The jacobian is j x s y s s t x t y t e est s t e est

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Unformatted text preview: 6 1 = (− cos θ + cos3 θ)|π = 64/15 0 5 3 (c) Use spherical coordinates: 1 π /2 2π z3 (ρ3 cos3 φ)ρ(ρ2 sin φ) dρ dφ dθ x2 + y 2 + z 2 dV = 0 0 0 E π /2 2π = 0 0 1 cos3 φ sin φ dφ dθ 7 = π/14 9. The Jacobian is J= = ∂x ∂s ∂y ∂s s+ t ∂x ∂t ∂y ∂t e es+t s− t e −es−t = es+t (−es−t ) − es+t es−t = −2es+t es−t = −2e2s 10. First, compute the Jacobian: J= = ∂x ∂v ∂y ∂v ∂x ∂u ∂y ∂u 20 03 =6 Second, notice the ellipse becomes 9x2 + 4y 2 = 36 ⇒ 9(2u)2 + 4(3v )2 = 36 under the transformat...
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This document was uploaded on 03/08/2014.

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