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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 ?

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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".

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  • $\begingroup$ 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
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    $\begingroup$ @LittleChild really? Great! $\endgroup$ – Avitus Jun 21 '13 at 6:23

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