# PS6 - f g ā Z 5 1 f x g x dx 4 Strauss 5.3#6-1st order...

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MATH 412: Problem Set 6 due Thursday, April 3, 2008 1. Strauss 5.2 #11 - full Fourier series - (complex form only) 2. Strauss 5.3 #2 - Legendre polynomials 3. Using the following generalized deﬁnition of the angle between two elements of an inner product space cos θ ( f, g ) p ( f, f )( g, g ) (a) show that the angle θ between x and x 2 is about 14.5 , where the inner product ( f, g ) Z 2 0 f ( x ) g ( x ) dx ; (b) what would the angle between the same two functions be for the innner product
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Unformatted text preview: ( f, g ) ā” Z 5 1 f ( x ) g ( x ) dx 4. Strauss 5.3 #6 -1st order diļ¬erential operator- (consider dX 1 /dx = Ī» 1 X 1 , and follow what we did in class, or pp.118-119) 5. Strauss 5.3 #12 -Greenās First Identity in 1D 6. Strauss 5.4 #12 -using Parsevalās equality...
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