Elliptic Functions and Elliptic Integrals

Author: Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev

Publisher: American Mathematical Soc.

ISBN: 9780821897805

Category: Mathematics

Page: 185

View: 3278

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.

Handbook of Elliptic Integrals for Engineers and Physicists

Author: Paul F. Byrd,Morris D. Friedman

Publisher: Springer

ISBN: 3642528031

Category: Mathematics

Page: 358

View: 7152

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 Integrals

Author: Harris Hancock

Publisher: N.A


Category: Elliptic functions

Page: 104

View: 7092

Table of Integrals, Series, and Products

Author: I. S. Gradshteyn,I. M. Ryzhik

Publisher: Academic Press

ISBN: 1483265641

Category: Mathematics

Page: 1206

View: 3427

Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

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

Author: Johannes Blümlein,Carsten Schneider,Peter Paule

Publisher: Springer

ISBN: 9783030044794

Category: Computers

Page: 509

View: 2006

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.

Mathematics and Its History

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 9780387953366

Category: Mathematics

Page: 544

View: 1084

This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added as well as commentary that helps place the exercises in context.

Elliptic Integrals

Author: Francis William Newman

Publisher: Franklin Classics

ISBN: 9780343320249


Page: 220

View: 7137

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.

Elements of the Theory of Elliptic Functions

Author: Naum Ilʹich Akhiezer

Publisher: American Mathematical Soc.

ISBN: 9780821886779

Category: Mathematics

Page: 237

View: 7799

This book contains a systematic presentation of the theory of elliptic functions and some of its applications. A translation from the Russian, this book is intended primarily for engineers who work with elliptic functions. It should be accessible to those with background in the elements of mathematical analysis and the theory of functions contained in approximately the first two years of mathematics and physics courses at the college level.

Elliptic Functions

Author: J. V. Armitage,W. F. Eberlein

Publisher: Cambridge University Press

ISBN: 9781139457491

Category: Mathematics

Page: N.A

View: 5596

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' 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 then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.