Mathematic Methods HW Solutions 27

Mathematic Methods HW Solutions 27 - Chapter 6 27 6.11 6.12...

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Chapter 6 27 6.11 φ = 2 x i - 2 y j , E = - 2 x i + 2 y j 6.12 (a) 2 5, - 2 i + j (b) 3 i + 2 j (c) 10 6.13 (a) i + j , |∇ φ | = e (b) - 1 / 2 (c) i , | E | = 1 (d) e - 1 6.14 (b) Down, at the rate 11 2 6.15 (a) 4 2 , up (b) 0, around the hill (c) - 4 / 10, down (d) 8 / 5, up 6.17 e r 6.18 i 6.19 j 6.20 2 r e r 7.1 ∇ · r = 3, ∇ × r = 0 7.2 ∇ · r = 2, ∇ × r = 0 7.3 ∇ · V = 1, ∇ × V = 0 7.4 ∇ · V = 0, ∇ × V = - ( i + j + k ) 7.5 ∇ · V = 2( x + y + z ), ∇ × V = 0 7.6 · V = 5 xy , ∇ × V = i xz - j yz + k ( y 2 - x 2 ) 7.7 ∇ · V = 0, ∇ × V = x i - y j - x cos y k 7.8 ∇ · V = 2 + x sinh z , ∇ × V = 0 7.9 6 y 7.10 0 7.11 - ( x 2 + y 2 ) / ( x 2 - y 2 ) 3 / 2 7.12 4( x + y ) - 3 7.13 2 xy 7.14 0 7.15 0 7.16 2( x 2 + y 2 + z 2 ) - 1 7.18 2 k 7.19 2 /r 7.20 0 8.1 - 11 / 3 8.2 (a) - 4 π (b) - 16 (c) - 8 8.3 (a) 5 / 3 (b) 1 (c) 2 / 3 8.4 (a) 3 (b) 8 / 3 8.5 (a) 86 / 3 (b) - 31 / 3 8.6 (a) 3 (b) 3 (c) 3 8.7 (a) - 2 π (b) 0 (c) - 2 (d) 2 π 8.8 yz - x 8.9 3 xy - x 3 yz - z 2 8.10 1 2 kr 2 8.11 - y sin 2 x 8.12 - ( xy + z ) 8.13 - z 2 cosh y 8.14 - arcsin xy 8.15 - ( x 2 + 1) cos 2 y 8.16 (a) F 1 ; φ 1 = y
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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