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# Q HW2 - EML 6154 Homework Set 2 Due Friday September 11 1...

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EML 6154 Homework Set 2 Due Friday, September 11 1) Separation of variables leads to the following orthogonal function, n ( x ) = cos( n x ), with eigenvalues n = (2n+1) /2L, for n = 0, 1, 2….. over the interval x = 0 to L, noting that the weighting function is one. i) Show that the integral dx x x m L x n ) ( ) ( 0 0 for n m . ii) Evaluate the integral dx x L x n ) ( 0 2 iii) Determine the general Fourier series expansion coefficients (a n ) for the following: ) cos( 2 0 2 x a x n n n . Simplify integrals as much as possible . 2) Work problems 1.12 in text. Note: Mathematical formulation requires statement of the simplified governing equation and the appropriate boundary and/or initial conditions. Do NOT solve . 3) Consider a solid copper sphere of diameter 10 cm, see figure below. The sphere has 6 equally spaced solid copper cylinders that extend from the sphere as shown in the figure. Each cylinder is 1-cm in diameter, and 10 cm long.

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