再说明一下，这是关于这两个向量场，多少有点奇怪的偏微分方程。
And just to tell you again that is a strange partial differential equation relating these two vector fields.
这个是符号化的向量算子，其中它的分量是偏微分算子。
That was this symbolic vector operator in which the components are the partial derivative operators.
对你们来说这可能很让人头疼，就像你们在5。60里体验过的那样，这有很多偏微分和变量。
This should be particularly bothersome to you because, as you've already experienced in 5.60, There are a lot of partial derivatives.
总的来讲，所有你想解决的问题，都可以用偏微分方程来做。
Basically, to every problem you might want to consider there is a partial differential equation to solve.
然后，可以用微分关系,或受约束的偏微分来表示,曲线的切向量，就是这样了。
Then actually there are ways you can use basically differentials and constrained partials to figure out what the tangent vector to the curve is and so on.
这是一个，由电场e确定的偏微分方程。
It is a partial differential equation satisfied by the electric field e.
可以通过隐函数微分法和乘法法则得到，或者直接,把关于x，y，z的偏微分放进来。
You can get this either by implicit differentiation and the product rule, or you could get this just by putting here, here,and here the partial derivatives of this with respect to x, y, and z.
偏微分方程在科学和工程上有着广泛的应用。
Partial differential equation is widely used in problems of science and engineering.
区域分解算法是在并行机上求解偏微分方程数值解的一种方法。
The domain decomposition is a numerically approximating solution to partial differential equations on parallel computers.
现在，虽然这一切听起来很简单，在理论上，明显有相当数量的实际问题之前，必须克服偏微分方程的工作，可建。
Now while this all sounds pretty simple in theory, there are clearly quite a number of practical problems to be overcome before a working PDE can be built.
这将是对偏微分方程数值分析方法的新的重要尝试。
This is a important attempt for the numerical analysis methods of PDEs.
类似的方法还可以用在其它类型的偏微分方程数值解中。
Similar method may be applied in other types of partial differential equations.
你什么有效的偏微分方程做的是不断掀起一小负责高科技金属管内爆炸。
What you're effectively doing with a PDE is repeatedly setting off a small charge of hi-explosive inside a metal tube.
本文讨论了一类含奇异系数双曲偏微分方程柯西问题解的可微性与低阶项之间的关系。
The relationship between the differentiability of solution of Cauchy problem of weak—hyperbolic differential equationand its lower term is studied in this paper.
针对传统扩散模型中的边界模糊问题，提出一种基于非局部信息的非线性偏微分方程去噪模型。
A nonlinear partial differential equation model based on nonlocal information was proposed to remove noise and preserve the edges.
加州理工学院也纷纷发表自己的偏微分方程研究的一些优秀的信息。
CalTech have also published some excellent information on their own PDE research.
将小波配置法与广义能量积分相结合，提出了一种求解非线性偏微分方程的高精度数值方法。
A high accuracy algorithm for numerical solution of nonlinear partial differential equation (PDE) is suggested combining wavelet collocation method with generalized energy integral.
本文提出了用沃尔什级数求解高阶线性偏微分方程的一种新方法。
This paper proposes a new method of solving the high order linear partial differential equation by means of Walsh Series.
本文给出了一种高效率求解油气二次运移偏微分方程的方法。
An effective method for solving a partial differential equation of secondary hydrocarbon migration is put forward.
根据一阶拟线性偏微分方程组的特征理论，讨论内弹道两相流方程组的类型。
Following the theory on characteristics of first order quasi-linear partial differential equations, classification of the balance equations for two-phase flow in interior ballistics is discussed.
在物理学中，物理参量随时间的演化往往是由非线性的偏微分方程支配的。
In physics, the physical parameter evolution along with the time is often controlled by the non-linear partial differential equation.
自适应有限元方法是科学研究和工程设计领域中非常有效的一种求解偏微分方程的数值计算方法。
The adaptive finite element methods are very effective for solving partial differential equations in scientific researches and engineering designs.
根据曲线演化和水平集函数演化的思想，提出了一种基于偏微分方程的图像处理方法。
We propose a new image processing method based on PDE with the reference of curve and level-set function involution theories.
在本文中，考虑到传染病对宿主生物群体生长动力学的影响，对终身免疫型传染病的动力学建立了一个偏微分方程的模型。
In this paper, regarding the influence of infectious diseases on the dynamics of host population growth, a PDE model is established for the dynamics of infectious diseases with lifelong immunity.
本文证明了关于对称泛函临界点的一个定理并用以研究非线性椭园型偏微分方程的多重解。
In this paper we prove a theorem for the critical points of symmetric functionals through which we research the multiple solutions of nonlinear elliptic PDE.
并利用随机微分方程和偏微分方程之间的关系，对股票投资风险进行了估计，得到关于风险指标的动态轨线。
By using the relation between the stochastic, differential equations and the PDEs, we estimate the risk of investing stocks, and obtain the dynamic traces 'of risk functions.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
本文利用物理学中常见的热传导理论，形象地阐释了二阶齐次线性偏微分方程的本质。
With the ordinary theory of Heat Exchange in physics this essay visualizes the essence of second-order homogenous linear partial differential equations.
本文利用物理学中常见的热传导理论，形象地阐释了二阶齐次线性偏微分方程的本质。
With the ordinary theory of Heat Exchange in physics this essay visualizes the essence of second-order homogenous linear partial differential equations.
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