MATH 630. Introduction to Complex Analysis. (3) The goals of this introductory course are to study the underlying mathematical structure of Complex Analysis and also to cover some of its many applications. The answers we seek in subjectivg physical models to mathematical analysis are most frequently real, but to arrive at these answers we often invoke the powerful theory of analytic functions. The arithmetic of complex numbers, the Cauchy-Riemann equations, contour integrals, Cauchy's Integral Theorms, power series expansions, the applications of harmonic functions and of simple conformal mappings to the Laplace euqations, and the theory of residues are covered. Units on Laplace transforms and on conformal mappings are also covered when time permits. Most of the students enrolling in this course are upper division or beginning graduate students in engineering, mathematics, or one of the physical sciences. Definitions and important theorems are emphasized, whereas proofs of the theorems are de-emphasized. Students must be proficient in simplifying algebraic expressions and in computing partial derivatives. Most of the assigned exercises are computational. The conceptually difficult part of the course deals with infinite series. The better a student understands infinite series the better will be the student's appreciation for the meta-principle of complex analysis: an analytic funtions in essentially a polynomial of infinite degree.