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Applications Of Elliptic Functions
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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 .
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:
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.
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.
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.
Author :Komaravolu Chandrasekharan Publisher :Springer Science & Business Media ISBN 13 :3642522440 Total Pages :199 pages Book Rating :4.6/5 (425 download)
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.
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.
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.
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.
Book Synopsis The 1-2-3 of Modular Forms by : Jan Hendrik Bruinier
Download or read book The 1-2-3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Book Synopsis Fundamenta Nova Theoriae Functionum Ellipticarum by : Carl Gustav Jakob Jacobi
Download or read book Fundamenta Nova Theoriae Functionum Ellipticarum written by Carl Gustav Jakob Jacobi and published by Franklin Classics. This book was released on 2018-10-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences by : Ivor Grattan-Guiness
Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by Ivor Grattan-Guiness and published by Routledge. This book was released on 2004-11-11 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
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 (...).
Book Synopsis Elliptic Curves by : Lawrence C. Washington
Download or read book Elliptic Curves written by Lawrence C. Washington and published by CRC Press. This book was released on 2008-04-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Book Synopsis Kernel Functions and Elliptic Differential Equations in Mathematical Physics by : Stefan Bergman
Download or read book Kernel Functions and Elliptic Differential Equations in Mathematical Physics written by Stefan Bergman and published by Courier Corporation. This book was released on 2005-09-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
Book Synopsis Elliptic Curves and Their Applications to Cryptography by : Andreas Enge
Download or read book Elliptic Curves and Their Applications to Cryptography written by Andreas Enge and published by Springer Science & Business Media. This book was released on 1999-08-31 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their invention in the late seventies, public key cryptosystems have become an indispensable asset in establishing private and secure electronic communication, and this need, given the tremendous growth of the Internet, is likely to continue growing. Elliptic curve cryptosystems represent the state of the art for such systems. Elliptic Curves and Their Applications to Cryptography: An Introduction provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems. Even though the elegant mathematical theory underlying cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The Adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention. Elliptic Curves and Their Applications: An Introduction has been used successfully for teaching advanced undergraduate courses. It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics.
Book Synopsis Elliptic Functional Differential Equations and Applications by : Alexander L. Skubachevskii
Download or read book Elliptic Functional Differential Equations and Applications written by Alexander L. Skubachevskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved only in some subdomains. The symbol of a self-adjoint semibounded functional differential operator can change its sign. The purpose of this book is to present for the first time general results concerning solvability and spectrum of these problems, a priori estimates and smoothness of solutions. The approach is based on the properties of elliptic operators and difference operators in Sobolev spaces. The most important features distinguishing this work are applications to different fields of science. The methods in this book are used to obtain new results regarding the solvability of nonlocal elliptic boundary value problems and the existence of Feller semigroups for multidimensional diffusion processes. Moreover, applications to control theory and aircraft and rocket technology are given. The theory is illustrated with numerous figures and examples. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations. It will also be of use to engineers in control theory and elasticity theory.
