This book highlights the remarkable importance of special functions,
operational calculus, and variational methods. A considerable portion of
the book is dedicated to second-order partial differential equations, as
they offer mathematical models of various phenomena in physics and
engineering.
The book provides students and researchers with essential help on key
mathematical topics, which are applied to a range of practical problems.
These topics were chosen because, after teaching university courses for
many years, the authors have found them to be essential, especially in
the contexts of technology, engineering and economics. Given the
diversity topics included in the book, the presentation of each is
limited to the basic notions and results of the respective mathematical
domain. Chapter 1 is devoted to complex functions. Here, much emphasis
is placed on the theory of holomorphic functions, which facilitate the
understanding of the role that the theory of functions of a complex
variable plays in mathematical physics, especially in the modeling of
plane problems.
In addition, the book demonstrates the importance of the theories of
special functions, operational calculus, and variational calculus. In
the last chapter, the authors discuss the basic elements of one of the
most modern areas of mathematics, namely the theory of optimal control.
