And so I could now make a plot x whereby I could have here x F and I could have here this force F, which I know because I know the masses.
现在我可以,画一张图,这里是,这是力，这个力我们知道,因为它就是重物质量。
The function f in the y=f(x) equation that is behind that graph is how scalable your application is.
这个y=f(x)方程的图像所显示出来的f函数，就是你的应用的伸缩能力。
Whenever this linear relation between F and x holds, that is referred to as Hooke's Law.
不管F和x之间的,线性关系是多少，这就是所谓的胡克定律。
F is the continuous probability distribution for x.
是x的连续型随机变量的概率分布。
For Lockheed Martin, F-X III would provided a badly needed boost to the troubled, but still promising, F-35 programme. The blue skies of the DMZ await.
对于洛克希德·马丁，F-XIII项目将会对麻烦重重但又潜力十足的F-35项目产生巨大的同时又是亟需的推动作用。
The first person let me go ahead and check out before him because of (x); other people did the same thing because of f(x). The essence of (x) is unknown.
第一个让我先结账的人是因为（x），而其他人这么做是因为（x），而这个x却是未知的。
We have the integral from minus infinity to plus infinity of F(x)*x*dx, and that's really--you see it's the same thing because an integral is analogous to a summation.
我们用从负无穷到正无穷的积分公式F(x)*x*dx,你看到的，这是相同的事，因为积分是类似的求和过程。
Partial f over partial x, and partial f over partial u, well, unless you believe that one equals two, they are really not the same thing, OK?
∂f/∂x和∂/f/∂u确实不一样，1当然不可能等于2嘛，这样来看，它们又是不一样的？
For example, the focal length of an 8" (203.2mm) aperture with a focal ratio of f/10 would be 203.2 x 10 = 2032mm.
比如，孔径为8英寸(203.2mm)，焦比为f/10的透镜，其焦距为203.2x 10 = 2032mm。
What we would start doing immediately is taking the partial derivatives. What is f sub x?
我们首先要做的事是,求偏导数，fx是多少？
Start Emacs and open a file ([Ctrl]-x[Ctrl]-f) called test.html.
启动Emacs，然后打开（[Ctrl]-x[Ctrl]-f）test.html 文件。
z I do F dot n. That just gives me the z component which might involve x, y and z.
把F和n做内积，于是得到,它由x，y，z组成。
So, that means that the value of F depends actually on y two different parameters, say,if the variables are x and y, or they can have any names you want.
这意味者F的值取决于,两个不同的参数x和，或者其他名字。
Well, we have seen that it is given by the partial derivative f sub x.
我们已经发现,它由f对x的偏导数给出。
Remember, partial f, partial x was obtained by y That means I am slicing the graph of f by a plane that is parallel to the x, z plane.
要记得，在这里的fx中,是作为常量保持不变的。，looking，at，the，situation，where，y，is，held，constant。,这是我用一个平行于xz坐标系的平面,横截了f，所得到的图形。
Well, the change in f is the value of f at the upper point here, which is x0+delta x, and minus its value at the lower point P, which is f of x0, divided by delta x.
f的变量就是f在上面的点时的值，x0+deltax，减去f在下面的点P时的值，x0，再除以delta x。
x Maybe f depends on the variable x.
也许f依赖于变量。
So, let's do our first example. Let's say I give you a function f = -y because it doesn't depend on x.
让我们举出第一个例子，给出一个函数,它看上去有点奇怪，f，=，-y。，OK，，so，it，looks，a，little，bit，silly,因为它跟x无关。
We know that f sub x and f sub y are the slopes of two tangent lines to this plane, two tangent lines to the graph.
我们知道fx和fy是,曲面上两条切线的斜率。
Why is that? Well, let's say that f sub x is zero.
为什么呢？我们令fx为。
Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.
假设我的方程是这样，然后给出了一个解。
Because the gradient vectors here are f sub x, z If you have a third variable z gz then you have also an equation f sub z equals lambda g sub z.
因为这里，梯度向量就是，如果还有一个变量,那就还有一个等式fz等于λ乘以。
Namely, let's say that you have a function maybe of three variables, x, y, z, df = fxdx+fydy +fzdz then you would write df equals f sub x dx plus f sub y dy plus f sub z dz.
即是说，如果你有一个,含自变量，x，y，z的函数，那么。
What I'm integrating to is f of x of t and y of t.
我积分的是f，y
The power of linearity is F=k1+k2 if I come across f of x, y, z equals k1 plus k2, if it is a linear equation, I don't have to go and solve it all over again.
线性的威力是,一个方程，如果它是个线性方程，那么我就不用再去解他了。
We want to know whether a given vector field with components P, Q and R can be written as f sub x, f sub y and f sub z for a same function f.
要看向量场,能否写成，其中f是同一个函数。
x And then, I can write partial f over partial x.
接着，我可以写出∂f/∂
C or F value, the X and Y coordinates of the center of a pixel at the up-left corner of the image, can be measured according to characteristic point in topographic map.
值为栅格图像左上角像素中心在地图上的X，Y坐标，其值可以根据特征点在地形图中的坐标量测获得。
C or F value, the X and Y coordinates of the center of a pixel at the up-left corner of the image, can be measured according to characteristic point in topographic map.
值为栅格图像左上角像素中心在地图上的X，Y坐标，其值可以根据特征点在地形图中的坐标量测获得。
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