M402-FIN.cover.pages

M402-FIN.cover.pages - Math 402 Final Exam 2005...

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Unformatted text preview: Math 402 Final Exam 2005 Name___________________ This exam will not be returned. However, you may examine your graded solutions. 1. _________( 75 points) g 11 =1, g 22 =r, g 33 =rsin (spherical coord.) 2. _________( 20 points) 3. _________( 10 points) dx i = A i j dq j 4. _________( 20 points) 5. _________( 25 points) A T i j = B-1 i j = A j I total /150 points B Tm n = A-1m n = B n m Course Average __________ Grade _______ x = rsin cos = cos y = rsin sin = sin z = rcos = z dx i = R-1 ( , , ) i j dx' j ; counter clockwise angles,------------------------------------------------------------------------------------------------------------------------------------- ds = g ij dq i dq j g ij = 3 n ( M x 6 / M q i )( M x 6 / M q j ) u i = % g ii q^ i no sum, L @ F = (1/ % g) L ' i % g F' i L f = (1/ % g) L ' i % g g ij L j 'f, L x F = (1/ % g) ijk u i L ' j F' k = % g ijk u i L ' j F' k-------------------------------------------------------------------------------------------------------------------------------------...
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M402-FIN.cover.pages - Math 402 Final Exam 2005...

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