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, Cauchy's integral formula, singularities, an introduction to residue theory and Laurent series, Liouville's Theorem and the fundamental theorem of algebra. PREREQ: MATH 2037. (lec 3) cr 3. Students may not retain credit for both MATH 3046 and MATH 4046.