Students will learn complex number geometry and algebra and be able to manipulate and solve algebraic equations.
Students will learn the properties of and necessary and sufficient conditions defining analytic functions.
Students will learn how to perform integration in the complex plane through parameterization as well as integration theorems including the Cauchy integral formula.
Students will learn how to construct and analyze infinite power series of complex functions.
Students will learn the connections between residues and poles of complex functions and their applications to complex function integration.
Students will also learn several applications of complex analysis to improper integrals, including Fourier and Laplace transforms and inverse transforms.
In addition to topical content, students will also gain experience and further mastery of problem solving fluency. Students will be able to read and interpret problem objectives, be able to select and execute appropriate methods to achieve objectives, and finally, be able to interpret and communicate results.