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第8讲-高阶偏导数与极值[宝典].doc
第8讲-高阶偏导数与极值[宝典].doc
第8讲-高阶偏导数与极值[宝典].doc
简介：本文档为《第8讲-高阶偏导数与极值[宝典]doc》，可适用于综合领域，主题内容包含第讲高阶偏导数与极值宝典第讲高阶导数与二元函数极值授课题目高阶导数与二元函数极值教学内容多元函数的高阶偏导数二元函数的二阶混合偏导数相同的充分条件二符等。
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资料评价：偏导数还有一个重要用处,就是最优化以及解决最值问题。
One important application we have seen of partial derivatives is to try to optimize things, try to solve minimum/maximum problems.
有一个极值问题，也有关于拉格朗日乘数法的，链式法则也会有的,约束条件下偏导数当然不会漏掉。
Expect one about a min/max problem, something about Lagrange multipliers, something about the chain rule and something about constrained partial derivatives.
但是有一件事情，我必须指出来,在现实中，很多函数的偏导数之间,存在着很好的关系。
But one thing at a time. I wanted to point out to you that very often functions that you see in real life satisfy many nice relations between the partial derivatives.
现在它成了一个只关于a和θ的函数，我知道保持a恒定不变,关于θ的偏导数是什么，我知道这怎么做。
Well, now that it's only a function of a and theta, I know what it means to take the partial derivative with respect to theta, keeping a constant. I know how to do it.
例如我们有一个三元函数，它的梯度向量的分量就是那些偏导数。
For example, if we have a function of three variables, the vector whose components are the partial derivatives.
现在可以看到，全微分里面的这些偏导数系数,都可以用一个变量表示出来。
Now you see how the total differential accounts for, somehow, all the partial derivatives that come as coefficients of the individual variables in these expressions.
然而，画图的工具是一样的，偏导数，梯度和向量，等等，我们所学习的这些工具,在处理任意变量的函数都是适用的。
But, the tools are the same, the notion of partial derivatives, grade and vector, and so on, all the tools that we will develop work exactly the same way no matter how many variables you have.
来看一个非常简单的情形,即在水平面上，不变，函数恒定，，z，equals，constant，，the，function，is，just，a，constant，偏导数变为。
Actually, if we look at a very easy case where this is just a horizontal plane, z 0 well, the partial derivatives become just zero.
我们首先要做的事是,求偏导数，fx是多少？
What we would start doing immediately is taking the partial derivatives. What is f sub x?
,在一个没有限制的最小值或者最大值，偏导数都是0，而在我们现在讨论的时候，偏导数只有在固定的方向上才是。
In this case, 0 derivatives are zero only in the allowed directions.
这很简单，然后我们得到了偏导数，关于a的偏导数，formal，partial，derivative，，of，A，with，respect，to,在这种情形下，a的变化率。
So, that's pretty easy. Plus, then we have the partial derivative, A little a times the rate of change of a in our situation.
这意味着,当我们对吉布斯自由能求它的变量,的偏导数的时候,我们会得到我们以前学过的东西。
So this means that they were taking the derivatives of the Gibbs free energy with respect to one of its variables is something that we should know.
你可以想象一下对它们继续求偏导数,将会得到很多偏导数，所以我们要,仔细考虑那时的情形。
You can imagine that if you keep taking partials you may end up with more and more, so we will have to figure out carefully what the condition should be.
对于任意两分量，混合偏导数相等。
For every pair of components the mixed partials must be the same.
对三个热力学偏导数等于系统化学势给出了又一种证明方法。
Another method for proving the three thermodynamical partial derivatives equaling chemical potential is given.
那么dx和dy前面的系数就是偏导数。
OK, and so the coefficients of dx and dy are the partials.
选择任意两个分量，假定是x和，你得到fx对z的偏导数，对x的偏导数，the，partial，of，the，z，component，with，respect，to，x,让它们相等，对于任意一对变量做同样的事情。
z You pick any two components, say the x and the z component, and you take the partial of the x component with respect to z, fz and you must make them equal. And the same with every pair of variables.
首先考虑第一个分量，求出它关于x的偏导数。
Ry-Qz Well, so we have to take the first component,Ry minus Qz, and take its partial with respect to x.
反演过程不需要提供初始模型，在首次迭代时使用一均匀介质地下模型作为初始模型，该模型的视电阻率偏导数值可以用解析法得到。
In the first iteration, a homogeneous earth model is used as the starting model. Its apparent resistivity partial derivative values can be calculated analytically.
本文利用一条等熵参考线和两个等焓偏导数建立了火箭发动机性能参数的外推公式。
In this paper, the extrapolation formulas of rocket engine performance parameters are established utilizing one isentropic reference line and two partial derivatives for fixed enthalpy.
介绍一种基于数表插值的水蒸汽密度及其偏导数的综合函数生成方法。
A combined method to generate functions of water and steam density and its partial derivatives is described in this paper.
该文的方法适用于求取较为简单的二维逆Z变换问题，尤以偏导数法和逆卷积法更具实际意义。
So the methods given in this paper can be used to get some simple inverse Z transform. The partial derivative method and deconvolution method are of practical use.
本文建立了多元复合函数的二阶偏导数公式。
In this paper, the formula of partial derivative of second order on compound function of many varables is established.
第三部分讨论最高阶偏导数项具有时滞的变分不等式的最优控制问题。
Finally in the third part, we study the optimal control problems for the variational inequality with delays in the highest order spatial derivatives.
本文根据海洋结构物的物面对称性，在有限水深复合格林函数表达式的基础上推导出了格林函数偏导数的数值计算表达式，并对格林函数的奇异性进行了分析。
The numerical expressions of the derivative of finite water-depth composite Green function were deducted based on the symmetrical surface of ocean structures, and the singularities were analyzed.
该滤波器采用有限差分法计算非线性函数的偏导数，扩大其应用范围。
The filter uses finite-difference method to calculate partial derivatives of nonlinear functions to enlarge its application scope.
多元函数的偏导数；
Multi-function partial derivative;
我现在所要做的一切就是，考察自由能对，温度，体积和压强的偏导数。
So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
对于数学分析教材中所讲到的求解多元函数的偏导数的方法，大家都很熟悉，但是在遇到比较复杂的函数形式时，求偏导数的复杂程度也会随着增加。
We are familiar with the algorithm of the partial derivatives from the calculus. But the algorithm will become more complicated when the function is more complicated.
对于数学分析教材中所讲到的求解多元函数的偏导数的方法，大家都很熟悉，但是在遇到比较复杂的函数形式时，求偏导数的复杂程度也会随着增加。
We are familiar with the algorithm of the partial derivatives from the calculus. But the algorithm will become more complicated when the function is more complicated.
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感谢您的反馈，我们会尽快进行适当修改！在高阶混合偏导数中，我把第一个和第二个求出来了，怎么样求第三个图的混合偏导数？_百度知道
在高阶混合偏导数中，我把第一个和第二个求出来了，怎么样求第三个图的混合偏导数？
有具体题目吗？我可以给你讲解，这个东西比较抽象。第三个图的意思就是先求Z对Y的偏导再求Z对X的偏导。
嗯，比如说，题目是 z=arctan x/y,求它的混合偏导数。求解答，谢谢！
可是我们的教科书上的答案和你做的不一样啊……
是吗？答案怎么写的呢？最好有图片~呃，原来是这样，我懂了，我看错了，我以为那个arctan（x/y)是arctanx/y同学你忘记加括号了.......
不好意思啊……
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