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Unformatted text preview: of the component of F in the direction of normal to S ). ( Hint: This is easiest to do using the Divergence Theorem.) (3) Let F ( x,y,z ) = [ e y ,-z, ye x ], S is the hemisphere x 2 + y 2 + z 2 = 1 , x 0 and n is the unit normal vector eld to S that points toward the origin. Dene the vector eld F by (i) Let C denote the boundary of S . Find a vector function r that parametrizes C . (ii) Invoke the Stokess Theorem to nd a line integral whose value is equal to Z Z S F n dA. (iii) Evaluate the line integral from part (ii). 3. Fourier Series (1) Expand the function f ( x ) = x-3 (0 < x < 3) in a Fourier cosine series, and (b) Fourier sine series. (2) Find the complex Fourier series of f ( x ) = x 2 if- < x < and f ( x + 2 ) = f ( x ). Convert the series to real form 1...
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This note was uploaded on 06/03/2008 for the course MA 441 taught by Professor Kaba during the Fall '08 term at Embry-Riddle FL/AZ.
- Fall '08