Mathematic Methods HW Solutions 50

# Mathematic Methods HW Solutions 50 - 8.5 V = e r cos θ e...

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Unformatted text preview: Chapter 10 50 8.5 V = e r cos θ- e θ sin θ- e φ r sin θ 8.6 h u = h v = ( u 2 + v 2 ) 1 / 2 , h z = 1 d s = ( u 2 + v 2 ) 1 / 2 ( e u du + e v dv ) + e z dz dV = ( u 2 + v 2 ) du dv dz a u = i u + j v = ( u 2 + v 2 ) 1 / 2 e u a v =- i v + j u = ( u 2 + v 2 ) 1 / 2 e v a z = k = e z 8.7 h u = h v = a (sinh 2 u + sin 2 v ) 1 / 2 , h z = 1 d s = a (sinh 2 u + sin 2 v ) 1 / 2 ( e u du + e v dv ) + e z dz dV = a 2 (sinh 2 u + sin 2 v ) du dv dz a u = i a sinh u cos v + j a cosh u sin v = h u e u a v =- i a cosh u sin v + j a sinh u cos v = h v e v a z = k = e z 8.8 h u = h v = ( u 2 + v 2 ) 1 / 2 , h φ = uv d s = ( u 2 + v 2 ) 1 / 2 ( e u du + e v dv ) + uv e φ dφ dV = uv ( u 2 + v 2 ) du dv dφ a u = i v cos φ + j v sin φ + k u = h u e u a v = i u cos φ + j u sin φ- k v = h v e v a φ =- i uv sin φ + j uv cos φ = h φ e φ 8.9 h u = h v = a (cosh u + cos v )- 1 d s = a (cosh u + cos v )- 1 ( e u du + e v dv ) dA = a 2 (cosh u + cos v )- 2 du dv a u = ( h 2 u /a )[ i (1 + cos...
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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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