Elliptic Functions And Elliptic Integrals

Author : Johannes Blümlein,Carsten Schneider,Peter Paule
Publisher : Springer
Page : 509 pages
File Size : 51,9 Mb
Release : 2019-01-30
Category : Computers
ISBN : 9783030044800

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Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by Johannes Blümlein,Carsten Schneider,Peter Paule Pdf

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
Page : 67 pages
File Size : 41,9 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 : Paul F. Byrd,Morris D. Friedman
Publisher : Springer
Page : 370 pages
File Size : 52,6 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9783642528033

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Handbook of Elliptic Integrals for Engineers and Physicists by Paul F. Byrd,Morris D. Friedman Pdf

Engineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transeendental functions. Such integrations frequently involve (not always in immediately re cognizable form) elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems. As a result, he may entirely avoid problems which lead to elliptic integrals, or is likely to resort to graphical methods or other means of approximation in dealing with all but the siruplest of these integrals. It became apparent in the course of my work in theoretical aero dynamics that there was a need for a handbook embodying in convenient form a comprehensive table of elliptic integrals together with auxiliary formulas and numerical tables of values. Feeling that such a book would save the engineer and physicist much valuable time, I prepared the present volume.

Author : Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 46,7 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 : Serge Lang
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461247524

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Elliptic Functions by Serge Lang Pdf

Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.

Author : Derek F. Lawden
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 48,8 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 .

Author : Viktor Prasolov,Yuri Solovyev
Publisher : American Mathematical Society
Page : 198 pages
File Size : 47,7 Mb
Release : 1997-09-16
Category : Mathematics
ISBN : 9780821813461

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Elliptic Functions and Elliptic Integrals by Viktor Prasolov,Yuri Solovyev 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 : Sir George Greenhill
Publisher : Unknown
Page : 377 pages
File Size : 44,7 Mb
Release : 1892
Category : Elliptic functions
ISBN : UOMDLP:acq7072:0001.001

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The Applications of Elliptic Functions by Sir George Greenhill Pdf

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 41,5 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 : Patrick Du Val
Publisher : Cambridge University Press
Page : 257 pages
File Size : 42,6 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 : Anonim
Publisher : Unknown
Page : 185 pages
File Size : 52,5 Mb
Release : 1962
Category : Elliptic functions
ISBN : 0821805878

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Translations of Mathematical Monographs by Anonim Pdf

Author : Naum Ilʹich Akhiezer,H. H. McFaden
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 53,8 Mb
Release : 1990
Category : Mathematics
ISBN : 0821809008

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Elements of the Theory of Elliptic Functions by Naum Ilʹich Akhiezer,H. H. McFaden Pdf

Presents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.

Author : Louis Melville Milne-Thomson
Publisher : Unknown
Page : 152 pages
File Size : 54,8 Mb
Release : 1950
Category : Elliptic functions
ISBN : WISC:89043105261

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Jacobian Elliptic Function Tables by Louis Melville Milne-Thomson Pdf

Author : Arthur Cayley
Publisher : Unknown
Page : 422 pages
File Size : 53,8 Mb
Release : 1876
Category : Elliptic functions
ISBN : NYPL:33433069105173

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An Elementary Treatise on Elliptic Functions by Arthur Cayley Pdf

Author : Harris Hancock
Publisher : Courier Corporation
Page : 544 pages
File Size : 41,8 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.