"In this course we consider familiar concepts encountered in calculus in the new setting of functions of a complex variable. Topics covered include: the arithmetic, algebra, and geometry of the complex number system and complex plane; elementary functions of a complex variable; the derivative (analyticity and harmonicity); the integral (line and contour integrals); the topological aspects of the plane needed to develop the theory of differentiability and integrability (including Cauchy's Theorem, Cauchy's Integral Formula, and the Maximum Modulus Theorem); and series representations for functions. "