18.02 Pset 8

# 18.02 Pset 8 - 18.02 HOMEWORK#8 DUE DECEMBER 2 2010 BJORN...

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18.02 HOMEWORK #8, DUE DECEMBER 2, 2010 BJORN POONEN 1. Part A (After Nov. 18) p. 1063: 15, 27* (7 pts.) (After Nov. 18) 6C-7b* (5 pts.), 6C-9* (3 + 7 + 5 + 10 pts.) (After Nov. 19) p. 1018: 11–14, 29, 32* (5 pts.) (After Nov. 19) 6D-2, 6D-5, 6D-6* (5 pts.) (After Nov. 19) 6E-1c, 6E-4, 6E-6 (After Nov. 19) p. 1071: 12 (After Nov. 19) 6F-2, 6F-3, 6F-4b 2. Part B B.1) (After Nov. 5) The diﬀerential operators , div, and curl can be expressed in cylindrical or spherical coordinates. This exercise works out the formula for the f in spherical coordinates. At each point in space with spherical coordinates ( ρ, φ, θ ) not at a pole, choose a coordinate system of orthogonal unit vectors ˆ ρ , ˆ φ , and ˆ θ , each of which represents the direction that the point moves if the corresponding spherical coordinate is increased. Let f be a function on R 3 , re-expressed as a function of the independent variables ( ρ, φ, θ ). (a) (5 pts.) Let

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18.02 Pset 8 - 18.02 HOMEWORK#8 DUE DECEMBER 2 2010 BJORN...

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