- #1

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## Homework Statement

(

**A**.∇)

**B**

What does this mean and how do I go about trying to expand this (using cartesian components)?

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- Thread starter BOYLANATOR
- Start date

- #1

- 198

- 18

(

What does this mean and how do I go about trying to expand this (using cartesian components)?

- #2

SammyS

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Well, [itex]\displaystyle \vec{\text{A}}\cdot\vec{\nabla}=\text{A}_x\,\frac{ \partial}{\partial x}+\text{A}_y\,\frac{ \partial}{\partial y}+\text{A}_z\,\frac{ \partial}{\partial z}\ .## Homework Statement

(A.∇)B

What does this mean and how do I go about trying to expand this (using cartesian components)?

[/itex]

So that [itex]\displaystyle \left(\vec{\text{A}}\cdot\vec{\nabla}\right) \vec{\text{B}}=\text{A}_x\,\frac{ \partial\vec{\text{B}}}{\partial x}+\text{A}_y\,\frac{ \partial\vec{\text{B}}}{\partial y}+\text{A}_z\,\frac{ \partial\vec{\text{B}}}{\partial z}\ .

[/itex]

- #3

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- #4

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A.∇) rather than (∇.A) that confused me but now I realise that these are obviously equivalent. Thanks

Actually that's wrong isn't it?

If the order is reversed you find the derivatives of each component of

- #5

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Yes, it's correct. The whole expression is called the derivative of B along A.

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