التحليل Books in Integration Theory

الموضوع في 'قسم الرياضيات' بواسطة ابن الخطاب, بتاريخ ‏نوفمبر 26, 2008.

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    المصدر: Books in Integration Theory
    في منتدى : قسم الرياضيات





    by Hassler Whitney



    Book Description:

    This treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. Covers the theory of the Riemann integral; abstract integration theory; some relations between chains and functions; Lipschitz mappings; chains and additive set functions, more. 1957 edition​




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    by Steven G. Krantz, Harold Parks



    Description:

    This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis.
    The text provides considerable background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. Topics include the deformation theorem, the area and coareas formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces.
    Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for both self-study and for use in the classroom​




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    by Klaus Bichteler




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    by Peter Medvegyev



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    by Frank Jones



    Book Description:
    Lebesgue Integration on Euclidean Space contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. Throughout the text, many exercises are incorporated, enabling students to apply new ideas immediately. Jones strives to present a slow introduction to Lebesgue integration by dealing with n-dimensional spaces from the outset. In addition, the text provides students a through treatment of Fourier analysis, while holistically preparing students to become "workers" in real analysis.​




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    الهاشمي و gabesien معجبون بهذا.
  2. ابن الخطاب

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    by Herbert Federer




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    by H. A. Priestley

    Product Description:

    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 examples and exercises. Intended as a first course in integration theory for students familiar with real analysis, the book begins with a simplified Lebesgue integral, which is then developed to provide an entry point for important results in the field. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measures. Designed as an undergraduate or graduate textbook, it is a companion volume to the author's Introduction to Complex Analysis and is aimed at both pure and applied mathematicians.



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    by Alan J. Weir



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    by Colloquium on Functional Integration Theory and Applications




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    by Augustus J. E. M. Janssen, P. van der Steen



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    A Modern Theory of Integration
    by Robert G. Bartle




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    by Jewgeni H. Dshalalow





     
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    by G. H. Hardy


    Book Description:

    Famed for his achievements in number theory and mathematical analysis, G. H. Hardy ranks among the twentieth century's great mathematicians and educators. In this classic treatise, Hardy explores the integration of functions of a single variable with his characteristic clarity and precision. Following an Introduction, Hardy discusses elementary functions, their classification and integration, and he presents a summary of results. After a survey of the integration of rational functions, he proceeds to the integration of algebraical functions and concludes with an examination of the integration of transcendental functions.



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    by Klaus Bichteler


    This books covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory.
    From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of Sigma-algebras, and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further.
    The book is intended for the reader who has some experience with proofs, a beginning graduate students for example. It will as well be useful to the advanced mathematician who is confronted with situations -- such as stochastic integration -- where the set-measuring approach to integration does not work.



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    Topics in Banach Space Integration (Series in Real Analysis) (Series in Real Analysis)
    By Stefan Schwabik


    Product Description:

    The relatively new concepts of the HenstockKurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The HenstockKurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.









    by Douglas S Kurtz, Charles W. Swartz,




    Book Description:
    This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.



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  6. gabesien

    gabesien New Member

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  7. ابن الخطاب

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    Author: George Boros, Victor Moll



     
  8. tawba

    tawba New Member

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    Introduction to Gauge Integrals
    By Charles Swartz


    Product Description:
    This book presents the Henstock-Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock-Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.



     
  10. hamouri24

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    By Richard Wheeden,&nbspAntoni Zygmund,



    Book Description:
    This volume develops the classical theory of the Lebesgue integral and some of its applications. Following a thorough study of the concepts of outer measure and measure, the author initially presents the integral in the context of n-dimensional Euclidean space. A more general treatment of the integral, based on an axiomatic approach, is given later. The book examines closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p) classes, and various results about differentiation. Several applications of the theory to a specific branch of analysis-harmonic analysis-are also provided




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    Henstock-Kurzweil, and McShane



     
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    by George Boros, Victor Moll,




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    by Hui-Hsiung Kuo




     
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    by M. Carter



    Book Description:

    Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory. However, those whose interests lie more in the direction of applied mathematics will in all probability find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral without having the necessary theoretical background. It is to such readers that this book is addressed. The authors aim to introduce the Lebesgue-Stieltjes integral on the real line in a natural way as an extension of the Riemann integral. They have tried to make the treatment as practical as possible. The evaluation of Lebesgue-Stieltjes integrals is discussed in detail, as are the key theorems of integral calculus as well as the standard convergence theorems. The book then concludes with a brief discussion of multivariate integrals and surveys ok L^p spaces and some applications. Exercises, which extend and illustrate the theory, and provide practice in techniques, are included. Michael Carter and Bruce van Brunt are senior lecturers in mathematics at Massey University, Palmerston North, New Zealand. Michael Carter obtained his Ph.D. at Massey University in 1976. He has research interests in control theory and differential equations, and has many years of experience in teaching analysis. Bruce van Brunt obtained his D.Phil. at the University of Oxford in 1989. His research interests include differential geometry, differential equations, and analysis. His publications include





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    By D. C. Khandekar, S. V. Lawande, K. V. Bhagwat,


    Publisher: World Scientific Publishing Company
    Number Of Pages: 343
    Publication Date: 1993-08
    Sales Rank: 1301641
    ISBN / ASIN: 9810205635
    EAN: 9789810205638
    Binding: Hardcover

    This book presents the major developments in this field with emphasis on application of path integration methods in diverse areas. After introducing the concept of path integrals, related topics like random walk, Brownian motion and Wiener integrals are discussed. Several techniques of path integration including global and local time transformations, numerical methods as well as approximation schemes are presented. The book provides a proper perspective of some of the most recent exact results and approximation schemes for practical applications

    Contents:

    * Introduction to Path Integrals
    * Propagators for Local Quadratic Lagrangians
    * Non-Local Quadratic Actions
    * Path Integrals in General Coordinate Systems
    * Coordinate Time Transformations in Path Integrals
    * Constrained Path Integrals
    * Time Dependent Invariants and Feynman Propagator
    * The Cumulant Approximation for Feynman Propagators
    * The Perturbation Approach
    * Semiclassical Propagator
    * Numerical Methods of Summing Over Paths
    * Mathematical Nature of Feynman Path-Integral





     
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