My curriculum for math has the first chapter on complex variables. It is as stated below:
Functions of complex variables:
- Continuity and derivability of a function
- Analytic functions
- Necessary condition for $f(z)$ to be analytic, sufficient conditions (without proof)
- Cauchy-Riemann equations in polar form
- Harmonic functions
- Orthogonal trajectories
- Analytical and Milne-Thomson method to find $f(z)$ from its real or imaginary parts.
- Complex integration
- Taylor’s and Laurent’s series (without proof)
- Cauchy’s residue theorem (statement & application)
I have been able to locate some of it on MIT OpenCourseware but I am not sure if that will be enough.
Can someone please point me out to more resources for this chapter ?