Welcome back mechanically, I did you know that Millet Thompson method was developed by LM Millet Thompson and helped greatly simplify the process of finding a holomorphic function whose real or imaginary or any combination of the two parts is given? This makes us wonder what is Millet Thompson method? Before we jump in, check the previous part of this series to learn about what analytic functions are. Now Millet Thompson method is used to construct an analytic function when its real or imaginary components are known. If a given function f of z is analytic in a given domain, then f of z can be integrated in the domain using antiderivative. That is by finding a capital f of z such that capital f dash of z equals f of z. Let's look at an example to understand a little better. Consider u equal to the following expression. We need to find f of z by Millet Thompson method. So we first find partial derivative of u with respect to x called ux and then find partial derivative of u with respect to y and call it uy. Next we substitute y equals to 0 in both ux and uy to get psi 1 of x comma 0 and psi 2 of x comma 0. After finding these values, we simply substitute z in place of x in both psi 1 and psi 2 and write it in the form of antiderivative f dash of z. We then integrate this antiderivative to find f of z and obtain the solution. Hence we first saw what Millet Thompson method is and then went out to see an example of it.