Consider the polar coordinate on R^2,i.e
x= rcosθ ; y = rsinθ
Compute the following partial derivatives in term of coordinate (r,θ)
a) ∂/∂x=?
b) ∂/∂y=?
c) ((∂^2)/(∂x^2))+((∂^2)/(∂y^2))=?
I know ∂/∂x= (∂/∂r)(∂r/∂x)+(∂/∂θ)(∂θ/∂x)
Is ∂r/∂x = cosθ and ∂θ/∂x = -rsinθ ?
Partial Derivative
2015-05-19 9:24 am
回答 (1)
2015-05-23 5:48 am
✔ 最佳答案
∂/∂x= (∂/∂r)(∂r/∂x)+(∂/∂θ)(∂θ/∂x)Therefore,
x=rcosθ
r=x/cosθ dr/dx=1/cosθ
r=y/sinθ dr/dy=1/sinθ
I think you can solve the problem by the above,
參考: A Theoretical Physics talent (in string&M theory and quantum topological field theory)
收錄日期: 2021-04-15 20:11:28
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