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Problem #1 : Using separation of variables and the formalism demonstrated in class, find the general solution...

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Advance Math

Problem #1 :

Using separation of variables and the formalism demonstrated inclass, find the general solution to the Helmholtz equation (alsoknown as the time independent wave equation) :

?^2 F + k^2 F = 0

Assume that k is a real number. For clarification, the generalsolution is the solution in the case where boundary conditions arenot specified.

Problem #2 :

Express the following functions as an infinite Fourier sineseries using sin(n?x/a)

a)f(x) = x

b)f(x) = e^x

c)f(x) = cos(x)

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