3 credits
Spring 2026 Lecture Upper Division
Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping.
Learning Outcomes1Apply complex number theory and understand algebraic and geometric representations.
2Solve complex equations and analyze limits, continuity, and differentiability.
3Use Cauchy-Riemann equations to identify analytic functions.
4Evaluate integrals using Cauchy's integral theorem and formula.
5Apply the residue theorem for evaluating integrals in engineering and science problems.
6Use Taylor and Laurent series to expand complex functions.
7Solve boundary value problems in fluid dynamics, electrostatics, and potential theory.
8Apply complex analysis techniques to engineering and science applications.
Prerequisites
made by Purdue students.