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AUTHOR'S PREFACE. IN the following pages is contained a brief introductory account of some of the more fundamental portions of the theory of functions of a complex variable. The work was prepared originally as a chapter for the volume called Higher Mathematics, published in 1896. It has been enlarged by the addition of sections on power series, algebraic functions and their integrals, functions of two or more independent variables, and differential equations. Furthermore, the section on uniform convergence has been extended, and the treatment of Weierstrass's theorem and of Mittag-Leffler's theorem has been simplified. It is hoped that the present work will give the uninitiated some idea of the nature of one of the most important branches of modern mathematics, and will also be useful as an introduction to larger works, such as those in English by Forsyth, Whittaker, and Harkness and Morley; in French by Jordan, Picard, Goursat, and Vallee-Poussin; and in German by Burkhardt, Stolz and Gmeiner, and Osgood.

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