Description A first course in theory of analytic functions of one complex variable: complex differentiability and the Cauchy-Riemann equations, Cauchy Integral Theorem and Cauchy Integral Formula, ...

The specific topics that will be covered are: the geometry of complex numbers, complex differentiation, Cauchy-Riemann equations, Cauchy's integral theorem and its consequences, Taylor and Laurent ...

Holomorphic functions in Rn are defined to generalize those in R2. A Taylor formula and a Cauchy integral formula are presented. An application of the Taylor formula to the kernel of the Cauchy ...