An Introduction To Lebesgue Integration And Fourier Series

Author : Howard J. Wilcox,David L. Myers
Publisher : Courier Corporation
Page : 194 pages
File Size : 53,7 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486137476

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An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox,David L. Myers Pdf

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Author : Frank Jones
Publisher : Jones & Bartlett Learning
Page : 626 pages
File Size : 49,7 Mb
Release : 2001
Category : Computers
ISBN : 0763717088

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Lebesgue Integration on Euclidean Space by Frank Jones Pdf

"'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --

Author : Horatio Scott Carslaw
Publisher : Unknown
Page : 440 pages
File Size : 45,7 Mb
Release : 1930
Category : Definite integrals
ISBN : UCSD:31822014010458

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Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw Pdf

Author : John M. Franks
Publisher : American Mathematical Soc.
Page : 219 pages
File Size : 50,8 Mb
Release : 2009
Category : Lebesgue integral
ISBN : 9780821848623

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A (Terse) Introduction to Lebesgue Integration by John M. Franks Pdf

Provides a student's first encounter with the concepts of measure theory and functional analysis. This book reflects the belief that difficult concepts should be introduced in their simplest and most concrete forms. It is suitable for an advanced undergraduate course or for the start of a graduate course.

Author : Hilary A. Priestley
Publisher : Oxford University Press, USA
Page : 321 pages
File Size : 40,9 Mb
Release : 1997
Category : Integrals
ISBN : 9780198501244

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Introduction to Integration by Hilary A. Priestley Pdf

Introduction to integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditionalRiemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functionsrather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians.Prerequisites are the rudiments of integral calculus and a first course in real analysis.

Author : Harold Widom
Publisher : Courier Dover Publications
Page : 177 pages
File Size : 54,8 Mb
Release : 2016-11-16
Category : Mathematics
ISBN : 9780486810287

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Lectures on Measure and Integration by Harold Widom Pdf

These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

Author : Robert T. Seeley
Publisher : Courier Corporation
Page : 116 pages
File Size : 48,5 Mb
Release : 2014-02-20
Category : Mathematics
ISBN : 9780486151793

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An Introduction to Fourier Series and Integrals by Robert T. Seeley Pdf

A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.

Author : Ferenc Weisz
Publisher : Springer Nature
Page : 299 pages
File Size : 43,8 Mb
Release : 2021-06-12
Category : Mathematics
ISBN : 9783030746360

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Lebesgue Points and Summability of Higher Dimensional Fourier Series by Ferenc Weisz Pdf

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

Author : Hari Bercovici,Arlen Brown,Carl Pearcy
Publisher : Springer
Page : 300 pages
File Size : 53,8 Mb
Release : 2016-03-17
Category : Mathematics
ISBN : 9783319290461

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Measure and Integration by Hari Bercovici,Arlen Brown,Carl Pearcy Pdf

This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems.

Author : Richard L. Wheeden
Publisher : CRC Press
Page : 524 pages
File Size : 40,6 Mb
Release : 2015-04-24
Category : Mathematics
ISBN : 9781498702904

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Measure and Integral by Richard L. Wheeden Pdf

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less

Author : William Johnston
Publisher : The Mathematical Association of America
Page : 297 pages
File Size : 52,7 Mb
Release : 2015-09-25
Category : Mathematics
ISBN : 9781939512079

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The Lebesgue Integral for Undergraduates by William Johnston Pdf

In 1902, modern function theory began when Henri Lebesgue described a new "integral calculus." His "Lebesgue integral" handles more functions than the traditional integral-so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.

Author : H. S. Bear
Publisher : Elsevier
Page : 164 pages
File Size : 51,6 Mb
Release : 2001-10-16
Category : Mathematics
ISBN : 0080525733

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A Primer of Lebesgue Integration by H. S. Bear Pdf

The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.

Author : Sheldon Axler
Publisher : Springer Nature
Page : 430 pages
File Size : 47,9 Mb
Release : 2019-11-29
Category : Mathematics
ISBN : 9783030331436

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Measure, Integration & Real Analysis by Sheldon Axler Pdf

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Author : H. S. Carslaw
Publisher : Forgotten Books
Page : 340 pages
File Size : 49,7 Mb
Release : 2017-10-15
Category : Mathematics
ISBN : 0265332206

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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint) by H. S. Carslaw Pdf

Excerpt from Introduction to the Theory of Fourier's Series and Integrals The modern theory of integration, associated chiefly with the name of Lebesgue, has introduced into the Theory of Fourier's Series and Integrals functions of a far more complicated nature. Various writers, notably W. H. Young, are engaged in building up a theory of these and allied series much more advanced than any thing treated in this book. These developments are in the meantime chiefly interesting to the Pure Mathematician specialising in the Theory of Functions of a Real Variable. My purpose has been to remove some of the difficulties of the Applied Mathematician. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : C. Ray Rosentrater
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 45,7 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9781614442172

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Varieties of Integration by C. Ray Rosentrater Pdf

Historical introduction -- The Riemann integral -- The Darboux integral -- A functional zoo -- Another approach : measure theory -- The Lebesgue integral -- The Gauge integral -- Stieltjes-type integrals and extensions -- A look back -- Afterword : L2 spaces and Fourier series