Complex Analysis (Princeton Lectures in Analysis, No. 2) by Elias M. Stein, Rami Shakarchi - 2003

Princeton Univ Press, 2003. Hardback. Very Good. Very Good. No dust jacket as issued. Previous owners name on ffep. No marks noted in text. Light scoffing on corners. . . . . . . With this second volume in the series, we enter the world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The book includes coverage of: the main properties of holomorphic functions; and an introduction to elliptic functions. . . . . . . . TABLE OF CONTENTS: 1.) Preliminaries to complex analysis -- 2.) Cauchy's theorem and its applications -- 3.) Meromorphic functions and the logarithm -- 4.) The Fourier transform -- 5.) Entire functions -- 6.) The gamma and zeta functions -- 7.) The zeta function and prime number theorem -- 8.) Conformal mappings -- 9.) An introduction to elliptic functions -- 10.) Applications of theta functions -------- * APPENDICES: A.) Asymptotics -- B.) Simple connectivity and Jordan curve theorem