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Elliptic Functions : London Mathematical Society Student Texts - J. V. Armitage

Elliptic Functions

London Mathematical Society Student Texts


Published: 1st May 2006
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In its first six chapters this 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.

'This solid text is a good place to start when working with elliptic functions and it is the sort of book that you will keep coming back to as reference text.' Mathematics Today

The 'simple' pendulum
Jacobian elliptic functions of a complex variable
General properties of elliptic functions
Theta functions
The Jacobian elliptic functions for complex k
Introduction to transformation theory
The Weierstrass elliptic functions
Elliptic integrals
Applications of elliptic functions in geometry
An application of elliptic functions in algebra solution of the general quintic equation
An arithmetic application of elliptic functions
Applications in mechanics and statistics and other topics
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521780780
ISBN-10: 0521780780
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 404
Published: 1st May 2006
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 15.24  x 2.54
Weight (kg): 0.68