Lecturer: K.S. Narain , ICTP

lecture 8

*Cauchy-Rieman condition *and Binomial expansion and Integration,

Introducing branch cut

- We proved the necessary conditions for
*Cauchy-Rieman by continuity of**partial derivative.* - Binomial expansion was explained and we gave some examples of those
- given in page 16 equation 4.1.2. Also talk about Taylor expansion.
- We give an example of any function which satisfies Laplace equation which called Harmonic function and in particular we give example in 2 dimensions.
- The definition of integration with respect to z is given.
- Section 9 Conformal transformation is not given but we follow the
- rest of the chapter.
- We give an example of having anaytic function at some point which
- must be differentiable at that point as well as the other point.
- We introduce branch cut by applying Cauchy theorem.