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 ?


I would use Bak & Newman's "Complex Analysis" for an introduction to the above topics except for "CR in polar form", "harmonic functions" and "Milne-Thomson".

  • $\begingroup$ What is orthogonal trajectories ? $\endgroup$ – An SO User Jun 19 '13 at 20:21
  • $\begingroup$ @LittleChild I thought it was something about conformal maps "lines to lines and circles to circles" and related topics $\endgroup$ – Avitus Jun 19 '13 at 20:23
  • $\begingroup$ Out of curiosity: It is the second time today that I see you mention Bak's and Newman's names in reverse order. Is there a particular reason for doing this? $\endgroup$ – Martin Jun 19 '13 at 20:23
  • $\begingroup$ @Martin yes: because I am lazy and I did a copy paste :-). I edit it now, thanks $\endgroup$ – Avitus Jun 19 '13 at 20:24
  • 1
    $\begingroup$ @LittleChild really? Great! $\endgroup$ – Avitus Jun 21 '13 at 6:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.