Complements of Higher Mathematics

This book features the remarkable importance of special functions, operational calculus, and variational methods. This book provides students and researchers with much help in mathematical topics that are applied to many different practical problems. These topics were chosen because after teaching many years at universities the authors experienced that the topics are essential, especially in technology, engineering, and economics. The diversity of chapters included in the book limits the presentation to the basic notions and results of each mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding 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 considers the remarkable importance that the theories of special functions, operational calculus, and variational calculus have. A great part of the book is dedicated to second-order partial differential equations, since they offer mathematical models of various phenomena in physics and engineering. In the last chapter, we discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control.