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Author: C. Ray Rosentrater
Publisher: American Mathematical Soc.
Published: 2015-12-31
Total Pages: 325
ISBN-13: 1614442177
DOWNLOAD EBOOKHistorical 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
Author: C. Ray Rosentrater
Publisher: The Mathematical Association of America
Published: 2015-11-16
Total Pages: 343
ISBN-13: 0883853590
DOWNLOAD EBOOKVarieties of Integration explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation with little attention paid to the relationships between them or to the historical issues that motivated their definitions. Varieties of Integration redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals in a single volume using a common set of examples. This approach allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the Fundamental Theorems of Calculus.
Author: Hassler Whitney
Publisher: Princeton University Press
Published: 2015-12-08
Total Pages: 404
ISBN-13: 1400877571
DOWNLOAD EBOOKA complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: AnHai Doan
Publisher: Elsevier
Published: 2012-06-25
Total Pages: 522
ISBN-13: 0123914795
DOWNLOAD EBOOKPrinciples of Data Integration is the first comprehensive textbook of data integration, covering theoretical principles and implementation issues as well as current challenges raised by the semantic web and cloud computing. The book offers a range of data integration solutions enabling you to focus on what is most relevant to the problem at hand. Readers will also learn how to build their own algorithms and implement their own data integration application. Written by three of the most respected experts in the field, this book provides an extensive introduction to the theory and concepts underlying today's data integration techniques, with detailed, instruction for their application using concrete examples throughout to explain the concepts. This text is an ideal resource for database practitioners in industry, including data warehouse engineers, database system designers, data architects/enterprise architects, database researchers, statisticians, and data analysts; students in data analytics and knowledge discovery; and other data professionals working at the R&D and implementation levels. - Offers a range of data integration solutions enabling you to focus on what is most relevant to the problem at hand - Enables you to build your own algorithms and implement your own data integration applications
Author: Ralph Henstock
Publisher:
Published: 1991
Total Pages: 288
ISBN-13:
DOWNLOAD EBOOKEvery good mathematical book stands like a tree with its roots in the past and its branches stretching out towards the future. Whether the fruits of this tree are desirable and whether the branches will be quarried for mathematical wood to build further edifices, I will leave to the judgment of history. The roots of this book take nourishment from the concept of definite integration of continuous functions, where Riemann's method is the high water mark of the simpler theory.
Author: Gregor Hohpe
Publisher:
Published: 2003
Total Pages: 737
ISBN-13: 9788131741177
DOWNLOAD EBOOKAuthor: S. Kesavan (emeritus)
Publisher:
Published: 2019
Total Pages: 232
ISBN-13: 9789811366796
DOWNLOAD EBOOKThis book deals with topics on the theory of measure and integration. It starts with discussion on the Riemann integral and points out certain shortcomings, which motivate the theory of measure and the Lebesgue integral. Most of the material in this book can be covered in a one-semester introductory course. An awareness of basic real analysis and elementary topological notions, with special emphasis on the topology of the n-dimensional Euclidean space, is the pre-requisite for this book. Each chapter is provided with a variety of exercises for the students. The book is targeted to students of graduate- and advanced-graduate-level courses on the theory of measure and integration.
Author: L. S. Schulman
Publisher: Courier Corporation
Published: 2012-10-10
Total Pages: 434
ISBN-13: 0486137023
DOWNLOAD EBOOKSuitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.
Author: Helmut Brass
Publisher: American Mathematical Soc.
Published: 2011-10-12
Total Pages: 376
ISBN-13: 0821853619
DOWNLOAD EBOOKEvery book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.
Author: George Boros
Publisher: Cambridge University Press
Published: 2004-06-21
Total Pages: 326
ISBN-13: 9780521796361
DOWNLOAD EBOOKThis book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.
