Course Outcomes: Upon successful completion of this course, the student will be able to:

1. compute the region of convergence for power series,

2. prove the Cauchy-Riemann equations and apply them to complex functions in order to examine differentiability and analyticity of complex functions,

3. evaluate complex integration along the curve via Cauchy’s theorem and integral formula

4. prove the Cauchy residue theorem and apply it to several kinds of real integrals,

5. compute the Taylor series and Laurent series expansions of complex functions and apply it to for checking the nature of singularities and calculating residues,

6. demonstrate accurate and efficient use of complex analysis techniques to solve the problems in physics, engineering and other mathematical contexts.