This is the first of a two-quarter introductory course on complex analysis. Complex analysis is an old and beautiful subject, and it is also extremely useful. We will explore its analytic and geometric sides, balancing theory and computation. Topics will include complex numbers, differentiability of functions of one complex variable, Cauchy-Riemann equations, conformal mapping, Cauchy's Theorem, Cauchy Integral Formula and its consequences.
Marsden, Jerrold and Hoffman, Michael Basic Complex Analysis, 3rd edition W. H. Freeman