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Elliptic Functions (Hardcover, New)
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Elliptic Functions (Hardcover, New)
Series: London Mathematical Society Student Texts
Expected to ship within 12 - 17 working days
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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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