Topics include: functions of a complex variable, analyticity, the Cauchy-Riemann equations, special functions (trigonometric, exponential, hyperbolic and logarithmic), compositions, mappings, inverse and branch functions. This is followed by contour integration, the Cauchy-Goursat theorem, Cauchy146s integral formula, singularities, an introduction to residue theory and Laurent series, Liouville146s Theorem and the fundamental theorem of algebra. Students may not retain credit for both MATH 3046 & 4046. PREREQ: MATH 2037. (lec 3) cr 3