What Do I Need to Know?

Abstract

Complex analysis is not an elementary subject, and the author of a book like this has to make some reasonable assumptions about what his readers know already. Ideally one would like to assume that the student has some basic knowledge of complex numbers and has experienced a fairly substantial first course in real analysis. But while the first of these requirements is realistic the second is not, for in many courses with an “applied” emphasis a course in complex analysis sits on top of a course on advanced (multi-variable) calculus, and many students approach the subject with little experience of ∈-δ arguments, and with no clear idea of the concept of uniform convergence. This chapter sets out in summary the equipment necessary to make a start on this book, with references to suitable texts. It is written as a reminder: if there is anything you don’t know at all, then at some point you will need to consult another book, either the suggested reference or another similar volume.