1 Complex Numbers , 1-52 2 Analytic Functions , 53-98 3 Elementary Function , 99-148 4 Complex Integration , 149-234 5 Series Representations for Analytic Functions , 235-306 6 Residue Theory , 307-368 7 Conformal Mapping , 369-444 8 The Transforms of Applied Mathematics , 445-511 A Numerical Construction of Conformal Maps , A1-A26