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3. Consider the delta-function 8(x), which has the property S f(x)6(x-a) dr = f(a) since 8(r-a) = 0 whenever . # a. What is the Fourier expansion of o(x - a) in terms of coesines? 4. Consider a rectangular block of volume abe, defined by 0 < x a; 0 < y be 0 Z Solve the Laplace equation for u(x, y, z) within this rectangle for zero Dirichlet boundary conditions on each face, except the top face where u(x, y,c) = f(x,g). (a) Derive the solution = sin mar sin nity 6 sinh a m=1 m 2 2 Arrn = T + ; m,n E Z. (b) What is the integral to determine Bmn? (c) If f(x,g) = x, what are the coefficients Bmn and what is the solution x)? 1 of 1

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