Classical And Modern Integration Theories
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Classical And Modern Integration Theories
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Author : Ivan N. Pesin
language : en
Publisher: Academic Press
Release Date : 2014-07-03
Classical And Modern Integration Theories written by Ivan N. Pesin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.
Classical And Modern Integration Theories
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Author : Ivan Nikolaevich Pesin
language : en
Publisher:
Release Date : 1970
Classical And Modern Integration Theories written by Ivan Nikolaevich Pesin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Classical And Modern Integration Theories
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Author : Ivan Nikolaevyč Pešin
language : en
Publisher:
Release Date : 1970
Classical And Modern Integration Theories written by Ivan Nikolaevyč Pešin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Mathematical Feynman Path Integrals And Their Applications Second Edition
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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2021-11-16
Mathematical Feynman Path Integrals And Their Applications Second Edition written by Sonia Mazzucchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Science categories.
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
Theory Of Rank Tests
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Author : Zbynek Sidak
language : en
Publisher: Elsevier
Release Date : 1999-04-06
Theory Of Rank Tests written by Zbynek Sidak and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-06 with Mathematics categories.
The first edition of Theory of Rank Tests (1967) has been the precursor to a unified and theoretically motivated treatise of the basic theory of tests based on ranks of the sample observations. For more than 25 years, it helped raise a generation of statisticians in cultivating their theoretical research in this fertile area, as well as in using these tools in their application oriented research. The present edition not only aims to revive this classical text by updating the findings but also by incorporating several other important areas which were either not properly developed before 1965 or have gone through an evolutionary development during the past 30 years. This edition therefore aims to fulfill the needs of academic as well as professional statisticians who want to pursue nonparametrics in their academic projects, consultation, and applied research works. - Asymptotic Methods - Nonparametrics - Convergence of Probability Measures - Statistical Inference
A Modern Theory Of Integration
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Author : Robert G. Bartle
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-25
A Modern Theory Of Integration written by Robert G. Bartle and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-25 with Mathematics categories.
The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ?better? because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ?improper? integrals. This book is an introduction to a relatively new theory of the integral (called the ?generalized Riemann integral? or the ?Henstock-Kurzweil integral?) that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required. Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. The theory of Lebesgue measure from the integral is then developed, and the author makes a connection with some of the traditional approaches to the Lebesgue integral. Thus, readers are given full exposure to the main classical results. The text is suitable for a first-year graduate course, although much of it can be readily mastered by advanced undergraduate students. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately.
Functional Equations In Probability Theory
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Author : Ramachandran Balasubrahmanyan
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Functional Equations In Probability Theory written by Ramachandran Balasubrahmanyan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with particular reference to the context of the common distribution of these random variables being normal. Comprised of nine chapters, this volume begins with an introduction to Cauchy functional equations as well as distribution functions and characteristic functions. The discussion then turns to the nonnegative solutions of ICFE on R+; ICFE with a signed measure; and application of ICFE to the characterization of probability distributions. Subsequent chapters focus on stable and semistable laws; ICFE with error terms on R+; independent/identically distributed linear forms and the normal laws; and distribution problems relating to the arc-sine, the normal, and the chi-square laws. The final chapter is devoted to ICFE on semigroups of Rd. This book should be of interest to mathematicians and statisticians.
Fredholm Theory In Banach Spaces
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Author : Anthony Francis Ruston
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03
Fredholm Theory In Banach Spaces written by Anthony Francis Ruston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Mathematics categories.
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
Modern Sociological Theory
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Author : George Ritzer
language : en
Publisher: SAGE Publications
Release Date : 2017-01-23
Modern Sociological Theory written by George Ritzer and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Social Science categories.
The authors are proud sponsors of the 2020 SAGE Keith Roberts Teaching Innovations Award—enabling graduate students and early career faculty to attend the annual ASA pre-conference teaching and learning workshop. Now with SAGE Publishing, and co-authored by one of the foremost authorities on sociological theory, the Eighth Edition of Modern Sociological Theory by George Ritzer and Jeffrey Stepnisky provides a comprehensive overview of the major theorists and theoretical schools, from the Structural Functionalism of early 20th century through the cutting-edge theories of the late 20th and early 21st centuries. The integration of key theories with biographical sketches of theorists and the requisite historical and intellectual context helps students to better understand the original works of contemporary thinkers.
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences
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Author : Ivor Grattan-Guiness
language : en
Publisher: Routledge
Release Date : 2004-11-11
Companion Encyclopedia Of The History And Philosophy Of The Mathematical Sciences written by Ivor Grattan-Guiness and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-11 with History categories.
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.