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The Kurzweil Henstock Integral For Undergraduates
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Book Synopsis The Kurzweil-Henstock Integral for Undergraduates by : Alessandro Fonda
Download or read book The Kurzweil-Henstock Integral for Undergraduates written by Alessandro Fonda and published by Springer. This book was released on 2018-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.
Book Synopsis Henstock-Kurzweil Integration on Euclidean Spaces by : Tuo Yeong Lee
Download or read book Henstock-Kurzweil Integration on Euclidean Spaces written by Tuo Yeong Lee and published by World Scientific. This book was released on 2011 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
Book Synopsis Theories of Integration by : Douglas S. Kurtz
Download or read book Theories of Integration written by Douglas S. Kurtz and published by World Scientific. This book was released on 2004 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Henstock-Kurzweil Integration by : Jaroslav Kurzweil
Download or read book Henstock-Kurzweil Integration written by Jaroslav Kurzweil and published by World Scientific. This book was released on 2000 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: "the results of the book are very interesting and profound and can be read successfully without preliminary knowledge. It is written with a great didactical mastery, clearly and precisely It can be recommended not only for specialists on integration theory, but also for a large scale of readers, mainly for postgraduate students".Mathematics Abstracts
Book Synopsis Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral by : Jaroslav Kurzweil
Download or read book Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral written by Jaroslav Kurzweil and published by World Scientific. This book was released on 2002 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.
Book Synopsis Introduction To Gauge Integrals by : Charles W Swartz
Download or read book Introduction To Gauge Integrals written by Charles W Swartz and published by World Scientific. This book was released on 2001-05-30 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Kurzweil-Henstock Integral and Its Differential by : Solomon Leader
Download or read book The Kurzweil-Henstock Integral and Its Differential written by Solomon Leader and published by CRC Press. This book was released on 2001-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each section as well as appended sets of exercises.
Download or read book Integral written by Lee Peng Yee and published by Cambridge University Press. This book was released on 2000-04-20 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Textbook on the theory of integration. Suitable for beginning graduate and final year undergraduate students.
Book Synopsis A Modern Theory of Integration by : Robert G. Bartle
Download or read book A Modern Theory of Integration written by Robert G. Bartle and published by American Mathematical Soc.. This book was released on 2001-03-21 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Garden of Integrals by : Frank Burk
Download or read book A Garden of Integrals written by Frank Burk and published by MAA. This book was released on 2007-08-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Kurzweil-Henstock Integral and Its Differential by : Solomon Leader
Download or read book The Kurzweil-Henstock Integral and Its Differential written by Solomon Leader and published by CRC Press. This book was released on 2001-06-29 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each sec
Book Synopsis Lanzhou Lectures on Henstock Integration by : Peng Yee Lee
Download or read book Lanzhou Lectures on Henstock Integration written by Peng Yee Lee and published by World Scientific. This book was released on 1989 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on Henstock integration, otherwise known as generalized Riemann integral. It is self-contained and introductory. The author has included a series of convergence theorems for the integral, previously not available. In this book, he has also developed a technique of proof required to present the new as well as the classical results.
Book Synopsis Introduction to Gauge Integrals by : Charles Swartz
Download or read book Introduction to Gauge Integrals written by Charles Swartz and published by World Scientific. This book was released on 2001 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents: Introduction to the Gauge or Henstock-Kurzweil Integral; Basic Properties of the Gauge Integral; Henstock''s Lemma and Improper Integrals; The Gauge Integral over Unbounded Intervals; Convergence Theorems; Integration over More General Sets: Lebesgue Measure; The Space of Gauge Integrable Functions; Multiple Integrals and Fubini''s Theorem; The McShane Integral; McShane Integrability is Equivalent to Absolute Henstock-Kurzweil Integrability. Readership: Upper level undergraduates and mathematicians interested in gauge integrals.
Book Synopsis The Generalized Riemann Integral by : Robert M. McLeod
Download or read book The Generalized Riemann Integral written by Robert M. McLeod and published by American Mathematical Soc.. This book was released on 1980-12-31 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Generalized Riemann Integral is addressed to persons who already have an acquaintance with integrals they wish to extend and to the teachers of generations of students to come. The organization of the work will make it possible for the first group to extract the principal results without struggling through technical details which they may find formidable or extraneous to their purposes. The technical level starts low at the opening of each chapter. Thus, readers may follow each chapter as far as they wish and then skip to the beginning of the next. To readers who do wish to see all the details of the arguments, they are given. The generalized Riemann integral can be used to bring the full power of the integral within the reach of many who, up to now, haven't gotten a glimpse of such results as monotone and dominated convergence theorems. As its name hints, the generalized Riemann integral is defined in terms of Riemann sums. The path from the definition to theorems exhibiting the full power of the integral is direct and short.
Book Synopsis Kurzweil-stieltjes Integral: Theory And Applications by : Tvrdy Milan
Download or read book Kurzweil-stieltjes Integral: Theory And Applications written by Tvrdy Milan and published by World Scientific. This book was released on 2018-09-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral by : Jaroslav Kurzweil
Download or read book Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral written by Jaroslav Kurzweil and published by World Scientific. This book was released on 2002 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this book are convergence and topoligization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear. The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.
Book Synopsis Theory of Integration by : Ralph Henstock
Download or read book Theory of Integration written by Ralph Henstock and published by . This book was released on 1963 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
