The Generalized Riemann Integral PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Generalized Riemann Integral PDF full book. Access full book title The Generalized Riemann Integral.
Author | : Robert M. McLeod |
Publisher | : American Mathematical Soc. |
Total Pages | : 275 |
Release | : 1980-12-31 |
Genre | : Riemann integral |
ISBN | : 1614440204 |
Download The Generalized Riemann Integral Book in PDF, ePub and Kindle
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.
Author | : A. G. Das |
Publisher | : |
Total Pages | : 0 |
Release | : 2008 |
Genre | : Integrals, Generalized |
ISBN | : 9788173199332 |
Download The Riemann, Lebesgue and Generalized Riemann Integrals Book in PDF, ePub and Kindle
"This book aims at the definition and development of the Henstock-Hurzeil integral and those of the McShane integral in the real line." "The Henstock-Kurzweil integral is of super Lebesgue power while the McShane integral is of Lebesgue power. For bounded functions, however, the Henstock-Kurzweil, the McShane and the Lebesgue integrals are equivalent. Owing to their simple construction and easy access, the Generalized Riemann integrals will surely be familiar to physicists, engineers and applied mathematicians. Each chapter of the book provides a good number of solved problems and counter examples along with selected problems left as exercises."--BOOK JACKET.
Author | : Robert G. Bartle |
Publisher | : American Mathematical Soc. |
Total Pages | : 480 |
Release | : 2001-03-21 |
Genre | : |
ISBN | : 9780821883853 |
Download A Modern Theory of Integration Book in PDF, ePub and Kindle
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.
Author | : Robert M. MacLeod |
Publisher | : |
Total Pages | : 275 |
Release | : 1980 |
Genre | : |
ISBN | : 9780883850008 |
Download The Generalized Riemann Integral Book in PDF, ePub and Kindle
Author | : Ioannis Roussos |
Publisher | : CRC Press |
Total Pages | : 681 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 146658808X |
Download Improper Riemann Integrals Book in PDF, ePub and Kindle
Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineering
Author | : Washek F. Pfeffer |
Publisher | : Cambridge University Press |
Total Pages | : 326 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9780521440356 |
Download The Riemann Approach to Integration Book in PDF, ePub and Kindle
A detailed exposition of generalised Riemann-Stieltjes integrals.
Author | : Ioannis Roussos |
Publisher | : CRC Press |
Total Pages | : 464 |
Release | : 2023-09-27 |
Genre | : Mathematics |
ISBN | : 1000958140 |
Download Improper Riemann Integrals Book in PDF, ePub and Kindle
The scope of this book is the improper or generalized Riemann integral and infinite sum (series). The reader will study its convergence, principal value, evaluation and application to science and engineering. Improper Riemann integrals and infinite sums are interconnected. In the new edition, the author has involved infinite sums more than he did in the first edition. Apart from having computed and listed a large number of improper integrals and infinite sums, we have also developed the necessary theory and various ways of evaluating them or proving their divergence. Questions, problems and applications involving various improper integrals and infinite sums (series) of numbers emerge in science and application very often. Their complete presentations and all rigorous proofs would require taking the graduate-level courses on these subjects. Here their statements are adjusted to a level students of all levels can understand and use them efficiently as powerful tools in a large list of problems and applications.
Author | : Open University. M431 Course Team |
Publisher | : |
Total Pages | : 27 |
Release | : 1992 |
Genre | : Integrals, Generalized |
ISBN | : 9780749220686 |
Download The Lebesgue Integral Book in PDF, ePub and Kindle
Author | : Douglas S. Kurtz |
Publisher | : World Scientific |
Total Pages | : 286 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9789812388438 |
Download Theories of Integration Book in PDF, ePub and Kindle
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.
Author | : Ralph Henstock |
Publisher | : World Scientific |
Total Pages | : 223 |
Release | : 1988-04-01 |
Genre | : Mathematics |
ISBN | : 9814551805 |
Download Lectures On The Theory Of Integration Book in PDF, ePub and Kindle
This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.