whether pure or applied, aspiring or established. The two books together containwhat the young mathematician needs to know about real analysis in order tocommunicate well with colleagues in all branches of mathematics.The books are written as textbooks, and their primary audience is students whoare learning the material for the first time and who are planning a career in whichthey will use advanced mathematics professionally. Much of the material in thebooks corresponds to normal course work. Nevertheless, it is often the case thatcore mathematics curricula, time-limited as they are, do not include all the topicsthat one might like. Thus the book includes important topics that may be skippedin required courses but that the professional mathematician will ultimately wantto learn by self-study.The content of the required courses at each university reflects expectations ofwhat students need before beginning specialized study and work on a thesis. Theseexpectations vary from country to country and from university to university. Evenso, there seems to be a rough consensus about what mathematics a plenary lecturerat a broad international or national meeting may take as known by the audience.The tables of contents of the two books represent my own understanding of whatthat degree of knowledge is for real analysis today.Key topics and features of Basic Real Analysis are as follows:* Early chapters treat the fundamentals of real variables, sequences and seriesof functions, the theory of Fourier series for the Riemann integral, metricspaces, and the theoretical underpinnings of multivariable calculus and ordi-nary differential equations.* Subsequent chapters develop the Lebesgue theory in Euclidean and abstractspaces, Fourier series and the Fourier transform for the Lebesgue integral,point-set topology, measure theory in locally compact Hausdorff spaces, andthe basics of Hilbert and Banach spaces.* The subjects of Fourier series and harmonic functions are used as recurringmotivation for a number of theoretical developments.* The development proceeds from the particular to the general, often introducingexamples well before a theory that incorporates them.* More than 300 problems at the ends of chapters illuminate aspects of thetext, develop related topics, and point to additional applications. A separate55-page section "Hints for Solutions of Problems" at the end of the book givesdetailed hints for most of the problems, together with complete solutions formany.Beyond a standard calculus sequence in one and several variables, the mostimportant prerequisite for using Basic Real Analysis is that the reader alreadyknow what a proof is, how to read a proof, and how to write a proof. Thisknowledge typically is obtained from honors calculus courses, or from a coursein linear algebra, or from a first junior-senior course in real variables. In addition,it is assumed that the reader is comfortable with a modest amount of linear algebra,including row reduction of matrices, vector spaces and bases, and the associatedgeometry. A passing acquaintance with the notions of group, subgroup, andquotient is helpful as well.Chapters I-IV are appropriate for a single rigorous real-variables course andmay be used in either of two ways. For students who have learned about proofsfrom honors calculus or linear algebra, these chapters offer a full treatment of realvariables, leaving out only the more familiar parts near the beginning--such aselementary manipulations with limits, convergence tests for infinite series withpositive scalar terms, and routine facts about continuity and differentiability.
Author :Teodora-Liliana Radulescu Publisher :Springer Science & Business Media ISBN 13 :0387773789 Total Pages :462 pages Book Rating :4.3/5 (877 download)
Book Synopsis Problems in Real Analysis by : Teodora-Liliana Radulescu
Download or read book Problems in Real Analysis written by Teodora-Liliana Radulescu and published by Springer Science & Business Media. This book was released on 2009-05-29 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Grundbegriffe der Wahrscheinlichkeitsrechnung by : Andreĭ Nikolaevich Kolmogorov
Download or read book Grundbegriffe der Wahrscheinlichkeitsrechnung written by Andreĭ Nikolaevich Kolmogorov and published by . This book was released on 1933 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introductory Real Analysis by : A. N. Kolmogorov
Download or read book Introductory Real Analysis written by A. N. Kolmogorov and published by Dover Publications. This book was released on 1975-06-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in Richard Silverman's exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus. The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched. With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.
Download or read book Real Analysis written by Frank Morgan and published by American Mathematical Soc.. This book was released on 2005 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as ``closed and bounded,'' via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. The text not only provides efficient proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a real analysis text that is short enough for the student to read and understand and complete enough to be the primary text for a serious undergraduate course. Frank Morgan is the author of five books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this book, Morgan has finally brought his famous direct style to an undergraduate real analysis text.
Book Synopsis Real Analysis for Beginners by : Steve Warner
Download or read book Real Analysis for Beginners written by Steve Warner and published by . This book was released on 2020-06-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Basic Real Analysis and Advanced Real Analysis Set by : Anthony W. Knapp
Download or read book Basic Real Analysis and Advanced Real Analysis Set written by Anthony W. Knapp and published by Birkhäuser. This book was released on 2005-08-09 with total page 1176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds * The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.
