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Unformatted text preview: .. so we can go to c 5 c 5 = 100 11 2 Z 1 1 8 ( 63 x 570 x 3 + 15 x ) dx = 100 11 32 Steadystate temperature in a sphere, continued Now that we have our Legendre coecients, c = 100 ( 1 2 ) , c 1 = 100 ( 3 4 ) , c 2 = 0, c 3 = 100 (7 16 ) , c 4 = 0, c 5 = 100 ( 11 32 ) , etc., we can write a series solution T ( r , ) = X l =0 c l r l P l (cos ) T ( r , ) = 100 1 2 + 3 4 r cos 7 16 r 3 5 2 cos 3 3 2 cos + ... Notice that we write T ( r , ) since we determined from the beginning that the solution is independent of It is crucial to remember that we solved this only for r < 1! Our solution does not apply outside of this region...
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This note was uploaded on 07/30/2011 for the course PHZ 3113 taught by Professor Staff during the Spring '03 term at University of Central Florida.
 Spring '03
 Staff

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