Apply Fourier series expansion method to solve the following Dirichlet problem for the Laplace equation Pu(x1,...

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Apply Fourier series expansion method to solve the following Dirichlet problem for the Laplace equation Pu(x1, x2), Pu(x1, x2) = 0, 21 E (0,b1), r2 E (0, b2), %3D u(x1,0) = f(x1), u(x1, b2) = g(a1), r1 E (0, b1), X2 € (0, b2), %3D u(0, r2) = 0, u(b1, 22) = 0, %3D where bi >0, b2 > 0 are given constants, f(x1), g(x1) are given continuous functions depending on xı € [0, b1]. Apply Fourier series expansion method to solve the following Dirichlet problem for the Laplace equation Pu(x1, x2), Pu(x1, x2) = 0, 21 E (0,b1), r2 E (0, b2), %3D u(x1,0) = f(x1), u(x1, b2) = g(a1), r1 E (0, b1), X2 € (0, b2), %3D u(0, r2) = 0, u(b1, 22) = 0, %3D where bi >0, b2 > 0 are given constants, f(x1), g(x1) are given continuous functions depending on xı € [0, b1].