Elliptic Functions and Elliptic Integrals PDF Download

Author: Viktor Vasil_evich Prasolov
Publisher: American Mathematical Soc.
ISBN: 9780821897805
Category : Mathematics
Languages : en
Pages : 202

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Book Description
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: Paul F. Byrd
Publisher: Springer
ISBN: 3642528031
Category : Mathematics
Languages : en
Pages : 370

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Book Description
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: Johannes Blümlein
Publisher: Springer
ISBN: 3030044807
Category : Computers
Languages : en
Pages : 511

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Book Description
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
ISBN: 1681742306
Category : Science
Languages : en
Pages : 67

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Book Description
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
ISBN: 3642522440
Category : Mathematics
Languages : en
Pages : 199

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Book Description
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: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461247527
Category : Mathematics
Languages : en
Pages : 319

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Book Description
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
ISBN: 147573980X
Category : Mathematics
Languages : en
Pages : 349

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Book Description
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: Andre Weil
Publisher: Springer Science & Business Media
ISBN: 9783540650362
Category : Mathematics
Languages : en
Pages : 112

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Book Description
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 (...).

Author: Patrick Du Val
Publisher: Cambridge University Press
ISBN: 0521200369
Category : Mathematics
Languages : en
Pages : 257

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Book Description
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: Viktor Vasil_evich Prasolov
Publisher: American Mathematical Soc.
ISBN: 0821802364
Category : Mathematics
Languages : en
Pages : 250

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Book Description
There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.