Analytic functions

1. Mar 28, 2013

morganmkm

find an analytic function F where F' = f

f(z) = z-2
f(z) = ((z^4) +1)/(z^2)
f(z) = sinzcosz

I know I have to put these into the cauchy riemann equations but I dont know what to use for my du/dx or du/dy because im not sure to use x-2 for my du/dx etc or if im supposed to integrate first. I dont know which parts of the equations fit into the riemann-cauchy equations. My book only gives one example and I dont know how to relate these, please help

2. Mar 28, 2013

micromass

Staff Emeritus
Just integrate like in calculus?

3. Mar 28, 2013

mathman

All these expressions can be handled by ordinary integration (the second one is more difficult).
For example f(z) = z-2, them F(z) = z2/2 - 2z + C.

4. Apr 2, 2013

Bacle2

The second function is not entire , so you need to specify a domain. Depending on the level of your class, it would be nice to have an argument for why the antiderivative is analytic (hint, use something like independence of path and Morera's thm.)