Complex Analysis - Maths KU

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Complex Fuctions
and Mappings
2.1 Complex Functions
2.2 Complex Functions as Mappings
2.3 Linear Mappings
2.4 Special Power Functions
2.4.1 The Power Function z n
2.4.2 The Power Function z 1/n
2.5 Reciprocal Function
2.6 Limits and Continuity
2.6.1 Limits
2.6.2 Continuity
2.7 Applications
Chapter 2 Review Quiz
Introduction In the last chapter we introduced
complex numbers and examined some of their algebraic
and geometric properties. In this chapter
we turn our attention to the study of functions
from a set of complex numbers to another
set of complex numbers. Unlike the functions
studied in elementary calculus, we shall see that
we cannot draw the graph of a complex function.
Therefore, we introduce the notion of a mapping
as an alternative way of graphically representing
a complex function. The concepts of a limit of a
complex function and continuity of a complex
function are also introduced 49
in this chapter.