 Welcome back MechanicalEI. Did you know that Milne-Thompson method was developed by Alam Milne-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 Milne-Thompson method? Before we jump in, check out the previous part of this series to learn about what analytic functions are. Now, Milne-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-of z equals f of z. Let's look an example to understand a little better. Consider u equal to the following expression. We need to find f of z by Milne-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 Milne-Thompson method is and then went on to see an example of it. So, like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You helped the channel grow. So, here are the top mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what harmonic functions are.