Applied Theory of Functional Differential Equations

The purpose of this book is to consider in sufficient detail problems and methods con- neQted with the application of systems with memory, also called hereditary systems, that can be described by functional differential equations (FDEs).
A distinguishing feature of the FDEs under consideration is that the evolution rate of the processes described by such equations depends on the past history.
During the last two decades, the theory and application of FDEs has developed and spread to an extent never experienced earlier. In this book we study mathematical models described by FDEs which are applicable to phenomena of quite different na- tures. Appropriate applications include: immunology, nuclear power generation, heat transfer, track signal processing, regulation systems, medicine, economy, etc.
This book gives an introduction to the theory of FDEs. We have attempted to give the reader an insight into the wide environment in which this theory is embedded.
We have made every attempt to include the most important methods and techniques used in applications. The first chapter plays a special role. Its function is largely motivational, and it also serves to show 'where FDEs come from', and what kind of problems typically arise in applications.
This part of the book is also concerned with modeling. The basic view on scientific modeling is that a model is any 'simplified description of a system (etc.) that assists calculations and predictions' (Oxford English Dictionary). The main reason to model something is to provide for an efficient organization of information and experiences in order to enhance understanding and enable (wise) decision making.
Modeling is ubiquitous in human activities, because a model is a condensed repre- sentation of available information. Models are used to describe aspects of experience, and to predict, influence and regulate future developments.