**Author**: Sterling K. Berberian

**Publisher:**Springer Science & Business Media

**ISBN:**9780387984803

**Category:**Mathematics

**Page:**479

**View:**303

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# Search Results for: fundamentals-of-real-analysis-universitext

**Author**: Sterling K. Berberian

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387984803

**Category:** Mathematics

**Page:** 479

**View:** 303

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

**Author**: Sterling K. Berberian

**Publisher:** Springer Science & Business Media

**ISBN:** 1441985484

**Category:** Mathematics

**Page:** 240

**View:** 3414

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

**Author**: Paul J. Sally, Jr.

**Publisher:** American Mathematical Soc.

**ISBN:** 0821891413

**Category:** Mathematics

**Page:** 362

**View:** 7461

This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.

**Author**: Douglas Farenick

**Publisher:** Springer

**ISBN:** 3319456334

**Category:** Mathematics

**Page:** 451

**View:** 6047

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.

**Author**: Sterling K. Berberian

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387984803

**Category:** Mathematics

**Page:** 479

**View:** 6596

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

**Author**: Ethan D. Bloch

**Publisher:** Springer Science & Business Media

**ISBN:** 0387721762

**Category:** Mathematics

**Page:** 553

**View:** 9781

This rigorous, detailed introduction to real analysis presents the fundamentals clearly and includes definitions, theorems and proofs. Mirroring the structure of standard calculus courses makes it especially accessible to university students of mathematics.

**Author**: Agamirza Bashirov

**Publisher:** Academic Press

**ISBN:** 0128010509

**Category:** Mathematics

**Page:** 362

**View:** 9292

The author’s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options. Friendly and well-rounded presentation of pre-analysis topics such as sets, proof techniques and systems of numbers. Deeper discussion of the basic concept of convergence for the system of real numbers, pointing out its specific features, and for metric spaces Presentation of Riemann integration and its place in the whole integration theory for single variable, including the Kurzweil-Henstock integration Elements of multiplicative calculus aiming to demonstrate the non-absoluteness of Newtonian calculus.

**Author**: Steven G. Krantz

**Publisher:** CRC Press

**ISBN:** 9780849371561

**Category:** Mathematics

**Page:** 312

**View:** 2752

Real Analysis and Foundations is an advanced undergraduate and first-year graduate textbook that introduces students to introductory topics in real analysis (or real variables), point set topology, and the calculus of variations. This classroom-tested book features over 350 end-of-chapter exercises that clearly develop and reinforce conceptual topics. It also provides an excellent review chapter on math foundations topics, as well as accessible coverage of classical topics, such as Weirstrass Approximation Theorem, Ascoli-Arzela Theorem and Schroeder-Bernstein Theorem. Explanations and discussions of key concepts are so well done that Real Analysis and Foundations will also provide valuable information for professional aerospace and structural engineers.

**Author**: Anthony W. Knapp

**Publisher:** Springer Science & Business Media

**ISBN:** 0817644415

**Category:** Mathematics

**Page:** 656

**View:** 3490

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**: Peter G. Hinman

**Publisher:** CRC Press

**ISBN:** 1439864276

**Category:** Mathematics

**Page:** 896

**View:** 9227

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

**Author**: Michael Falk,Frank Marohn,Bernward Tewes

**Publisher:** Birkhäuser

**ISBN:** 3034881959

**Category:** Mathematics

**Page:** 402

**View:** 8384

This book links up the theory of a selection of statistical procedures used in general practice with their application to real world data sets using the statistical software package SAS (Statistical Analysis System). These applications are intended to illustrate the theory and to provide, simultaneously, the ability to use the knowledge effectively and readily in execution.

**Author**: Sterling K. Berberian

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821853283

**Category:** Mathematics

**Page:** 312

**View:** 6349

This highly flexible text is organized into two parts: Part I is suitable for a one-semester course at the first-year graduate level, and the book as a whole is suitable for a full-year course. Part I treats the theory of measure and integration over abstract measure spaces. Prerequisites are a familiarity with epsilon-delta arguments and with the language of naive set theory (union, intersection, function). The fundamental theorems of the subject are derived from first principles, with details in full. Highlights include convergence theorems (monotone, dominated), completeness of classical function spaces (Riesz-Fischer theorem), product measures (Fubini's theorem), and signed measures (Radon-Nikodym theorem). Part II is more specialized; it includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group. The group algebra of a locally compact group is constructed in the last chapter, by an especially transparent method that minimizes measure-theoretic difficulties. Prerequisites for Part II include Part I plus a course in general topology. To quote from the Preface: ``Finally, I am under no illusions as to originality, for the subject of measure theory is an old one which has been worked over by many experts. My contribution can only be in selection, arrangement, and emphasis. I am deeply indebted to Paul R. Halmos, from whose textbook I first studied measure theory; I hope that these pages may reflect their debt to his book without seeming to be almost everywhere equal to it.''

**Author**: Bryan Rynne,M.A. Youngson

**Publisher:** Springer Science & Business Media

**ISBN:** 9781848000056

**Category:** Mathematics

**Page:** 324

**View:** 2389

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.
*With Applications to Engineering and Science (Classic Version)*

**Author**: Edward Saff,Arthur D. Snider

**Publisher:** Math Classics

**ISBN:** 9780134689487

**Category:** Mathematics

**Page:** 576

**View:** 4198

Originally published in 2003, reissued as part of Pearson's modern classic series.
*An Application-Oriented Introduction*

**Author**: Hans Wilhelm Alt

**Publisher:** Springer

**ISBN:** 1447172809

**Category:** Mathematics

**Page:** 435

**View:** 9521

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

**Author**: Rod Haggarty

**Publisher:** Addison-Wesley Longman

**ISBN:** 9780201631975

**Category:** Calculus

**Page:** 332

**View:** 6925

Providing students with an introduction to the fundamentals of analysis, this book continues to present the fundamental concepts of analysis in as painless a manner as possible. To achieve this aim, the second edition has made many improvements in exposition.

**Author**: Oliver Dimon Kellogg

**Publisher:** Courier Corporation

**ISBN:** 9780486601441

**Category:** Science

**Page:** 384

**View:** 1441

Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.

**Author**: Eberhard Freitag,Rolf Busam

**Publisher:** Springer Science & Business Media

**ISBN:** 3540939830

**Category:** Mathematics

**Page:** 532

**View:** 1194

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

**Author**: Richard A. Silverman

**Publisher:** Courier Corporation

**ISBN:** 0486318524

**Category:** Mathematics

**Page:** 400

**View:** 2056

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

**Author**: Douglas Farenick

**Publisher:** Springer

**ISBN:** 3319456334

**Category:** Mathematics

**Page:** 451

**View:** 1604

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.

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