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

After completing this course, students will be able to:

• LO1: Analyze analytic and harmonic functions using the Cauchy-Riemann equations.
  
• LO2: Evaluate contour integrals using Cauchy's Integral Formula.
  
• LO3: Analyze Taylor and Laurent series expansions of complex-valued functions, determining regions of convergence, singularities, poles, and zeros.
  
• LO4: Evaluate contour integrals and complicated real-valued integrals using residues and the Residue Theorem.