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Using the familiar software Microsoft ® Excel, this book examines
the applications of complex variables. Implementation of the
included problems in Excel eliminates the “black box” nature of
more advanced computer software and programming languages and
therefore the reader has the chance to become more familiar with
the underlying mathematics of the complex variable problems. This
book consists of two parts. In Part I, several topics are covered
that one would expect to find in an introductory text on complex
variables. These topics include an overview of complex numbers,
functions of a complex variable, and the Cauchy integral formula.
In particular, attention is given to the study of analytic complex
variable functions. This attention is warranted because of the
property that the real and imaginary parts of an analytic complex
variable function can be used to solve the Laplace partial
differential equation (PDE). Laplace's equation is ubiquitous
throughout science and engineering as it can be used to model the
steady-state conditions of several important transport processes
including heat transfer, soil-water flow, electrostatics, and ideal
fluid flow, among others. In Part II, a specialty application of
complex variables known as the Complex Variable Boundary Element
Method (CVBEM) is examined. CVBEM is a numerical method used for
solving boundary value problems governed by Laplace's equation.
This part contains a detailed description of the CVBEM and a guide
through each step of constructing two CVBEM programs in Excel. The
writing of these programs is the culminating event of the book.
Students of complex variables and anyone with interest in a novel
method for approximating potential functions using the principles
of complex variables are the intended audience for this book. The
Microsoft Excel applications (including simple programs as well as
the CVBEM program) covered will also be of interest in the
industry, as these programs are accessible to anybody with
Microsoft Office.
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