Starting with an introduction to the complex plane, this course covers holomorphic functions and power series, Cauchy's Theorem, contour integration and its applications.
- Understand and apply conformal mappings.
- Understand complex-variable calculus, including the Cauchy-Riemann equations and the Cauchy-Goursat Theorem.
- Understand the basic theory of complex numbers.
- Understand the theory of convergence of series, including power series.