a question on differential

👨🏻‍🏫 學術台數學

2009-12-03 4:52 am

given x = r * cos, y = r * sin,

can you show that dx * dy = r * dr * d ?

回答 (2)

2009-12-03 5:21 am

✔ 最佳答案

x=rcosθ,y=rsinθ

dx=cosθdr-rsinθdθ
dy=sinθdr+rcosθdθ

dxdy=
|cosθ -rsinθ| * drdθ
|sinθ rcosθ|
=rdrdθ

👍 0 👎 0

2009-12-03 5:23 am

Jacobian

👍 0 👎 0

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