Real Analysis
Real Analysis

Author: Gerald B. Folland

Publisher: John Wiley & Sons

Published: 2013-06-11

Total Pages: 368

ISBN-13: 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.

Modern Analysis and Applications
Modern Analysis and Applications

Author: Vadim Adamyan

Publisher: Springer Science & Business Media

Published: 2009-08-29

Total Pages: 497

ISBN-13: 3764399198

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This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

A Course in Modern Analysis and its Applications
A Course in Modern Analysis and its Applications

Author: Graeme L. Cohen

Publisher: Cambridge University Press

Published: 2010-07-06

Total Pages: 333

ISBN-13: 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 of Modern Analysis
A Course of Modern Analysis

Author: E. T. Whittaker

Publisher: Cambridge University Press

Published: 1927

Total Pages: 620

ISBN-13: 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.

An Introduction to Modern Analysis
An Introduction to Modern Analysis

Author: Vicente Montesinos

Publisher: Springer

Published: 2015-05-04

Total Pages: 884

ISBN-13: 3319124811

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Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

Foundations of Modern Analysis
Foundations of Modern Analysis

Author: Avner Friedman

Publisher: Courier Corporation

Published: 1982-01-01

Total Pages: 276

ISBN-13: 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.

Integration and Modern Analysis
Integration and Modern Analysis

Author: John J. Benedetto

Publisher: Springer Science & Business Media

Published: 2010-01-08

Total Pages: 589

ISBN-13: 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.

Modern Analysis
Modern Analysis

Author: William H. Ruckle

Publisher: Brooks/Cole

Published: 1991

Total Pages: 296

ISBN-13:

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This book should be of interest to second and third year undergraduates in mathematics.

Modern Discrete Mathematics and Analysis
Modern Discrete Mathematics and Analysis

Author: Nicholas J. Daras

Publisher: Springer

Published: 2018-07-05

Total Pages: 516

ISBN-13: 3319743252

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A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.

Modern Real Analysis
Modern Real Analysis

Author: William P. Ziemer

Publisher: Springer

Published: 2017-11-30

Total Pages: 389

ISBN-13: 331964629X

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This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.