In today's lecture: i defined ¡­

In today's lecture: i defined the logarithm as a complex valued function and showed analyticity of the principal branch of the Logarithm on a sub-domain of the complex plane. Most of the material was from chapter 3.3.

In the next lecture: i will introduce the notion of branches of a complex function and illustrate their domains of analyticity. I will also cover powers of a complex function and introduce inverse trigonometric functions (chapter 3.5).