Elliptic Functions

Erscheinungsjahr 2011
ISBN: 978-0-521-78563-1
Verlag: Cambridge University Press

Buch, Englisch, Band 67, 402 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 650 g

Reihe: London Mathematical Society Student Texts

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.

Autoren/Hrsg.

Armitage, J. V.

Eberlein, W. F.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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; 12. Applications in mechanics and statistics and other topics; Appendix; Bibliography.

Über Autor(innen)

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