Complex analysis books
I own two:
One by Priestley entitled “Introduction to Complex Analysis” and one by Needham entitled “Visual Complex Analysis”.
Priestley came highly recommended but seems a dense read to me.
Needham is less well-known in the main, I think, but it’s the one I’m living in.
A few reviews say it requires pre-existing knowledge of the subject in order to make proper use of it. A few say it broaches the undergrad/post-grad boundary (will refrain from topological jokes here).
All I know is:
a) it’s beautifully written – by someone with a good grasp of “English, proper”,
b) it’s full of good quality drawings which illuminate the subject,
c) it helped me to make sense of such things as visualising integrals (as far as is possible) on the complex plane,
d) I’m reading it in tandem with the OU course – OU course for absolute rigour and proofs, Needham for an even more “layman’s terms” explanation of the latest new concept (outdoing even the OU books in this regard, in my opinion), followed by geometrical visualisation courtesy of the well-explained drawings.
Oddly, I’d say someone with a good A level in maths and an appreciation that i, the imaginary unit, exists could make a good go at getting into this book. Such an easy read.
I have two functional analysis texts on the way too – both kick off with defining various metrics but rapidly move on. More on those later – I expect to get very stuck quite quickly.