Download or read book The Generalized Riemann Integral in R2 written by Mark Conway and published by . This book was released on 2018 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their undergraduate studies, new calculus students learn how to integrate a function using the Riemann integral. The Riemann integral is used in Mathematics and Engineering and is a fairly simple concept to understand. However, the Riemann integral has some drawbacks and limitations. These limitations include improper integrals, application of the Fundamental theorem of Calculus, and others that will be discussed. By using the generalized Riemann integral, we can eliminate these limitations by only slightly changing our definition of the Riemann integral. However, what has been written on it isn't particularly easy to understand. Because of this, the theory is only taught at the higher undergraduate or graduate level. This paper will take a look at the generalized Riemann integral. Being a more general version of the standard Riemann integral, it is not subject to these restrictions. The focus of this paper will be in one and two dimensions, but the theory from there can be easily generalized into higher dimensions. In this paper we will look at the generalized Riemann integral and will show all the ways all in which it is more powerful than the standard Riemann integral taught in calculus courses. While showing that the generalized Riemann is superior, we will also break the theory down for both the one and two-dimensional cases in a more understandable way.

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.

Download or read book The Generalized Riemann Integral written by Robert M. MacLeod and published by . This book was released on 1980 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Generalized Riemann Integral written by Kevin Herbert Strobel and published by . This book was released on 1988 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Generalized Riemann Integral written by Michael McClure and published by . This book was released on 2007 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Riemann Lebesgue and Generalized Riemann Integrals written by A. G. Das and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Download or read book The Generalized Riemann Integral written by Diana K. Stuart (M.S.) and published by . This book was released on 2005 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Thev Generalized Riemann Integral written by Robert M. Mc Leod and published by . This book was released on 1980 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to the Generalized Riemann Integral and Its Role in Undergraduate Mathematics Education written by Ryan Bastian and published by . This book was released on 2016 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann integral is often introduced to undergraduate calculus students, as its definition and related theorems are relatively straightforward to understand. However, the Riemann integral is limited in its power to integrate a wide variety of functions. This paper introduces an alternate definition of the integral, known as the generalized Riemann integral. This version of the integral was introduced around 1960 by Ralph Henstock and Jaroslav Kurzweil, and its definition and theorems are almost as simple as the traditional Riemann integral, yet its power to integrate functions far surpasses Riemann's integral. This paper includes an overview of the most important theorems and definitions related to the generalized Riemann integral and explains how it can be used to supplement, or even replace, the Riemann integral in undergraduate calculus and analysis courses.

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.

Download or read book The Laplace Transformation I General Theory written by and published by Bookboon. This book was released on with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Quantitative Finance Book V General Measure and Integration Theory written by Robert R. Reitano and published by CRC Press. This book was released on 2024-02-27 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the competitive edge these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books develops the advanced topics in mathematics that finance professionals need to advance their careers. These books expand the theory most do not learn in graduate finance programs, or in most financial mathematics undergraduate and graduate courses. As an investment executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial services industry and two decades in academia where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the earlier books in the set. While the set offers a continuous progression through these topics, each title can be studied independently. Features Extensively referenced to materials from earlier books Presents the theory needed to support advanced applications Supplements previous training in mathematics, with more detailed developments Built from the author's five decades of experience in industry, research, and teaching Published and forthcoming titles in the Robert R. Reitano Quantitative Finance Series: Book I: Measure Spaces and Measurable Functions Book II: Probability Spaces and Random Variables Book III: The Integrals of Lebesgue and (Riemann-)Stieltjes Book IV: Distribution Functions and Expectations Book V: General Measure and Integration Theory Book VI: Densities, Transformed Distributions, and Limit Theorems Book VII: Brownian Motion and Other Stochastic Processes Book VIII: Itô Integration and Stochastic Calculus 1 Book IX: Stochastic Calculus 2 and Stochastic Differential Equations Book X: Classical Models and Applications in Finance

Download or read book Multivariable and Vector Calculus written by Joseph D. Fehribach and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers multivariable and vector calculus. It can be used as a textbook for a one-semester course or self-study. It includes worked-through exercises, with answers provided for many of the basic computational ones and hints for the more complex ones.. This second edition features new exercises, new sections on twist and binormal vectors for curves in space, linear approximations, and the Laplace and Poisson equations.

Download or read book Understanding Analysis written by Stephen Abbott and published by Springer. This book was released on 2015-05-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Download or read book Generalized Riemann Integration written by Geoffrey Hungerford and published by . This book was released on 1990 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Mathematics written by Vialar Thierry and published by BoD - Books on Demand. This book was released on 2023-08-22 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry Revised written by William Munger Boothby and published by Gulf Professional Publishing. This book was released on 2003 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields