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Published in:
2011 | OriginalPaper | Chapter
Behavior of Analytic Mappings
Authors : Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
Published in: An Introduction to Complex Analysis
Publisher: Springer US
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In this lecture, we shall use the Rouché Theorem to investigate the behavior of the mapping
f
generated by an analytic function
w
=
f
(
z
)
.
Then, we shall study some properties of the inverse mapping f
-1
. We shall also discuss functions that map the boundaries of their domains to the boundaries of their ranges. Such results are of immense value for constructing solutions of the Laplace equation with boundary conditions.