Elliptic Integrals (Classic Reprint) - Couverture souple

Ball, W. W. Rouse

Couverture souple

ISBN 10 : 1440053545 ISBN 13 : 9781440053542

Editeur : Forgotten Books, 2018

Synopsis

Elliptic Integrals: A Practical Guide for Students and Professionals Explore the foundations and applications of elliptic integrals with a clear, methodical approach. This edition presents the Legendre–Jacobi theory, focuses on the first and second kinds, and shows how to reduce complex integrals to standard forms for precise calculation.

Elliptic integrals unlock a range of problems in mathematics and its applications. The book explains how to transform difficult expressions into normal forms, uses tables to achieve exact results, and introduces the associated elliptic functions with their doubly periodic properties. It also covers numerical techniques and practical examples, helping readers apply theory to real problems.

• Step-by-step reductions of complex integrals to Legendre’s normal forms


• How to compute elliptic integrals with accuracy using tables and transformations


• Introduction to elliptic functions and their key properties


• Numerical methods and worked examples for practical problem solving

Ideal for readers with a background in calculus and an interest in applied mathematics, including students, instructors, and professionals who need reliable methods for elliptic integrals and related functions.

A propos du livre

Présentation de l'éditeur

The editors of the present series of mathematical monographs have requested me to write a work on elliptic integrals which shall relate almost entirely to the three well-known elliptic integrals, with tables and examples showing practical applications, and which shall fill about one hundred octavo pages. In complying with their request, I shall limit the monograph to what is known as theL egendre-J acobi theory; and to keep the work within the desired number of pages I must confine the discussion almost entirely to what is known as the elliptic integrals of the first and second kinds. In the elementary calculus are found methods of integrating any rational expression involving under a square root sign a quadratic in one variable; in the present work, which may be regarded as a somewhat more advanced calculus; we have to integrate similar expressions where cubics and quarries in one variable occur under the root sign. Whatever be the nature of these cubics and quarries, it will be seen that the integrals may be transformed into standard normal forms. Tables are given of these normal forms, so that the integral in question may be calculated to any degree of exactness required. With the trigonometric sine function is associated its inverse function, an integral; and similarly with the normal forms of elliptic integrals there are associated elliptic functions. A short account is given of these functions which emphasizes their doubly periodic properties. By making suitable transformations and using the inverse of these functions, it is found that the integrals in question may be expressed more concisely through the normal forms and in a manner that indicates the transformation employed.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklo

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440053545
• ISBN 13: 9781440053542
• Reliure: Broché
• Nombre de pages: 106
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible