Improper Riemann Integrals PDF Download
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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 | : Ioannis Markos Roussos |
Publisher | : CRC Press |
Total Pages | : 692 |
Release | : 2013-12-16 |
Genre | : Mathematics |
ISBN | : 1466588071 |
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 problems. The book contains the necessary background, theorems, and tools, along with two lists of the most important integrals and sums computed in the text. Numerous examples at various levels of difficulty illustrate the concepts and theorems. The book uses powerful tools of real and complex analysis not only to compute the examples and solve the problems but also to justify that the computation methods are legitimate. Enriched with many examples, applications, and problems, this book helps students acquire a deeper understanding of the subject, preparing them for further study. It shows how to solve the integrals without exclusively relying on tables and computer packages.
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 | : 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 | : 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 | : Gilbert Strang |
Publisher | : Wellesley-Cambridge Press |
Total Pages | : 500 |
Release | : 2017-09-14 |
Genre | : Mathematics |
ISBN | : 9780980232752 |
Download Calculus Book in PDF, ePub and Kindle
Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of calculus to areas such as physics, engineering and economics are included in order to enhance students' understanding. New to the third edition is a chapter on the 'Highlights of calculus', which accompanies the popular video lectures by the author on MIT's OpenCourseWare. These can be accessed from math.mit.edu/~gs.
Author | : Vladimir I. Bogachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 1075 |
Release | : 2007-01-15 |
Genre | : Mathematics |
ISBN | : 3540345140 |
Download Measure Theory Book in PDF, ePub and Kindle
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Author | : Charles W Swartz |
Publisher | : World Scientific |
Total Pages | : 169 |
Release | : 2001-05-30 |
Genre | : Mathematics |
ISBN | : 9814493511 |
Download Introduction To Gauge Integrals Book in PDF, ePub and Kindle
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.
Author | : Gregory Hartman |
Publisher | : |
Total Pages | : 0 |
Release | : 2015 |
Genre | : Calculus |
ISBN | : 9781514225158 |
Download APEX Calculus Book in PDF, ePub and Kindle
APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).