Complex numbers can be viewed in several ways: as an element in a
field, as a point in the plane, and as a two-dimensional vector.
Examined properly, each perspective provides crucial insight into
the interrelations between the complex number system and its
parent, the real number system. The authors explore these
relationships by adopting both generalization and specialization
methods to move from real variables to complex variables, and vice
versa, while simultaneously examining their analytic and geometric
characteristics, using geometry to illustrate analytic concepts and
employing analysis to unravel geometric notions.
The engaging exposition is replete with discussions, remarks,
questions, and exercises, motivating not only understanding on the
part of the reader, but also developing the tools needed to think
critically about mathematical problems. This focus involves a
careful examination of the methods and assumptions underlying
various alternative routes that lead to the same destination.
The material includes numerous examples and applications
relevant to engineering students, along with some techniques to
evaluate various types of integrals. The book may serve as a text
for an undergraduate course in complex variables designed for
scientists and engineers or for mathematics majors interested in
further pursuing the general theory of complex analysis. The only
prerequistite is a basic knowledge of advanced calculus. The
presentation is also ideally suited for self-study.
General
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