K.S. Narain , ICTP

### lecture 9

*Simply connected or not simply connected region, Stokes theorem,*

- We define Cauchy theorem is simply connected Region R if f(z) is analytic in R, note that we do not follow its proof from the book.
*The proof of Stokes theorem in 2 dimension is given .We also give some**application for it.(Total flux of electric field is equal to total charged enclosed**the sphere).**We mention Cauchy integral representation for an analytic function.**Proof of this statement is directly given in the class and we give some example.**By taking modulus of an analytic function we prove this does not**make a local maximum.**We will see that Cauchy theorem says if a function is analytic in any region**then the integral over any closed contour vanishes.*