This Field Guide is designed to provide engineers and scientists with a quick reference for special functions that are crucial to resolving modern engineering and physics problems. The functions treated in this book apply to many fields, including electro-optics, electromagnetic theory, wave propagation, heat conduction, quantum mechanics, probability theory, and electric circuit theory, among many other areas of application. A brief review of these important topics is included in this guide, as well as an introduction to some useful engineering functions such as the step function, rectangle function, and delta (impulse) function.

Most of the material chosen for the Field Guide is condensed from two textbooks: Special Functions of Mathematics for Engineers by L. C. Andrews and Mathematical Techniques for Engineers and Scientists by L. C. Andrews and R. L. Phillips. Both books are SPIE Press publications.

Many modern engineering and physics problems demand a thorough knowledge of mathematical techniques. In particular, it is important to recognize the various special functions (beyond the elementary functions) that may arise in practice as a solution to a differential equation or as a solution to some integral. It also helps to have a good understanding of their basic properties. The functions treated in this Field Guide are among the most important for engineers and scientists. They commonly occur in problems involving electro-optics, electromagnetic theory, wave propagation, heat conduction, quantum mechanics, probability theory, and electric circuit theory, among many other areas of application.

Because of the close association of power series and improper integrals with special functions, a brief review of these important topics is included in this guide. In addition, we also briefly introduce some of the useful engineering functions like the step function, rectangle function, and delta (impulse) function.

Unfortunately, notation for various engineering and special functions is not consistent among disciplines. Also, some special functions have more than one definition depending on the area of application. For these reasons, the reader is advised to be careful when using more than one reference source. The notation for the special functions adopted in this Field Guide is that which the author considers most widely used in practice.

Larry C. Andrews

Professor Emeritus, UCF