Prerequisites: MATH 3331, Differential Equations
Required Text: Visual Complex Analysis by Tristan Needham, Oxford University Press.
Course Description:
This course introduces the mathematical techniques that are commonly used to analyze those problems in the sciences and engineering that are inherently two dimensional in nature. Its content is the analysis, in both the classical and geometric sense, of differentiable functions of a single complex variable. Topics will include: the complex plane, analytic functions, the Cauchy-Riemann equations, the Cauchy integral formula, Taylor and Laurent series, the residue theorem, and conformal mappings. The course focuses on a geometric understanding of complex numbers and analytic maps.
Topics Covered:
The complex number system, analytic functions, Cauchy integral theory, series representation, residue theory, and conformal mappings.
There will be a number of optional problems which will require a numerical equation solver. You may use Matlab, Mathematica, or any other program you are comfortable with.