Elliptic Integrals And Elliptic Functions

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Lectures on Selected Topics in Mathematical Physics

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681742306
Total Pages : 67 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Lectures on Selected Topics in Mathematical Physics by : William A. Schwalm

Download or read book Lectures on Selected Topics in Mathematical Physics written by William A. Schwalm and published by Morgan & Claypool Publishers. This book was released on 2015-12-31 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

Author : Johannes Blümlein
Publisher : Springer
ISBN 13 : 3030044807
Total Pages : 511 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory by : Johannes Blümlein

Download or read book Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory written by Johannes Blümlein and published by Springer. This book was released on 2019-01-30 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Elliptic Integrals for Engineers and Physicists

Author : Paul F. Byrd
Publisher : Springer
ISBN 13 : 3642528031
Total Pages : 370 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Handbook of Elliptic Integrals for Engineers and Physicists by : Paul F. Byrd

Download or read book Handbook of Elliptic Integrals for Engineers and Physicists written by Paul F. Byrd and published by Springer. This book was released on 2013-11-21 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Functions and Elliptic Integrals

Author : Viktor Vasil_evich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897805
Total Pages : 202 pages
Book Rating : 4.8/5 (978 download)

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Book Synopsis Elliptic Functions and Elliptic Integrals by : Viktor Vasil_evich Prasolov

Download or read book Elliptic Functions and Elliptic Integrals written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1997-09-16 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Functions

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
ISBN 13 : 3642522440
Total Pages : 199 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Elliptic Functions by : Komaravolu Chandrasekharan

Download or read book Elliptic Functions written by Komaravolu Chandrasekharan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Functions

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1461247527
Total Pages : 319 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Elliptic Functions by : Serge Lang

Download or read book Elliptic Functions written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Functions and Applications

Author : Derek F. Lawden
Publisher : Springer Science & Business Media
ISBN 13 : 147573980X
Total Pages : 349 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elliptic Functions and Applications by : Derek F. Lawden

Download or read book Elliptic Functions and Applications written by Derek F. Lawden and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .

Elliptic Functions According to Eisenstein and Kronecker

Author : Andre Weil
Publisher : Springer Science & Business Media
ISBN 13 : 9783540650362
Total Pages : 112 pages
Book Rating : 4.6/5 (53 download)

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Book Synopsis Elliptic Functions According to Eisenstein and Kronecker by : Andre Weil

Download or read book Elliptic Functions According to Eisenstein and Kronecker written by Andre Weil and published by Springer Science & Business Media. This book was released on 1999 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

Elliptic Integrals

Author : Harris Hancock
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Elliptic Integrals by : Harris Hancock

Download or read book Elliptic Integrals written by Harris Hancock and published by . This book was released on 1917 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Functions and Elliptic Curves

Author : Patrick Du Val
Publisher : Cambridge University Press
ISBN 13 : 0521200369
Total Pages : 257 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Elliptic Functions and Elliptic Curves by : Patrick Du Val

Download or read book Elliptic Functions and Elliptic Curves written by Patrick Du Val and published by Cambridge University Press. This book was released on 1973-08-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic Curves

Author : Henry McKean
Publisher : Cambridge University Press
ISBN 13 : 9780521658171
Total Pages : 300 pages
Book Rating : 4.6/5 (581 download)

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Book Synopsis Elliptic Curves by : Henry McKean

Download or read book Elliptic Curves written by Henry McKean and published by Cambridge University Press. This book was released on 1999-08-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.

Handbook of Mathematical Functions

Author : Milton Abramowitz
Publisher : Courier Corporation
ISBN 13 : 9780486612720
Total Pages : 1068 pages
Book Rating : 4.6/5 (127 download)

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Book Synopsis Handbook of Mathematical Functions by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

Elliptic Functions

Author : J. V. Armitage
Publisher : Cambridge University Press
ISBN 13 : 9780521780780
Total Pages : 404 pages
Book Rating : 4.7/5 (87 download)

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Book Synopsis Elliptic Functions by : J. V. Armitage

Download or read book Elliptic Functions written by J. V. Armitage and published by Cambridge University Press. This book was released on 2006-09-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Applications of Elliptic Functions

Author : Sir George Greenhill
Publisher :
ISBN 13 :
Total Pages : 386 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Applications of Elliptic Functions by : Sir George Greenhill

Download or read book The Applications of Elliptic Functions written by Sir George Greenhill and published by . This book was released on 1892 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Modular Functions

Author : B. Schoeneberg
Publisher : Springer Science & Business Media
ISBN 13 : 3642656633
Total Pages : 244 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Elliptic Modular Functions by : B. Schoeneberg

Download or read book Elliptic Modular Functions written by B. Schoeneberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students' progress. The study of the book requires an elementary knowledge of algebra, number theory and topology and a deeper knowledge of the theory of functions. An extensive discussion of the modular group SL(2, Z) is followed by the introduction to the theory of automorphic functions and auto morphic forms of integral dimensions belonging to SL(2,Z). The theory is developed first via the Riemann mapping theorem and then again with the help of Eisenstein series. An investigation of the subgroups of SL(2, Z) and the introduction of automorphic functions and forms belonging to these groups folIows. Special attention is given to the subgroups of finite index in SL (2, Z) and, among these, to the so-called congruence groups. The decisive role in this setting is assumed by the Riemann-Roch theorem. Since its proof may be found in the literature, only the pertinent basic concepts are outlined. For the extension of the theory, special fields of modular functions in particular the transformation fields of order n-are studied. Eisen stein series of higher level are introduced which, in case of the dimension - 2, allow the construction of integrals of the 3 rd kind. The properties of these integrals are discussed at length.

Elements of the Theory of Elliptic Functions

Author : Naum Ilʹich Akhiezer
Publisher : American Mathematical Soc.
ISBN 13 : 9780821809006
Total Pages : 237 pages
Book Rating : 4.8/5 (9 download)

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Book Synopsis Elements of the Theory of Elliptic Functions by : Naum Ilʹich Akhiezer

Download or read book Elements of the Theory of Elliptic Functions written by Naum Ilʹich Akhiezer and published by American Mathematical Soc.. This book was released on 1990 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematical-Function Computation Handbook

Author : Nelson H.F. Beebe
Publisher : Springer
ISBN 13 : 3319641107
Total Pages : 1145 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis The Mathematical-Function Computation Handbook by : Nelson H.F. Beebe

Download or read book The Mathematical-Function Computation Handbook written by Nelson H.F. Beebe and published by Springer. This book was released on 2017-08-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.