Review by Choice Review
Approaches to the theory of elliptic functions usually proceed along one of two broad lines. Older developments focus on various special elliptic functions, particularly those of Jacobi, and the differential equations they satisfy, as in H. Hancock's classic Lectures on the Theory of Elliptic Functions (1910). Modern treatments emphasize general elliptic functions by way of those of Weierstrass, and the algebraic equations they parametrize, the elliptic curves of algebraic geometry, and number theory, as in S. Lang's Elliptic Functions (1973; 2nd ed. 1987). Lawden's coverage is similar to Hancock's, but with the significant addition of a variety of interesting physical applications that constitute the major strength of the book. The style is thoroughly 19th century in spirit. In an effort to keep the exposition elementary, Lawden long delays the introduction of complex analysis. Without the benefit of unifying principles from the modern viewpoint, the undergraduate reader to whom the book is addressed may well become swamped in myriad formulae. Perhaps the author's stated hostility to 20th-century abstraction prevented him from writing a more interesting book, one that would show the neglected gems of the 19th century in the clear light of the modern theory, exposing the deeper meanings of the former while illuminating the historical evolution of the latter. Another missed opportunity: the ubiquity of theta functions in the current physics literature, from solitons to conformal field theory, belies the author's contention that these functions have "relatively few applications." Narrowly conceived, but well executed, this book should be of interest to some engineering students. Mathematics students ought to have a look as well, but they can do better. -D. V. Feldman, University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
