Functions of a Complex Variable

Abstract

The answers we seek in subjecting physical models to mathematical analysis are most frequently real, but to arrive at these answers we often invoke the powerful theory of analytic functions. This theory often provides major results with little calculation, and the frequency with which we resort to it is a testimony to its utility. In this chapter we summarize the rudiments of complex analysis. Many techniques that rely on complex analysis, e.g., transforms of various types, are treated in subsequent chapters, and consequently, are not mentioned or mentioned only briefly here. Although it is arranged somewhat differently, nearly all of the material presented here will be found in substantially greater detail in Ref. (5-1). A succinct treatment of the basic results of the theory, with some regard for applications, may be found in Ref. (5-2). A less discursive summary of much of this material is contained in Chapter 7 of Ref. (5-3).