MATH 4024 - Complex Variables

Description

This course provides a rigorous introduction to the theory of functions of one complex variable. Topics include the algebra and geometry of complex numbers, analytic functions, Cauchy–Riemann equations, harmonic functions, complex differentiation and integration, Cauchy’s Theorem and Integral Formula, Laurent series, and residue theory. Problem- solving is an integral component of the course.

Learning Objectives

• Analyze analytic and harmonic functions using the Cauchy–Riemann equations.
• Evaluate contour integrals using Cauchy’s Integral Formula.
• Analyze Taylor and Laurent series expansions of complex-valued functions, determining regions of convergence, singularities, poles, and zeros.
• Evaluate contour integrals and complicated real-valued integrals using residues and the Residue Theorem.