Druck auf Anfrage Neuware - Printed after ordering - 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.

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Bibliographic Details

Title: Elliptic Functions
Publisher: Cambridge University Press
Publication Date: 2006
Language: English
ISBN 10: 0521780780
ISBN 13: 9780521780780
Binding: Buch
Condition: Neu
Dimensions: 235 millimeters width by 157 millimeters height by 28 millimeters depth
Weight: 804 grams

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Synopsis

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.

About the Author

J. V. Armitage is an Honorary Senior Fellow in Mathematical Sciences at the University of Durham.

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