dy x dt That tells us dx is x prime of t dt.
是y’dt，dy，becomes，y，prime，of，t，dt。,是x，So，，we，know，x，is，x，of，t。,它告诉我们dx是x
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。
So, if we want to set it up instead dx dy, then it means we are going to actually look at the converse question which is, for a given value of y, what is the range of values of x?
如果要用dxdy来替换，就是说,转化为与之相反的问题来看，给定y的一个值，那么x的取值范围是什么呢？
We could do it dy dx. Or, maybe we will want to actually make a change of variables to first shift this to the origin, x-2 you know, change x to x minus two and then switch to polar coordinates.
也可以dy，dx来划分，或者,对变量做一下变化，移动到原点，就是把x变成,然后再转化成极坐标。
dxdy So that's just x. So, that means that du dv is x dx dy.
这个就是x，这就意味着dudv是x倍的。
OK, so I'm computing the integral of y dx x dy.
我来计算ydx+xdy的积分。
x And, so if we want partial z over partial x, well, so one way is just to say that's going to be the coefficient of dx in here or just to write down the other way.
如果想知道∂z/∂,一种观点认为，它是这里dx前面的系数,或者从别的观点来看。
the general notation for vector dr-- y equals dx, x roof, plus dy, y roof, z plus dz, z roof.
总的向量dr的符号-,=dr向量x+dy向量，+dz向量。
dx/a OK, so if we set u equals x over a, that means du is one over adx.
如果令u等于x/a，就意味着du就是。
dx/dt So and I have something of the form dx/dt is x equal to constant times x.
我有一些关于这个形式,等于常量乘以。
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。
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。
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