Lectures On The Theory Of Integration PDF Download
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Author | : Ralph Henstock |
Publisher | : World Scientific |
Total Pages | : 224 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9789971504519 |
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.
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.
Author | : Harold Widom |
Publisher | : Courier Dover Publications |
Total Pages | : 177 |
Release | : 2016-11-16 |
Genre | : Mathematics |
ISBN | : 0486810283 |
Download Lectures on Measure and Integration Book in PDF, ePub and Kindle
These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.
Author | : Ralph Henstock |
Publisher | : |
Total Pages | : 288 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
Download The General Theory of Integration Book in PDF, ePub and Kindle
Every good mathematical book stands like a tree with its roots in the past and its branches stretching out towards the future. Whether the fruits of this tree are desirable and whether the branches will be quarried for mathematical wood to build further edifices, I will leave to the judgment of history. The roots of this book take nourishment from the concept of definite integration of continuous functions, where Riemann's method is the high water mark of the simpler theory.
Author | : A. O. Gogolin |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2013-10-22 |
Genre | : Science |
ISBN | : 3319002120 |
Download Lectures on Complex Integration Book in PDF, ePub and Kindle
The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.
Author | : Max Shiffman |
Publisher | : |
Total Pages | : 45 |
Release | : 1968 |
Genre | : Integrals, Generalized |
ISBN | : |
Download Lectures on the Theory of Measure and Integration Book in PDF, ePub and Kindle
Author | : I. G. Petrovskii |
Publisher | : Courier Corporation |
Total Pages | : 142 |
Release | : 1996-09-01 |
Genre | : Mathematics |
ISBN | : 9780486697567 |
Download Lectures on the Theory of Integral Equations Book in PDF, ePub and Kindle
Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Author | : Peng Yee Lee |
Publisher | : World Scientific |
Total Pages | : 194 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9789971508920 |
Download Lanzhou Lectures on Henstock Integration Book in PDF, ePub and Kindle
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.
Author | : Vilmos Komornik |
Publisher | : Springer |
Total Pages | : 417 |
Release | : 2016-06-03 |
Genre | : Mathematics |
ISBN | : 1447168119 |
Download Lectures on Functional Analysis and the Lebesgue Integral Book in PDF, ePub and Kindle
This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
Author | : G De Barra |
Publisher | : Elsevier |
Total Pages | : 240 |
Release | : 2003-07-01 |
Genre | : Mathematics |
ISBN | : 0857099523 |
Download Measure Theory and Integration Book in PDF, ePub and Kindle
This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject Includes numerous worked examples necessary for teaching and learning at undergraduate level Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided