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Real Analysis: A Comprehensive Course in Analysis, Part 1

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470410990
Total Pages : 789 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Real Analysis: A Comprehensive Course in Analysis, Part 1 by : Barry Simon

Download or read book Real Analysis: A Comprehensive Course in Analysis, Part 1 written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

A Course in Analysis

Author : Niels Jacob
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811216336
Total Pages : 0 pages
Book Rating : 4.2/5 (163 download)

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Book Synopsis A Course in Analysis by : Niels Jacob

Download or read book A Course in Analysis written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2020-01-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.

A Course in Abstract Analysis

Author : John B. Conway
Publisher : American Mathematical Soc.
ISBN 13 : 0821890832
Total Pages : 385 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Abstract Analysis by : John B. Conway

Download or read book A Course in Abstract Analysis written by John B. Conway and published by American Mathematical Soc.. This book was released on 2012-10-03 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.

A Companion to Analysis

Author : Thomas William Körner
Publisher : American Mathematical Soc.
ISBN 13 : 0821834479
Total Pages : 608 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Companion to Analysis by : Thomas William Körner

Download or read book A Companion to Analysis written by Thomas William Körner and published by American Mathematical Soc.. This book was released on 2004 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.

A First Course in Analysis

Author : John B. Conway
Publisher : Cambridge University Press
ISBN 13 : 1107173140
Total Pages : 357 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis A First Course in Analysis by : John B. Conway

Download or read book A First Course in Analysis written by John B. Conway and published by Cambridge University Press. This book was released on 2018 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

A Course of Modern Analysis

Author : E. T. Whittaker
Publisher : Cambridge University Press
ISBN 13 : 9780521588072
Total Pages : 620 pages
Book Rating : 4.5/5 (88 download)

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Book Synopsis A Course of Modern Analysis by : E. T. Whittaker

Download or read book A Course of Modern Analysis written by E. T. Whittaker and published by Cambridge University Press. This book was released on 1927 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.

A First Course in Analysis

Author : Donald Yau
Publisher : World Scientific
ISBN 13 : 9814417858
Total Pages : 206 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis A First Course in Analysis by : Donald Yau

Download or read book A First Course in Analysis written by Donald Yau and published by World Scientific. This book was released on 2013 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included.

A Course in Real Analysis

Author : Hugo D. Junghenn
Publisher : CRC Press
ISBN 13 : 148221928X
Total Pages : 613 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Course in Real Analysis by : Hugo D. Junghenn

Download or read book A Course in Real Analysis written by Hugo D. Junghenn and published by CRC Press. This book was released on 2015-02-13 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the

A First Course in Analysis

Author : George Pedrick
Publisher : Springer Science & Business Media
ISBN 13 : 1441985549
Total Pages : 293 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A First Course in Analysis by : George Pedrick

Download or read book A First Course in Analysis written by George Pedrick and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.

A Course of Modern Analysis

Author : E.T. Whittaker
Publisher : Courier Dover Publications
ISBN 13 : 048684286X
Total Pages : 624 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis A Course of Modern Analysis by : E.T. Whittaker

Download or read book A Course of Modern Analysis written by E.T. Whittaker and published by Courier Dover Publications. This book was released on 2020-07-15 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historic text by two great mathematicians consists of two parts, The Processes of Analysis and The Transcendental Functions. Geared toward students of analysis and historians of mathematics. 1920 third edition.

A First Course in Functional Analysis

Author : Orr Moshe Shalit
Publisher : CRC Press
ISBN 13 : 1498771629
Total Pages : 257 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis A First Course in Functional Analysis by : Orr Moshe Shalit

Download or read book A First Course in Functional Analysis written by Orr Moshe Shalit and published by CRC Press. This book was released on 2017-03-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.

A First Course in Real Analysis

Author : M.H. Protter
Publisher : Springer Science & Business Media
ISBN 13 : 1461599903
Total Pages : 520 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis A First Course in Real Analysis by : M.H. Protter

Download or read book A First Course in Real Analysis written by M.H. Protter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Complex Analysis

Author : Saeed Zakeri
Publisher : Princeton University Press
ISBN 13 : 0691207585
Total Pages : 442 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis A Course in Complex Analysis by : Saeed Zakeri

Download or read book A Course in Complex Analysis written by Saeed Zakeri and published by Princeton University Press. This book was released on 2021-11-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--

A Course in Complex Analysis and Riemann Surfaces

Author : Wilhelm Schlag
Publisher : American Mathematical Society
ISBN 13 : 0821898477
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag

Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

A First Course in Functional Analysis

Author : Martin Davis
Publisher : Courier Corporation
ISBN 13 : 0486315819
Total Pages : 128 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis A First Course in Functional Analysis by : Martin Davis

Download or read book A First Course in Functional Analysis written by Martin Davis and published by Courier Corporation. This book was released on 2013-05-27 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate mathematics majors, this self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and more. 1966 edition.

A Second Course in Complex Analysis

Author : William A. Veech
Publisher : Courier Corporation
ISBN 13 : 048615193X
Total Pages : 257 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A Second Course in Complex Analysis by : William A. Veech

Download or read book A Second Course in Complex Analysis written by William A. Veech and published by Courier Corporation. This book was released on 2014-08-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.

A Course in Functional Analysis and Measure Theory

Author : Vladimir Kadets
Publisher : Springer
ISBN 13 : 3319920049
Total Pages : 539 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis A Course in Functional Analysis and Measure Theory by : Vladimir Kadets

Download or read book A Course in Functional Analysis and Measure Theory written by Vladimir Kadets and published by Springer. This book was released on 2018-07-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.