Reference request for complex variables

Question

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 ?

See also: Complex Analysis Book and What is a good complex analysis textbook? — Martin, Jun 19 '13 at 20:28

Avitus · Accepted Answer · 2013-06-19T20:24:49.170

2

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".

edited Jun 19 '13 at 20:24

answered Jun 19 '13 at 20:14

Avitus

14,018

What is orthogonal trajectories ? – An SO User Jun 19 '13 at 20:21
@LittleChild I thought it was something about conformal maps "lines to lines and circles to circles" and related topics – Avitus Jun 19 '13 at 20:23
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? – Martin Jun 19 '13 at 20:23
@Martin yes: because I am lazy and I did a copy paste :-). I edit it now, thanks – Avitus Jun 19 '13 at 20:24
Oh, okay. Fair enough :-) – Martin Jun 19 '13 at 20:25
@Avitus OK fine, I had a look at the book. I didn't grasp a thing :-D – An SO User Jun 20 '13 at 03:22
@LittleChild you mean chapter 13? Complex analysis is a false friend...I find it very tricky! – Avitus Jun 20 '13 at 06:09
@Avitus Churchill's book on Complex Variables has everything :) – An SO User Jun 21 '13 at 04:28
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@LittleChild really? Great! – Avitus Jun 21 '13 at 06:23

Reference request for complex variables

1 Answers1