I am an engineering student trying to study mathematical analysis because it will help me in my post graduate studies.
My problem is that when I searched the internet I found that some university sites recommend topology class while others do not. Also, some recommend a "mathematical analysis" text before going into real and complex analysis. The problem is in the diversity of titles.
So my question is, if I want to study real and complex analysis, what topics do I need and under what book titles are those topics given?
I want to emphasis that am searching in English so I ask that all book titles are according to an American or English syllabus. If you are of a different nationality, please tell me the order of studying real and complex analysis in your country.
P.S. The particular topics I want to study are functions of complex variables, integration in the complex plane, series and residues, and conformal mapping.