Complex Variables is concerned with the analysis of complex-valued functions of a complex variable. The development parallels that of functions of a real variable that are considered in calculus courses; although, as you will discover, the flavor is quite different. Graphing functions is not simple an activity since both the domain and range of the functions are two-dimensional. Integration is closely related to the contour integrals of calculus, and its applications are quite different from finding areas and volumes.
We will consider several applications of interest to engineers and physicists including, some in the areas of fluid flow, steady state temperatures, and electrostatics. Depending on the majority interests of students, we will end the course considering applications of either harmonic functions or Fourier and Laplace transforms.
Proofs are kept at an elementary level and are presented in a self-contained manner that is understandable for students having a sophomore calculus background.
Choose from the following topics to find out more about the course.