Green's function and Poisson's integral formula
Not what you're looking for?
Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts):
I need to construct Green's function for the Dirichlet problem (Laplace's equation) in the upper half plane R={(x,y) : y>0} and I must derive Poisson's integral formula for the half plane.
Please note that I am unable to use mathematical symbols (my computer does not allow me.) I will thus write out the following hints. For the first part of the problem we may consider log(R*/R) where R=|x-y|, R*=|x*-y|, with x* the mirror image of x=(x,y) with respect to y=0.
I have also know that the Poisson equation may be:
u(x,y) = [y divided by pi] times the integral (from negative infinity to positive infinity) of [u(m,o) divided by (m-x)squared + ysquared]dm.
I just need help deriving all of this. I have some idea but I cannot show you what I have (too complicated.) Thank you so much for taking the time in trying this question.
Purchase this Solution
Solution Summary
This shows how to construct Green's function for a given Dirichlet problem and derive Poisson's integral formula for the half plane.
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.