Download or read book Integration A Functional Approach written by Klaus Bichteler and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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 student for example. It might even 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.
Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Download or read book Functional Integration written by Pierre Cartier and published by Cambridge University Press. This book was released on 2006-11-30 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.
Download or read book Functional Integration written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.
Download or read book Functional Integration and Quantum Physics written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.
Download or read book A Radical Approach to Lebesgue s Theory of Integration written by David M. Bressoud and published by Cambridge University Press. This book was released on 2008-01-21 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
Download or read book Vector Integration and Stochastic Integration in Banach Spaces written by Nicolae Dinculeanu and published by John Wiley & Sons. This book was released on 2000-02-04 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.
Download or read book Lean Integration written by John G. Schmidt and published by Pearson Education. This book was released on 2010-05-18 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Use Lean Techniques to Integrate Enterprise Systems Faster, with Far Less Cost and Risk By some estimates, 40 percent of IT budgets are devoted to integration. However, most organizations still attack integration on a project-by-project basis, causing unnecessary expense, waste, risk, and delay. They struggle with integration “hairballs”: complex point-to-point information exchanges that are expensive to maintain, difficult to change, and unpredictable in operation. The solution is Lean Integration. This book demonstrates how to use proven “lean” techniques to take control over the entire integration process. John Schmidt and David Lyle show how to establish “integration factories” that leverage the powerful benefits of repeatability and continuous improvement across every integration project you undertake. Drawing on their immense experience, Schmidt and Lyle bring together best practices; solid management principles; and specific, measurable actions for streamlining integration development and maintenance. Whether you’re an IT manager, project leader, architect, analyst, or developer, this book will help you systematically improve the way you integrate—adding value that is both substantial and sustainable. Coverage includes Treating integration as a business strategy and implementing management disciplines that systematically address its people, process, policy, and technology dimensions Providing maximum business flexibility and supporting rapid change without compromising stability, quality, control, or efficiency Applying improvements incrementally without “Boiling the Ocean” Automating processes so you can deliver IT solutions faster–while avoiding the pitfalls of automation Building in both data and integration quality up front, rather than inspecting quality in later More than a dozen in-depth case studies that show how real organizations are applying Lean Integration practices and the lessons they’ve learned Visit integrationfactory.com for additional resources, including more case studies, best practices, templates, software demos, and reference links, plus a direct connection to lean integration practitioners worldwide.
Download or read book Measure and Integration written by Hari Bercovici and published by Springer. This book was released on 2016-03-17 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measure Integration Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/
Download or read book Real Analysis written by Gerald B. Folland and published by John Wiley & Sons. This book was released on 2013-06-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Explanation and Integration in Mind and Brain Science written by David Michael Kaplan and published by Oxford University Press. This book was released on 2017 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is the relationship between psychology and neuroscience one of autonomy or mutual constraint and integration? This volume includes new papers from leading philosophers seeking to address this issue by deepening our understanding of the similarities and differences between the explanatory patterns employed across these domains.
Download or read book Engineering Systems Integration written by Gary O. Langford and published by CRC Press. This book was released on 2016-04-19 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to address the underlying premises of systems integration and how to exposit them into a practical and productive manner, this book prepares systems managers and systems engineers to consider their decisions in light of systems integration metrics. The book addresses two questions: Is there a way to express the interplay of human actions and the result of system interactions of a product with its environment, and are there methods that combine to improve the integration of systems? The systems integration theory and integration frameworks proposed in the book tie General Systems Theory with practice.
Download or read book Connected by Design written by Barry Wacksman and published by John Wiley & Sons. This book was released on 2014-04-28 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a world of fierce global competition and rapid technological change, traditional strategies for gaining market share and achieving efficiencies no longer yield the returns they once did. How can companies drive consumer preference and secure sustainable growth in this digital, social, and mobile age? The answer is through functional integration. Some of the world's most highly valued companies—including Amazon, Apple and Google—have harnessed this new business model to build highly interactive ecosystems of interrelated products and digital services, gaining new levels of customer engagement. Functional integration offers forward-looking brands a unique competitive edge by using transformative digital technologies to deliver high-value customer experiences, generate repeat business, and unlock lucrative new business-to-business revenue streams. Connected By Design is the first book to show business leaders and marketers exactly how to use functional integration to achieve transformative growth within any type of company. Based on R/GA's pioneering work with firms at the forefront of functional integration, Barry Wacksman and Chris Stutzman identify seven principles companies must follow in order to create and deliver new value for customers and capture new revenues. Connected By Design explains how functional integration drove the transformation of market-leading companies as diverse as Nike, General Motors, McCormick & Co., and Activision to establish authentic brand relationships with their customers, enter new categories, and develop new sources of income. With Connected by Design, any company can leverage technological disruption to redefine its mission and foster greater brand loyalty and engagement.
Download or read book Principles of Analysis written by Hugo D. Junghenn and published by CRC Press. This book was released on 2018-04-27 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers’ benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis. The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter . Features: Contains direct and concise proofs with attention to detail Features a substantial variety of interesting and nontrivial examples Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises Provides an eclectic set of special topics and applications About the Author: Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
Download or read book Geometric Integration Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Download or read book Techniques and Applications of Path Integration written by L. S. Schulman and published by Courier Corporation. This book was released on 2012-10-10 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable 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.
