An Introduction To Infinite Products

Author : Charles H. C. Little
Publisher : Springer Nature
ISBN 13 : 3030906469
Total Pages : 258 pages
Book Rating : 4.67/5 ( download)

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Download or read book An Introduction to Infinite Products written by Charles H. C. Little and published by Springer Nature. This book was released on 2022-01-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

Author : Leonhard Euler
Publisher : Springer Science & Business Media
ISBN 13 : 1461210216
Total Pages : 341 pages
Book Rating : 4.14/5 ( download)

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Download or read book Introduction to Analysis of the Infinite written by Leonhard Euler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Author : Thomas John I'Anson Bromwich
Publisher :
ISBN 13 :
Total Pages : 532 pages
Book Rating : 4.32/5 ( download)

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Download or read book An Introduction to the Theory of Infinite Series written by Thomas John I'Anson Bromwich and published by . This book was released on 1908 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ludmila Bourchtein
Publisher : Springer Nature
ISBN 13 : 3030794318
Total Pages : 388 pages
Book Rating : 4.16/5 ( download)

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Download or read book Theory of Infinite Sequences and Series written by Ludmila Bourchtein and published by Springer Nature. This book was released on 2021-11-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.

Author : J. H. Heinbockel
Publisher : Trafford Publishing
ISBN 13 : 1426949545
Total Pages : 531 pages
Book Rating : 4.48/5 ( download)

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Download or read book Introduction to Finite and Infinite Series and Related Topics written by J. H. Heinbockel and published by Trafford Publishing. This book was released on 2010-12 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the analysis of finite series, infinite series, finite products and infinite products and continued fractions with applications to selected subject areas. Infinite series, infinite products and continued fractions occur in many different subject areas of pure and applied mathematics and have a long history associated with their development. The mathematics contained within these pages can be used as a reference book on series and related topics. The material can be used to augment the mathematices found in traditional college level mathematics course and by itself is suitable for a one semester special course for presentation to either upper level undergraduates or beginning level graduate students majoring in science, engineering, chemistry, physics, or mathematics. Archimedes used infinite series to find the area under a parabolic curve. The method of exhaustion is where one constructs a series of triangles between the arc of a parabola and a straight line. A summation of the areas of the triangles produces an infinite series representing the total area between the parabolic curve and the x-axis.

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
ISBN 13 : 3540290214
Total Pages : 217 pages
Book Rating : 4.16/5 ( download)

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Download or read book An Introduction to Infinite-Dimensional Analysis written by Giuseppe Da Prato and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.

Author : Jon Aaronson
Publisher : American Mathematical Soc.
ISBN 13 : 0821804944
Total Pages : 298 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to Infinite Ergodic Theory written by Jon Aaronson and published by American Mathematical Soc.. This book was released on 1997 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.

Author : Konrad Knopp
Publisher : Courier Corporation
ISBN 13 : 0486152049
Total Pages : 212 pages
Book Rating : 4.42/5 ( download)

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Download or read book Infinite Sequences and Series written by Konrad Knopp and published by Courier Corporation. This book was released on 2012-09-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.

Author : Konrad Knopp
Publisher :
ISBN 13 :
Total Pages : 596 pages
Book Rating : 4.65/5 ( download)

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Download or read book Theory and Application of Infinite Series written by Konrad Knopp and published by . This book was released on 1928 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trans from the 2nd German ed , pub 1923.

Author : J. van Mill
Publisher : Elsevier
ISBN 13 : 0080933688
Total Pages : 401 pages
Book Rating : 4.89/5 ( download)

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Download or read book Infinite-Dimensional Topology written by J. van Mill and published by Elsevier. This book was released on 1988-12-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.