This textbook accounts for two seemingly unrelated mathematical topics
drawn from two separate areas of mathematics that have no evident points
of contiguity. Green's function is a topic in partial differential
equations and covered in most standard texts, while infinite products
are used in mathematical analysis. For the two-dimensional Laplace
equation, Green's functions are conventionally constructed by either the
method of images, conformal mapping, or the eigenfunction expansion. The
present text focuses on the construction of Green's functions for a wide
range of boundary-value problems.
Green's Functions and Infinite Products provides a thorough
introduction to the classical subjects of the construction of Green's
functions for the two-dimensional Laplace equation and the infinite
product representation of elementary functions. Every chapter begins
with a review guide, outlining the basic concepts covered. A set of
carefully designed challenging exercises is available at the end of each
chapter to provide the reader with the opportunity to explore the
concepts in more detail. Hints, comments, and answers to most of those
exercises can be found at the end of the text. In addition, several
illustrative examples are offered at the end of most sections. This text
is intended for an elective graduate course or seminar within the scope
of either pure or applied mathematics.