6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: We solved this problem by Fourier Transform: We will solve this problem.

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6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: We solved this problem by Fourier Transform: We will solve this problem again by Fourier Integral: Goal

6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: We will solve this problem again by Fourier Integral: We looking for a bounded solution. Goal The Fourier Integral representation of f Fourier integral coefficients of f

6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem:

6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: To satisfy the boundary condition we must generally superimpose these conditions over all w >= 0. this is done by integration Boundary condition Fourier Integral expansion of f

6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: Fourier Integral expansion of f

6.9 Dirichlet Problem for the Upper Half-Plane Ex5/p279 In each Problem obtain the solution of the Dirichlet problem for the upper half-plane, using the given f(x).