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    Problem Sheet, Week 1
    2. Calculate the gradient of f(x) = 3 sin(x1 x2) + e^(2 x3)
    3. Knowing F: R3 to R2, G: R2 to R2, H: R2 to R4, which compositions exist
    (a) F∘G
    (b) H∘F
    4. Calculate the Jacobian of r(r, φ, θ). When is this non-zero?
    Problem Sheet, Week 1
    答 2. Calculate the gradient of f(x) = 3 sin(x1 x2) + e^(2 x3)
    ∇f = ( 3x2 cos(x1x2),  3x1 cos(x1x2),  2e2x3 )
    3. Which compositions exist (a) F∘G
    (b) H∘F
    4. Jacobian of r(r, φ, θ)
    Problem Sheet, Week 1
    2. Calculate the gradient of f(x) = 3 sin(x1 x2) + e^(2 x3)
    3. Which compositions exist (a) F∘G
    (b) H∘F
    (c) G∘F, and what dimensions
    4. Jacobian of r(r, φ, θ)

      Problem Sheet, Week 1p.2
      3. Knowing F: R3 to R2, G: R2 to R2, H: R2 to R4, which compositions exist (a) F∘G
      (b) H∘F

      — Alex

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