This book develops the fundamental properties of elliptic functions and illustrates them by applications in geometry, mathematical physics and engineering. Its purpose is to provide an introductory text for private study by students and research workers who wish to be able to use elliptic functions in the solution of both pure and applied mathematical problems. In the first half of the book, a knowledge of no more than first year university mathematics is assumed of the reader. In the later chapters, the theory of functions of a complex variable is increasingly employed as an analytical tool. Accordingly, the book should prove helpful to mathematicians at all stages of an undergraduate or post-graduate course. The book is liberally supplied with sets of exercises (over 180 total) with which the reader can gain practice in the use of the functions.
Edition description: Softcover reprint of hardcover 1st ed. 1989
Edition number: 1
Product dimensions: 0.73 (w) x 9.21 (h) x 6.14 (d)
Table of Contents
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.