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Author : Thomas John I'Anson Bromwich
Publisher : Unknown
Page : 560 pages
File Size : 51,6 Mb
Release : 1955
Category : Series, Infinite
ISBN : UOM:49015000670340
Author : Thomas John Ianson Bromwich
Publisher : Literary Licensing, LLC
Page : 526 pages
File Size : 44,6 Mb
Release : 2014-08-07
Category : Electronic
ISBN : 1498138705
This Is A New Release Of The Original 1908 Edition.
Author : Thomas John l'Anson Bromwich
Publisher : Unknown
Page : 0 pages
File Size : 50,8 Mb
Release : 1942
Category : Electronic
ISBN : OCLC:1411968989
Author : Thomas John I'Anson Bromwich
Publisher : Theclassics.Us
Page : 70 pages
File Size : 49,7 Mb
Release : 2013-09
Category : Electronic
ISBN : 1230448136
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ...investigations. In numerical work, however, they naturally used only series which are now called asymptotic (Art. 130 below); in such series the terms begin to decrease, and reach a minimum, afterwards increasing. If we take the sum to a stage at which the terms The majority of writers on these series use the word divergent as including oscillatory Beries; we shall, however, except in quotations, adopt the same distinction as in the previous part of the book. are sufficiently small, we may hope to obtain an approximation with a degree of accurac' represented by the last term retained; and it can be proved that this is the case with many series which are convenient for numerical calculations (see Art. 130 for examples). An important class of such series consists of the series used by astronomers to calculate the planetary positions: it has been proved by Poincare that these series do not converge, but yet the results of the calculations are confirmed by observation. The explanation of this fact may be inferred from Poincare"s theory of asymptotic series (Art. 133). But mathematicians have often been led to employ series of a different character, in which the terms never decrease, and may increase to infinity. Typical examples of such series are: Euler considered the " sum " of a non-convergent series as the finite numerical value of the arithmetical expression from the expansion of which the series was derived. Thus he defined the "sums" of the series (l)-(3) as follows: (1)=i+l=J; (2)=(TTI)2=4; (3)=T+2=3; and his discussion of the series (4) will be found at the end of Art. 98 (see p. 267). In principle, Kuler's definition depends on the inversion of two limits, which, taken in one order, give a definite value, ...
Author : THOMAS JOHN I'ANSON. BROMWICH
Publisher : Unknown
Page : 0 pages
File Size : 41,6 Mb
Release : 2018
Category : Electronic
ISBN : 1033271217
Author : T. J. IA. Bromwich
Publisher : Unknown
Page : 528 pages
File Size : 41,8 Mb
Release : 2020-07-13
Category : History
ISBN : 9354038743
Author : Thomas J. Bromwich,Thomas M. Macrobert
Publisher : Unknown
Page : 542 pages
File Size : 52,7 Mb
Release : 1965
Category : Series, Infinite
ISBN : OCLC:634703075
Author : T. J. l’a. Bromwich
Publisher : American Mathematical Society
Page : 554 pages
File Size : 51,6 Mb
Release : 2023-04-26
Category : Mathematics
ISBN : 9781470473365
This edition consists largely of a reproduction of the first edition (which was based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902–1907), with additional theorems and examples. Additional material 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; a discussion of trigonometrical series, including Stokes's transformation and Gibbs's phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.
Author : Thomas J. Bromwich
Publisher : Unknown
Page : 535 pages
File Size : 43,5 Mb
Release : 1959
Category : Electronic
ISBN : OCLC:630398627
Author : Konrad Knopp
Publisher : Courier Corporation
Page : 596 pages
File Size : 51,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9780486661650
This unusually clear and interesting classic offers a thorough and reliable treatment of an important branch of higher analysis. The work covers real numbers and sequences, foundations of the theory of infinite series, and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, and other topics). Exercises throughout. Ideal for self-study.
Author : Ludmila Bourchtein,Andrei Bourchtein
Publisher : Springer Nature
Page : 388 pages
File Size : 43,5 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 : Daniel Zwillinger
Publisher : Elsevier
Page : 1184 pages
File Size : 42,5 Mb
Release : 2014-09-18
Category : Mathematics
ISBN : 9780123849342
The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source. Over 10, 000 mathematical entries Most up to date listing of integrals, series and products (special functions) Provides accuracy and efficiency in industry work 25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend to approximately 35% of new updates
Author : I. S. Gradshteyn,I. M. Ryzhik
Publisher : Academic Press
Page : 1206 pages
File Size : 52,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265643
Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
Author : Louise S. Grinstein
Publisher : Taylor & Francis
Page : 496 pages
File Size : 52,6 Mb
Release : 1992
Category : Education
ISBN : 0824041143
This work provides access to approximately 5,000 reviews of English-language mathematical books published in North America. Included are works on mathematics, science, philosophy, and education appearing in the periodical literature from 1800 to 1940. It covers materials not reviewed in Book Review Index and Book Review Digest. It predates Mathematical Reviews, which first appeared in 1940. Books on all aspects of mathematics are included. There are subject, reviewer, and title indexes.
Author : Konrad Knopp
Publisher : Courier Corporation
Page : 212 pages
File Size : 49,8 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.