A Course of Modern Analysis

A Course of Modern Analysis
Author: E. T. Whittaker
Publisher: Cambridge University Press
Total Pages: 620
Release: 1927
Genre: Mathematics
ISBN: 9780521588072

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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 Course of Modern Analysis

A Course of Modern Analysis
Author: E.T. Whittaker
Publisher: Courier Dover Publications
Total Pages: 624
Release: 2020-07-15
Genre: Mathematics
ISBN: 048684286X

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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.

Foundations of Modern Analysis

Foundations of Modern Analysis
Author: Avner Friedman
Publisher: Courier Corporation
Total Pages: 276
Release: 1982-01-01
Genre: Mathematics
ISBN: 9780486640624

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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

A Course in Modern Analysis and its Applications

A Course in Modern Analysis and its Applications
Author: Graeme L. Cohen
Publisher: Cambridge University Press
Total Pages: 333
Release: 2010-07-06
Genre: Mathematics
ISBN: 9780511755125

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Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

A Course in Complex Analysis

A Course in Complex Analysis
Author: Saeed Zakeri
Publisher: Princeton University Press
Total Pages: 442
Release: 2021-11-02
Genre: Mathematics
ISBN: 0691207585

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"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"--

Real Analysis

Real Analysis
Author: Gerald B. Folland
Publisher: John Wiley & Sons
Total Pages: 368
Release: 2013-06-11
Genre: Mathematics
ISBN: 1118626397

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An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

A Course in Abstract Analysis

A Course in Abstract Analysis
Author: John B. Conway
Publisher: American Mathematical Soc.
Total Pages: 385
Release: 2012-10-03
Genre: Mathematics
ISBN: 0821890832

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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 First Course in Analysis

A First Course in Analysis
Author: John B. Conway
Publisher: Cambridge University Press
Total Pages: 357
Release: 2018
Genre: Mathematics
ISBN: 1107173140

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This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

A Course in Functional Analysis

A Course in Functional Analysis
Author: John B Conway
Publisher: Springer
Total Pages: 416
Release: 2019-03-09
Genre: Mathematics
ISBN: 1475743831

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This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS

Integration and Modern Analysis

Integration and Modern Analysis
Author: John J. Benedetto
Publisher: Springer Science & Business Media
Total Pages: 589
Release: 2010-01-08
Genre: Mathematics
ISBN: 0817646566

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This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.