Elliptic Functions and Applications

Lawden, Derek F.

ISBN 10: 0387969659 / ISBN 13: 9780387969657

Editore: Springer, 1989

Develops the fundamental properties of elliptic functions and illustrates them by applications in geometry, mathematical physics and engineering. This book employs the theory of functions of a complex variable as an analytical tool. It is suitable for mathematicians at various stages of an undergraduate or post-graduate course. Series: Applied Mathematical Sciences. Num Pages: 350 pages, biography. BIC Classification: PBKD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 241 x 163 x 25. Weight in Grams: 670. . 1989. 1989th Edition. hardcover. . . . . Codice articolo V9780387969657

Riassunto:

The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .

Contenuti: 1 Theta Functions.- 2 Jacobi’s Elliptic Functions.- 3 Elliptic Integrals.- 4 Geometrical Applications.- 5 Physical Applications.- 6 Weierstrass’s Elliptic Function.- 7 Applications of the Weierstrass Functions.- 8 Complex Variable Analysis.- 9 Modular Transformations..- Appendix A Fourier Series for a Periodic Analytic Function.- Appendix B Calculation of a Definite Integral.- Appendix C BASIC Program for Reduction of Elliptic Integral to Standard Form.- Appendix D Computation of Tables.- Table A. Theta Functions.- Table B. Nome and Complete Integrals of the First and Second Kinds as Functions of the Squared Modulus.- Table D. Legendre’s Incomplete Integrals of First and Second Kinds.- Table E. Jacobi’s Zeta and Epsilon Functions.- Table F. Sigma Functions.

Dati bibliografici

Titolo: Elliptic Functions and Applications
Casa editrice: Springer
Data di pubblicazione: 1989
Legatura: Rilegato
Condizione: New