Volume 1, i. e. the monograph The Cauchy Method of Residues - Theory and
Applications published by D. Reidel Publishing Company in 1984 is the
only book that covers all known applications of the calculus of
residues. They range from the theory of equations, theory of numbers,
matrix analysis, evaluation of real definite integrals, summation of
finite and infinite series, expansions of functions into infinite series
and products, ordinary and partial differential equations, mathematical
and theoretical physics, to the calculus of finite differences and
difference equations. The appearance of Volume 1 was acknowledged by the
mathematical community. Favourable reviews and many private
communications encouraged the authors to continue their work, the result
being the present book, Volume 2, a sequel to Volume 1. We mention that
Volume 1 is a revised, extended and updated translation of the book
Cauchyjev raeun ostataka sa primenama published in Serbian by Nau na
knjiga, Belgrade in 1978, whereas the greater part of Volume 2 is based
upon the second Serbian edition of the mentioned book from 1991. Chapter
1 is introductory while Chapters 2 - 6 are supplements to the
corresponding chapters of Volume 1. They mainly contain results missed
during the preparation of Volume 1 and also some new results published
after 1982. Besides, certain topics which were only briefly mentioned in
Volume 1 are treated here in more detail.