How to approach the problem using integral equations and solve it with numerical methods in matlab?
Are there any tutorials with code for begginers?
You want the Poisson Integral formula, http://en.wikipedia.org/wiki/Poisson_kernel#On_the_unit_disc
It is very likely this is implemented in Matlab already.
I think you need to be a bit clearer on what you have done, what precisely you want to do, and where you are stuck for people to give you a genuinely helpful answer.
The following outline may be helpful in reviewing how far you are (the order is not completely fixed). It may be considered a high-level answer for your question on how to approach your problem.
If you tell us where you are and what you have done then we might be able to help you with the next step. My experience with people without much programming experience is that they often think they are stuck at step 7 (the actual programming). In fact, the steps before that, in which the problem is analysed, are more difficult.