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eBook Elliptic Functions (London Mathematical Society Student Texts) download

by J. V. Armitage

eBook Elliptic Functions (London Mathematical Society Student Texts) download ISBN: 0521785634
Author: J. V. Armitage
Publisher: Cambridge University Press; 1 edition (October 23, 2006)
Language: English
Pages: 402
ePub: 1780 kb
Fb2: 1553 kb
Rating: 4.1
Other formats: lit mobi docx lrf
Category: Math Sciences
Subcategory: Mathematics

87 results in London Mathematical Society Student Texts

87 results in London Mathematical Society Student Texts. Relevance Title Sorted by Date. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces.

Excerpts from Alan Turing's 1937 paper in the Proceedings of the London Mathematical Society will appear on the new Bank of England £50 banknote. New Identity for the Proceedings.

Texts are frequently based on graduate courses given by the authors. To date, the series contains over 85 titles. Excerpts from Alan Turing's 1937 paper in the Proceedings of the London Mathematical Society will appear on the new Bank of England £50 banknote.

There is a lot of additional theory and application of elliptic modular functions in this book, which look fascinating but which my brain is currently unable to muster the energy to attack.

Series: London Mathematical Society Student Texts (Book 67). Paperback: 402 pages. There is a lot of additional theory and application of elliptic modular functions in this book, which look fascinating but which my brain is currently unable to muster the energy to attack.

V. Armitage, W. F. Eberlein. Скачать (pdf, . 3 Mb).

Items related to Elliptic Functions (London Mathematical Society Student. In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical essay. J. V. Armitage; W. Eberlein Elliptic Functions (London Mathematical Society Student Texts). ISBN 13: 9780521780780. Elliptic Functions (London Mathematical Society Student Texts). Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum.

In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical .

In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical essay. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and the reader is introduced to the richly varied applications of the elliptic and related functions.

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)). The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly

Book digitized by Google and uploaded to the Internet Archive by user tpb. Two v. of 3 issues each per year, "Papers presented to . Littlewood on his 80th birthday" issued as 3d se. 14 A, 1965. Some issues in 3d ser. accompanied by Abstracts of papers accepted for publication.

Book digitized by Google and uploaded to the Internet Archive by user tpb. 1886, with v. 17; Vols.

Article in Bulletin of the London Mathematical Society 32(6):746-747 · November 2000 with 9 Reads. How we measure 'reads'. 00, LMS Members' price £4. 5), isbn 0 521 65378 9 (Cambridge University Press, 1999). Do you want to read the rest of this article? Request full-text. Citations (1). References (0). Connectedness and Isomorphism Properties of the Zig-Zag Product of Graphs.

In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical essay. Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and the reader is introduced to the richly varied applications of the elliptic and related functions.
Comments: (3)
Ironrunner
I purchased this book as a follow-on to John Howie's "Fields and Galois Theory", in which at the end of the tenth chapter, after proving that there is no general solution by radicals of the general quintic equation, he states that the general solution of the quintic equation can be expressed in terms of elliptic modular functions. These are functions of the upper half-complex plane which are doubly periodic and obey certain transformation laws. The tenth chapter of "Elliptic Functions" covers this very nicely. However, I "cheated" in that I first read various entries in Wikipedia on the elliptic modular functions and related topics, in order to get a concise overview of the topic. I don't think I would have been able to achieve such a clear overview using this book, because I would probably have lost sight of the forest for the trees, or perhaps more aptly, for slogging through the dense underbrush, sweat burning my eyes.

In any event, my original plan was to go through the entire book in sequence, but after spending several weeks just going through the first two chapters, I decided to skip straight to chapter ten, which covers the general solution of the quintic. The first two chapters give an introduction to how elliptic functions were first discovered (by Niels Abel) as inversions of elliptic integrals, and how they might have been further developed along these lines, rather than as they were actually further developed, namely as theta functions by Jacobi after Abel's early death. They're interesting but not particularly essential to the core of the topic. If you want a standard exposition of the topic without this historical detour, you can start with the third chapter.

The tenth chapter clearly expounds the use of elliptic modular functions to solve the general quintic equation. It covers two different methods for doing so, of which I only studied the first. I stand in awe of how anyone could be smart enough to have figured this out. It is reasonably straightforward and concise, with references supplied to more detailed treatments. There are some minor typos, annoying but not seriously interfering with the comprehensibility of the text. (The subject matter itself provides sufficient such interference!)

There is a lot of additional theory and application of elliptic modular functions in this book, which look fascinating but which my brain is currently unable to muster the energy to attack. Perhaps some day.

I can recommend this book to anyone who wants to learn more about the theory and applications of elliptic modular functions, including the solution of the general quintic equation. The exposition is reasonably clear, there are good examples, and each chapter section is followed by exercises, the answers to which are unfortunately not provided. A background in complex analysis and linear algebra is required.

Good Luck!

Notes: (reader assumes all responsibility for relying on these notes!)

chapter 1: none

chapter 2:

p. 48 first integral (phi) should be from 0 to x, not 0 to 1

p. 48 right hand side of second equation should read
cos lemn (omega/2 - phi), not cos lemn (1/2 - phi). Omega is defined in (2.46)

Chapter 10

p. 281 (10.14): equation holds for each y sub k and x sub k where the y sub k are the roots of q(y) and the x sub k are the roots of
p(x)

p. 283 line 11 should be (10.13) not (10.12). Each of the q's (I'll call them q sub i's for convenience) are functions of the respective eta sub i's and therefore of sigma sub i; the sigma sub i's are functions of the set {alpha, beta, gamma, delta, epsilon} and the s sub i's; the s sub i's are functions of the p sub i's; the p sub i's are functions of the xi sub i's; therefore the q sub i's are functions of the set {alpha beta gamma delta epsilon} and the xi sub i's.

p. 286 first line of section 10.4 refers to (10.22), not (10.12)

p. 287 third line refers to (10.26) not (10.32)

p. 287 (10.40) see p. 153

p. 288 line 2 should be (10.26) not (10.32)

p. 289 after exercise 10.4 we have section 10.5 not section 10.4

p. 291 title of section 10.6 should be transformation singular not transformations plural

p. 298 table second row should be tau to -1/tau not tau to tau minus 1/tau

p. 301 first table same mistake

p. 304 line 7 should be u^24 + 2^12 u^-24, not u^24 + 12 u^-24
Fenius
The book on elliptic functions has a good introduction of the elliptic functions. It covers the functions of complex variable, the residues, the derivation of the addition formulas of the functions, the Fourier series of the dn(u) function. The book has a very introduction of the theta functions. After these basic properties the books goes to more advanced topics without covering other basics topics: no derivation of half angle formulas, no square of the functions as function of the double angle, no Maclaurin/Taylor expansions, no mapping of the functions to the integrals in the complex plane, no Fourier series of the elliptic sine and cosine which are left to the reader, no differential equation for the functions.
Golkree
Too bad this book was not proof read correctly. It is defined as a student text: there are way too many typos, sometime more than one per page in some chapters.

It would otherwise be an excellent book; this product should be recalled by the editor.

Wait for the next edition.