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Author : William Fogg Osgood
Publisher : Unknown
Page : 80 pages
File Size : 45,6 Mb
Release : 1897
Category : Mathematics
ISBN : HARVARD:32044019939784
Author : J. H. Heinbockel
Publisher : Trafford Publishing
Page : 531 pages
File Size : 54,7 Mb
Release : 2010-12
Category : Mathematics
ISBN : 9781426949548
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 : Thomas John I'Anson Bromwich
Publisher : Legare Street Press
Page : 0 pages
File Size : 41,7 Mb
Release : 2022-10-26
Category : History
ISBN : 101554469X
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Charles H. C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer Nature
Page : 258 pages
File Size : 43,7 Mb
Release : 2022-01-10
Category : Mathematics
ISBN : 9783030906467
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 : William Fogg Osgood
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 1920
Category : Series, Infinite
ISBN : OCLC:627520134
Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 500 pages
File Size : 50,6 Mb
Release : 2017-09-14
Category : Mathematics
ISBN : 0980232759
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 : Ludmila Bourchtein,Andrei Bourchtein
Publisher : Springer Nature
Page : 388 pages
File Size : 50,5 Mb
Release : 2021-11-13
Category : Mathematics
ISBN : 9783030794316
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 : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210214
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 : Konrad Knopp
Publisher : Courier Corporation
Page : 212 pages
File Size : 47,8 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9780486152042
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 : Daniel D. Bonar,Michael J. Khoury Jr.
Publisher : American Mathematical Soc.
Page : 261 pages
File Size : 44,9 Mb
Release : 2018-12-12
Category : Electronic
ISBN : 9781470447823
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Author : Thomas John I'Anson Bromwich
Publisher : American Mathematical Soc.
Page : 564 pages
File Size : 49,7 Mb
Release : 2005
Category : Mathematics
ISBN : 0821839764
Based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907, this title includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; and a discussion of trigonometrical series.
Author : THOMAS JOHN I'ANSON. BROMWICH
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 2018
Category : Electronic
ISBN : 1033271217
Author : Bernhard W. Bach, Jr.
Publisher : Cambridge University Press
Page : 201 pages
File Size : 42,5 Mb
Release : 2018-05-17
Category : Mathematics
ISBN : 9781107059825
An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.
Author : Thomas John I'Anson Bromwich
Publisher : Forgotten Books
Page : 530 pages
File Size : 53,8 Mb
Release : 2017-11-04
Category : Mathematics
ISBN : 0260270563
Excerpt from An Introduction to the Theory of Infinite Series The investigations of Chapter XI. Imply an acquaintance with the convergence of infinite integrals, but when the manu script was being prepared for printing no English book was available from which the necessary theorems could be quoted. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : T J I a Bromwich
Publisher : Gyan Books
Page : 528 pages
File Size : 54,9 Mb
Release : 2017
Category : Electronic
ISBN : 9351285936