M402-ex1.f05 - Name_ Math 402 Exam I 2005 g11=1, g22 = r,...

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Math 402 Exam I 2005 Name___________________ 1. _________(40 points) 2. _________(30 points) 3. _________(30 points) g 11 =1, g 22 = r², g 33 = r²sin² 2 dx i = A i j dq j total /100 points A T i j = B -1 i j = A j i x = rsin θ cos φ = ρ φ y = rsin θ sin φ = ρ φ B T m n A -1 m n = B n m z = rcos θ = z i = R -1 ( ψ , θ , φ ) i j dx' j ; counter clockwise angles, ds² = g i j d q i j g i j = 3 n ( M x 6 / M q i )( M x 6 / M q j ) u i = q^ i % g ii no sum on i, L F = (1/ % g) L ' i % g F' i L ² f = (1/ % L ' i % g g L j 'f, L × F = (1/ % g) ε ijk u i L ' j F' k F × G = % ε i j k u i F' j G' k = (1/ % ε i jk u i j G' k e^ j = [ v j - 3 k=1,j-1 ( k , v j ) k ] / | v j 3 ( k , v j k |
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1. Fill in the blanks with the best, simplest answer. Carry out all operations. It is not necessary to show work; however, some partial credit will be given if the work is shown on this page. . _________________________________________________________________________________________________ In the following r is the position vector, x i refers to x, y, or z, and q i refers to the three variables in the general coordinate system. The r, θ and φ are coordinates in the spherical system. F and f are function of x, y, and z. S is a vector space; p, w, and t are (non zero) vectors in the space S. α and β
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This note was uploaded on 12/20/2010 for the course PHYS 402 taught by Professor J. during the Fall '09 term at Missouri S&T.

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M402-ex1.f05 - Name_ Math 402 Exam I 2005 g11=1, g22 = r,...

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