The Stieltjes Integral
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The Stieltjes Integral
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Author : Gregory Convertito
language : en
Publisher: CRC Press
Release Date : 2023-02-28
The Stieltjes Integral written by Gregory Convertito and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-28 with Mathematics categories.
The Stieltjes Integral provides a detailed, rigorous treatment of the Stieltjes integral. This integral is a generalization of the Riemann and Darboux integrals of calculus and undergraduate analysis, and can serve as a bridge between classical and modern analysis. It has applications in many areas, including number theory, statistics, physics, and finance. It begins with the Darboux integral, builds the theory of functions of bounded variation, and then develops the Stieltjes integral. It culminates with a proof of the Riesz representation theorem as an application of the Stieltjes integral. For much of the 20th century the Stjeltjes integral was a standard part of the undergraduate or beginning graduate student sequence in analysis. However, the typical mathematics curriculum has changed at many institutions, and the Stieltjes integral has become less common in undergraduate textbooks and analysis courses. This book seeks to address this by offering an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project. Features: Written to be rigorous without sacrificing readability. Accessible to undergraduate students who have taken a one-semester course on real analysis. Contains a large number of exercises from routine to challenging.
On The Stieltjes Integral
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Author : Ben Dushnik
language : en
Publisher:
Release Date : 1931
On The Stieltjes Integral written by Ben Dushnik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with Integrals, Generalized categories.
The Lebesgue Stieltjes Integral
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Author : M. Carter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Lebesgue Stieltjes Integral written by M. Carter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
While mathematics students generally meet the Riemann integral early in their undergraduate studies, those whose interests lie more in the direction of applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral before they have acquired the necessary theoretical background. This book is aimed at exactly this group of readers. The authors introduce the Lebesgue-Stieltjes integral on the real line as a natural extension of the Riemann integral, making the treatment as practical as possible. They discuss the evaluation of Lebesgue-Stieltjes integrals in detail, as well as the standard convergence theorems, and conclude with a brief discussion of multivariate integrals and surveys of L spaces plus some applications. The whole is rounded off with exercises that extend and illustrate the theory, as well as providing practice in the techniques.
Kurzweil Stieltjes Integral Theory And Applications
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Author : Tvrdy Milan
language : en
Publisher: World Scientific
Release Date : 2018-09-24
Kurzweil Stieltjes Integral Theory And Applications written by Tvrdy Milan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.
The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.
A Riemann Type Integral That Includes Lebesgue Stieltjes Bochner And Stochastic Integrals
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Author : Edward James McShane
language : en
Publisher: American Mathematical Soc.
Release Date : 1969
A Riemann Type Integral That Includes Lebesgue Stieltjes Bochner And Stochastic Integrals written by Edward James McShane and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Integrals categories.
One of the difficulties with integration theory is that there are so many different detailed definitions that the non-expert is confused about their relative strengths and usefulness. A surprising recent development in the theory of integration has been the discovery that suitable modifications to the Riemann definition using approximating sums can produce a wide variety of different integrals including integrals of great power.
Riemann Stieltjes Integral Inequalities For Complex Functions Defined On Unit Circle
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Author : Silvestru Sever Dragomir
language : en
Publisher: CRC Press
Release Date : 2019-08-19
Riemann Stieltjes Integral Inequalities For Complex Functions Defined On Unit Circle written by Silvestru Sever Dragomir and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-19 with Mathematics categories.
The main aim of this book is to present several results related to functions of unitary operators on complex Hilbert spaces obtained, by the author in a sequence of recent research papers. The fundamental tools to obtain these results are provided by some new Riemann-Stieltjes integral inequalities of continuous integrands on the complex unit circle and integrators of bounded variation. Features All the results presented are completely proved and the original references where they have been firstly obtained are mentioned Intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, as well as by postgraduate students and scientists applying inequalities in their specific areas Provides new emphasis to mathematical inequalities, approximation theory and numerical analysis in a simple, friendly and well-digested manner. About the Author Silvestru Sever Dragomir is Professor and Chair of Mathematical Inequalities at the College of Engineering & Science, Victoria University, Melbourne, Australia. He is the author of many research papers and several books on Mathematical Inequalities and their Applications. He also chairs the international Research Group in Mathematical Inequalities and Applications (RGMIA). For details, see https://rgmia.org/index.php.
Volterra Stieltjes Integral Equations And Generalized Ordinary Differential Expressions
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Author : A.B. Mingarelli
language : en
Publisher: Springer
Release Date : 2006-11-15
Volterra Stieltjes Integral Equations And Generalized Ordinary Differential Expressions written by A.B. Mingarelli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
A First Course In Real Analysis
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Author : M.H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Real Analysis written by M.H. Protter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
Volterra Stieltjes Integral Equations
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-09-21
Volterra Stieltjes Integral Equations written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-21 with Mathematics categories.
Volterra Stieltjes-Integral Equations
A Garden Of Integrals
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Author : Frank Burk
language : en
Publisher: MAA
Release Date : 2007-08-30
A Garden Of Integrals written by Frank Burk and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-30 with Mathematics categories.
The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reasons for their existence and their uses are given, with plentiful historical information. The audience for the book is advanced undergraduate mathematics students, graduate students, and faculty members, of which even the most experienced are unlikely to be aware of all of the integrals in the Garden of Integrals. Professor Burk's clear and well-motivated exposition makes this book a joy to read. There is no other book like it.