Course overview
The course is an introduction to the theory and applications of complex-differentiable functions of a complex variable. Basic concepts of calculus (limits, differentiation, integration, power series) are adapted to the complex setting. The fundamental theorem of Cauchy is proved, and its numerous consequences and applications explored. Differences between the real and complex settings are highlighted.
Course learning outcomes
- Demonstrate an understanding of the theory and applications of holomorphic functions
- Calculate line integrals and apply the residue theorem to calculate real integrals.
- Demonstrate skills in constructing rigorous mathematical arguments
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty
- Demonstrate skills in communicating mathematics
- Complete a small research project as a member of a team