Question

In: Advanced Math

(a) Apply the chain rule to express ∂/∂ρ, ∂/∂ϕ, and ∂/∂θ using ∂/∂x, ∂/∂y, and ∂/∂z....

(a) Apply the chain rule to express ∂/∂ρ, ∂/∂ϕ, and ∂/∂θ using ∂/∂x, ∂/∂y, and ∂/∂z.

(b) Solve algebraically for ∂/∂x, ∂/∂y, and ∂/∂z with ∂/∂ρ, ∂/∂ϕ, and ∂/∂θ when ρ does NOT equal  0 and sin ϕ does NOT equal 0. (Hint: you can use method of elimination to reduce the number of variables.)

(c) Express ∂2/∂x2 with ρ, ϕ, θ, and their partials.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
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