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.