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Phaier School
Gradient (勾配)
∇
f
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∂
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∂
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∂
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∂
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\begin{aligned} \nabla f & = \frac{\partial f}{\partial x}\mathbf{e}_x + \frac{\partial f}{\partial y}\mathbf{e}_y + \frac{\partial f}{\partial z}\mathbf{e}_z \\ & = \frac{\partial f}{\partial \rho}\mathbf{e}_\rho + \frac{1}{\rho}\frac{\partial f}{\partial \theta}\mathbf{e}_\theta + \frac{\partial f}{\partial z}\mathbf{e}_z \\ & = \frac{\partial f}{\partial r}\mathbf{e}_r + \frac{1}{r}\frac{\partial f}{\partial \theta}\mathbf{e}_\theta + \frac{1}{r \sin\theta}\frac{\partial f}{\partial \phi}\mathbf{e}_\phi \end{aligned}
∇
f
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∂
x
∂
f
e
x
+
∂
y
∂
f
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∂
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∂
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∂
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∂
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∂
r
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r
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∂
θ
∂
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r
sin
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1
∂
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∂
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