ABSTRACT
Holomorphic functions are a generalization of complex polynomials. But they are more flexible objects than polynomials. The collection of all polynomials is closed under addition and multiplication. However, the collection of all holomorphic functions is closed under reciprocals, inverses, exponentiation, logarithms, square roots, and many other operations as well. There are several different ways to introduce the concept of holomorphic function. They can be referred to by way of power series, or using the complex derivative, or using the partial differential equations. This chapter discusses the Cauchy—Riemann equations, the relationship of holomorphic and harmonic functions, and complex differentiability and conformality.
