A Concise Introduction To The Theory Of Integration

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A Concise Introduction to the Theory of Integration

Author : Daniel W. Stroock
Publisher : Springer Science & Business Media
ISBN 13 : 1475723008
Total Pages : 193 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis A Concise Introduction to the Theory of Integration by : Daniel W. Stroock

Download or read book A Concise Introduction to the Theory of Integration written by Daniel W. Stroock and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This little book is the outgrowth of a one semester course which I have taught for each of the past four years at M. 1. T. Although this class used to be one of the standard courses taken by essentially every first year gradu ate student of mathematics, in recent years (at least in those when I was the instructor), the clientele has shifted from first year graduate students of mathematics to more advanced graduate students in other disciplines. In fact, the majority of my students have been from departments of engi neering (especially electrical engineering) and most of the rest have been economists. Whether this state of affairs is a reflection on my teaching, the increased importance of mathematical analysis in other disciplines, the superior undergraduate preparation of students coming to M. 1. T in mathematics, or simply the lack of enthusiasm that these students have for analysis, I have preferred not to examine too closely. On the other hand, the situation did force me to do a certain amount of thinking about what constitutes an appropriate course for a group of non-mathematicians who are courageous (foolish?) enough to sign up for an introduction to in tegration theory offered by the department of mathematics. In particular, I had to figure out what to do about that vast body of material which, in standard mathematics offerings, is "assumed to have been covered in your advanced calculus course".

A Concise Introduction to the Theory of Integration

Author : Daniel W. Stroock
Publisher : Springer Science & Business Media
ISBN 13 : 9780817640736
Total Pages : 276 pages
Book Rating : 4.6/5 (47 download)

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Book Synopsis A Concise Introduction to the Theory of Integration by : Daniel W. Stroock

Measure and Integration

Author : Leonard F. Richardson
Publisher : John Wiley & Sons
ISBN 13 : 0470501146
Total Pages : 255 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis Measure and Integration by : Leonard F. Richardson

Download or read book Measure and Integration written by Leonard F. Richardson and published by John Wiley & Sons. This book was released on 2009-07-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis. The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes: Measure spaces, outer measures, and extension theorems Lebesgue measure on the line and in Euclidean space Measurable functions, Egoroff's theorem, and Lusin's theorem Convergence theorems for integrals Product measures and Fubini's theorem Differentiation theorems for functions of real variables Decomposition theorems for signed measures Absolute continuity and the Radon-Nikodym theorem Lp spaces, continuous-function spaces, and duality theorems Translation-invariant subspaces of L2 and applications The book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign. Providing an efficient and readable treatment of this classical subject, Measure and Integration: A Concise Introduction to Real Analysis is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.

A Concise Introduction to Geometric Numerical Integration

Author : Sergio Blanes
Publisher : CRC Press
ISBN 13 : 1315354861
Total Pages : 218 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis A Concise Introduction to Geometric Numerical Integration by : Sergio Blanes

Download or read book A Concise Introduction to Geometric Numerical Integration written by Sergio Blanes and published by CRC Press. This book was released on 2017-11-22 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

A Concise Introduction to Analysis

Author : Daniel W. Stroock
Publisher : Springer
ISBN 13 : 3319244698
Total Pages : 218 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis A Concise Introduction to Analysis by : Daniel W. Stroock

Download or read book A Concise Introduction to Analysis written by Daniel W. Stroock and published by Springer. This book was released on 2015-10-31 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.

Essentials of Integration Theory for Analysis

Author : Daniel W. Stroock
Publisher : Springer Nature
ISBN 13 : 303058478X
Total Pages : 296 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Essentials of Integration Theory for Analysis by : Daniel W. Stroock

Download or read book Essentials of Integration Theory for Analysis written by Daniel W. Stroock and published by Springer Nature. This book was released on 2020-11-24 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on RN are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.

A Concise Introduction to Measure Theory

Author : Satish Shirali
Publisher : Springer
ISBN 13 : 9783030032401
Total Pages : 271 pages
Book Rating : 4.0/5 (324 download)

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Book Synopsis A Concise Introduction to Measure Theory by : Satish Shirali

Download or read book A Concise Introduction to Measure Theory written by Satish Shirali and published by Springer. This book was released on 2019-03-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration. The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book. This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.

Measure and Integration Theory

Author : Heinz Bauer
Publisher : Walter de Gruyter
ISBN 13 : 311086620X
Total Pages : 249 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Measure and Integration Theory by : Heinz Bauer

Download or read book Measure and Integration Theory written by Heinz Bauer and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.

Introduction to Stochastic Integration

Author : Hui-Hsiung Kuo
Publisher : Springer Science & Business Media
ISBN 13 : 0387310576
Total Pages : 290 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Introduction to Stochastic Integration by : Hui-Hsiung Kuo

Download or read book Introduction to Stochastic Integration written by Hui-Hsiung Kuo and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY

An Introduction to Lebesgue Integration and Fourier Series

Author : Howard J. Wilcox
Publisher : Courier Corporation
ISBN 13 : 0486137473
Total Pages : 194 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to Lebesgue Integration and Fourier Series by : Howard J. Wilcox

Download or read book An Introduction to Lebesgue Integration and Fourier Series written by Howard J. Wilcox and published by Courier Corporation. This book was released on 2012-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Analysis

Author : Bernd S. W. Schröder
Publisher : John Wiley & Sons
ISBN 13 : 9780470226766
Total Pages : 584 pages
Book Rating : 4.2/5 (267 download)

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Book Synopsis Mathematical Analysis by : Bernd S. W. Schröder

Download or read book Mathematical Analysis written by Bernd S. W. Schröder and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

A Guide to Integral Psychotherapy

Author : Mark D. Forman
Publisher : State University of New York Press
ISBN 13 : 1438430256
Total Pages : 342 pages
Book Rating : 4.4/5 (384 download)

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Book Synopsis A Guide to Integral Psychotherapy by : Mark D. Forman

Download or read book A Guide to Integral Psychotherapy written by Mark D. Forman and published by State University of New York Press. This book was released on 2012-02-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: A therapist's guide to psychotherapy, spirituality, and self-development.

Lectures on Measure and Integration

Author : Harold Widom
Publisher : Courier Dover Publications
ISBN 13 : 0486810283
Total Pages : 177 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Lectures on Measure and Integration by : Harold Widom

Download or read book Lectures on Measure and Integration written by Harold Widom and published by Courier Dover Publications. This book was released on 2016-11-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integration, Measure and Probability

Author : H. R. Pitt
Publisher : Courier Corporation
ISBN 13 : 0486488152
Total Pages : 130 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Integration, Measure and Probability by : H. R. Pitt

Download or read book Integration, Measure and Probability written by H. R. Pitt and published by Courier Corporation. This book was released on 2012-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

Measure and Integral

Author : Richard Wheeden
Publisher : CRC Press
ISBN 13 : 1482229536
Total Pages : 289 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Measure and Integral by : Richard Wheeden

Download or read book Measure and Integral written by Richard Wheeden and published by CRC Press. This book was released on 1977-11-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.

An Introduction to Phase-Integral Methods

Author : John Heading
Publisher : Courier Corporation
ISBN 13 : 0486316297
Total Pages : 176 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis An Introduction to Phase-Integral Methods by : John Heading

Download or read book An Introduction to Phase-Integral Methods written by John Heading and published by Courier Corporation. This book was released on 2013-06-03 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students. Topics include Stokes phenomenon, one and two transition points, applications. 1962 edition.

An Introduction to the Theory of Piezoelectricity

Author : Jiashi Yang
Publisher : Springer Science & Business Media
ISBN 13 : 0387235469
Total Pages : 310 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis An Introduction to the Theory of Piezoelectricity by : Jiashi Yang

Download or read book An Introduction to the Theory of Piezoelectricity written by Jiashi Yang and published by Springer Science & Business Media. This book was released on 2006-06-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lecture notes for a graduate course that has been offered at University of Nebraska-Lincoln on and off since 1998. The course is intended to provide graduate students with the basic aspects of the continuum modeling of electroelastic interactions in solids. A concise treatment of linear, nonlinear, static and dynamic theories and problems is presented. The emphasis is on formulation and understanding of problems useful in device applications rather than solution techniques of mathematical problems. The mathematics used in the book is minimal. The book is suitable for a one-semester graduate course on electroelasticity. It can also be used as a reference for researchers. I would like to take this opportunity to thank UNL for a Maude Hammond Fling Faculty Research Fellowship in 2003 for the preparation of the first draft of this book. I also wish to thank Ms. Deborah Derrick of the College of Engineering and Technology at UNL for editing assistance with the book, and Professor David Y. Gao of Virginia Polytechnic Institute and State University for recommending this book to Kluwer for publication in the series of Advances in Mechanics and Mathematics. JSY Lincoln, Nebraska 2004 Preface Electroelastic materials exhibit electromechanical coupling. They experience mechanical deformations when placed in an electric field, and become electrically polarized under mechanical loads. Strictly speaking, piezoelectricity refers to linear electromechanical couplings only.