Elliptic functions
להגדלת הטקסט להקטנת הטקסט- ספר
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.
כותר |
Elliptic functions / J.V. Armitage and W.F. Eberlein. |
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מוציא לאור |
Cambridge : Cambridge University Press |
שנה |
2006 |
הערות |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). English |
הערת תוכן ותקציר |
Cover Half-title Title Copyright Dedication Contents Preface Original partial preface Acknowledgements 1 The 'simple' pendulum 2 Jacobian elliptic functions of a complex variable 3 General properties of elliptic functions 4 Theta functions 5 The Jacobian elliptic functions for complex k 6 Introduction to transformation theory 7 The Weierstrass elliptic functions 8 Elliptic integrals 9 Applications of elliptic functions in geometry 10 An application of elliptic functions in algebra - solution of the general quintic equation 11 An arithmetic application of elliptic functions: the representation of a positive integer as a sum of three squares12 Applications in mechanics and statistics and other topics Appendix References Further reading Index |
סדרה |
London Mathematical Society student texts 67 |
היקף החומר |
1 online resource (xiii, 387 pages) : digital, PDF file(s). |
שפה |
אנגלית |
מספר מערכת |
997010709784205171 |
תצוגת MARC
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