Advanced Engineering Mathematics, 7th Edition

17.4 Functions of a Complex Variable

INTRODUCTION

One of the most important concepts in mathematics is that of a function. You may recall from previous courses that a function is a certain kind of correspondence between two sets; more specifically: A function f from a set A to a set B is a rule of correspondence that assigns to each element in A one and only one element in B. If b is the element in the set B assigned to the element a in the set A by f, we say that b is the image of a and write b = f(a). The set A is called the domain of the function f(but is not necessarily a domain in the sense defined in Section 17.3). The set of all images in B is called the range of the function. For example, suppose the set A is a set of real numbers ...