Lectures On The Theory Of Elliptic Functions Volume 1

Author : Harris Hancock
Publisher : Sagwan Press
Page : 566 pages
File Size : 44,7 Mb
Release : 2018-02-02
Category : Electronic
ISBN : 1376479265

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Lectures On the Theory of Elliptic Functions; Volume 1 by Harris Hancock Pdf

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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 : Harris Hancock
Publisher : Courier Corporation
Page : 544 pages
File Size : 43,5 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 0486438252

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Lectures on the Theory of Elliptic Functions by Harris Hancock Pdf

Prized for its extensive coverage of classical material, this text is also well regarded for its unusual fullness of treatment and its comprehensive discussion of both theory and applications. The author developes the theory of elliptic integrals, beginning with formulas establishing the existence, formation, and treatment of all three types, and concluding with the most general description of these integrals in terms of the Riemann surface. The theories of Legendre, Abel, Jacobi, and Weierstrass are developed individually and correlated with the universal laws of Riemann. The important contributory theorems of Hermite and Liouville are also fully developed. 1910 ed.

Author : Harris Hancock
Publisher : Legare Street Press
Page : 0 pages
File Size : 45,6 Mb
Release : 2022-10-27
Category : Electronic
ISBN : 1016144237

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Lectures on the Theory of Elliptic Functions; Volume I by Harris Hancock Pdf

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 : Harris Hancock
Publisher : Theclassics.Us
Page : 84 pages
File Size : 48,5 Mb
Release : 2013-09
Category : Electronic
ISBN : 1230731393

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Lectures on the Theory of Elliptic Functions by Harris Hancock Pdf

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. 1910 edition. Excerpt: ...Possibly the clearest and simplest method of treating this problem is in connection with the Riemann surface upon which the associated integrals may be represented. Before proceeding to the problem of inversion we shall therefore consider this surface in the next Chapter. EXAMPLE 1. If two doubly periodic functions f(z) and jz) have only two poles of the first order in the period-parallelogram and if each pole of the one function coincides with a pole of the other, then is m-cm + c where C and C are constants. CHAPTER VI THE RIEMANN SURFACE Article 108. At the close of the preceding Chapter we were left with the discussion of an integral which contained a radical. Such an expression is two-valued, and we must now consider more closely the meaning of such functions and their associated integrals. Take as simplest case the example 8= Vz-a= (z-a), where 2 is a complex variable and a an arbitrary constant. For the value z = o, we have s = 0; but for all other finite values of z there are two values of s that are equal and of opposite signs. The point a is called a branch-point of s. The point z = 00 is also a branch-point of this function; for-= = 0 for z = 00. Consequently--and likewise s has s V z-a s only one value for z = 00. There are other reasons why z = a and z = 00 are called branchpoints. Corresponding to the value z = zo, let s = s6 l)e a definite value of s. Along the curve (1) from z0 to z consider the values of s at all the points of the curve which differ from one another by infinitesimally small quantities, and similarly consider the values of s along the curve (2) until we again come to z. The value of s at this point will be the same whether we have gone over the first or second curve, provided the...

Author : Dr Robert Fricke
Publisher : Legare Street Press
Page : 0 pages
File Size : 48,7 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 101961658X

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Vorlesungen Uber Die Theorie For Elliptischen Modulfunctionen by Dr Robert Fricke Pdf

Fricke's groundbreaking study of the theory of elliptic modular functions is a must-read for anyone interested in the foundations of modern mathematics. With clear explanations and insightful examples, Fricke offers a comprehensive overview of this complex and fascinating subject. 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 : Harris Hancock
Publisher : Unknown
Page : 128 pages
File Size : 52,9 Mb
Release : 1976
Category : Electronic
ISBN : OCLC:1139864937

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Lectures on the Theory of Elliptic Functions by Harris Hancock Pdf

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
Page : 67 pages
File Size : 51,8 Mb
Release : 2015-12-31
Category : Science
ISBN : 9781681742304

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Lectures on Selected Topics in Mathematical Physics by William A. Schwalm Pdf

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642522444

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Elliptic Functions by Komaravolu Chandrasekharan Pdf

This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.

Author : Bruce C. Berndt,Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 47,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821812006

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Continued Fractions: From Analytic Number Theory to Constructive Approximation by Bruce C. Berndt,Fritz Gesztesy Pdf

This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Author : Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 47,8 Mb
Release : 1997-09-16
Category : Mathematics
ISBN : 0821897802

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Elliptic Functions and Elliptic Integrals by Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev Pdf

This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.

Author : Milton Abramowitz,Irene A. Stegun
Publisher : Unknown
Page : 1060 pages
File Size : 40,5 Mb
Release : 1968
Category : Mathematics
ISBN : UCBK:C036344959

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Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables by Milton Abramowitz,Irene A. Stegun Pdf

Author : Felix Klein,Robert Fricke
Publisher : Unknown
Page : 0 pages
File Size : 50,5 Mb
Release : 2017
Category : Modular functions
ISBN : OCLC:1025333532

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Lectures on the Theory of Elliptic Modular Functions: Part 1. Introduction to the study of the elliptic modular functions by Felix Klein,Robert Fricke Pdf

Author : Patrick Du Val
Publisher : Cambridge University Press
Page : 257 pages
File Size : 51,9 Mb
Release : 1973-08-02
Category : Mathematics
ISBN : 9780521200363

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Elliptic Functions and Elliptic Curves by Patrick Du Val Pdf

A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.

Author : Mario Gonzalez
Publisher : Routledge
Page : 544 pages
File Size : 51,7 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9781351459389

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Complex Analysis by Mario Gonzalez Pdf

A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Author : Derek F. Lawden
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 46,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739800

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Elliptic Functions and Applications by Derek F. Lawden Pdf

The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .