Chem Differential Eq HW Solutions Fall 2011 90

Chem Differential Eq HW Solutions Fall 2011 90 - 90 Chapter...

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90 Chapter 5 Partial Differential Equations in Spherical Coordinates it suffices to prove the inequality ± ± ± x + i ² 1 - x 2 cos θ ± ± ± 1 , which in turn will follow from ± ± ± x + i ² 1 - x 2 cos θ ± ± ± 2 1 . For any complex number α + , we have | α + | 2 = α 2 + β 2 .So ± ± ± x + i ² 1 - x 2 cos θ ± ± ± 2 = x 2 +( ² 1 - x 2 cos θ ) 2 = x 2 +(1 - x 2 ) cos 2 θ x 2 - x 2 )=1 , which proves the desired inequality.
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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