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5576

2016-08-30 10:29:42

$\left(\nabla f\left(x\right)\right)\cdot \mathbf\left\{v\right\} = D_\left\{\mathbf v\right\}f\left(x\right).$
In a rectangular coordinate system, the gradient is the vector field whose components are the s of f:
$\nabla f = \frac\left\{\partial f\right\}\left\{\partial x_1 \right\}\mathbf\left\{e\right\}_1 + \cdots + \frac\left\{\partial f\right\}\left\{\partial x_n \right\}\mathbf\left\{e\right\}_n$
where the ei are the orthogonal unit vectors pointing in the coordinate directions. When a function also depends on a parameter such as time, the gradient often refers simply to the vector of its spatial derivatives only.

## Cartesian coordinates

In the three-dimensional , the gradient is given by:
$\nabla f = \frac\left\{\partial f\right\}\left\{\partial x\right\} \mathbf\left\{i\right\} +$
\frac{\partial f}{\partial y} \mathbf{j} + \frac{\partial f}{\partial z} \mathbf{k}
where i, j, k are the s. For example, the gradient of the function
$f\left(x,y,z\right)= \ 2x+3y^2-\sin\left(z\right)$
is:
$\nabla f=$
\frac{\partial f}{\partial x} \mathbf{i} + \frac{\partial f}{\partial y} \mathbf{j} + \frac{\partial f}{\partial z} \mathbf{k} = 2\mathbf{i}+ 6y\mathbf{j} -\cos(z)\mathbf{k}.
In some applications it is customary to represent the gradient as a or of its components in a rectangular coordinate system.

## Cylindrical and spherical coordinates

{{main|Del in cylindrical and spherical coordinates}}
In , the gradient is given by:{{harvnb|Schey|1992|pp=139–142}}.
$\nabla f\left(\rho, \varphi, z\right) =$
\frac{\partial f}{\partial \rho}\mathbf{e}_\rho + \frac{1}{\rho}\frac{\partial f}{\partial \varphi}\mathbf{e}_\varphi + \frac{\partial f}{\partial z}\mathbf{e}_z
where φ is the azimuthal or angle, z is the , and eρ, eφ and ez are unit vectors pointing along the coordinate directions.
In , the gradient is given by:
$\nabla f\left(r, \theta, \varphi\right) =$
\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 \varphi}\mathbf{e}_\varphi
where φ is the angle and θ is the angle.
For the gradient in other s, see .
5575

2016-08-11 09:49:14

5574

2016-08-11 09:29:24

5573

2015-11-27 10:11:28

5503

2015-05-22 15:43:01

A代表选择A容器，R是红球

P(A|R) P(R)=P(R|A) P(A)=7/10*1/2=7/20 P(A|R)=7/20/(8/20)=7/8
5572

2015-05-22 15:38:47

5571

2015-04-21 11:21:46

5527

2015-04-20 17:51:07

5570

2015-04-16 10:10:36

$$e^{ix} = \cos x + i\sin x$$

5480

2015-03-24 09:55:07

5461

2014-08-04 10:32:14

5465

2014-08-04 10:32:14

5486

2014-08-04 10:32:14

5511