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.
第一种就是昨天讲的微分法，希望你们能明白，不明白也没关系，现在可以认真听一下。
Let me start with the one with differentials that hopefully you kind of understood yesterday, but if not here is a second chance.
要完全了解本课程，应必备微积分和微分方程的知识。
Calculus and Differential Equations are highly recommended for full understanding of the course.
相反，为了证明“红色效应”，我应该使用一张一个老男人用红笔求解微分方程系统的图像。
Instead, to demonstrate the "red effect" I should have used an image of an elderly man solving a system of differential equations using a red pen.
这种控制器的设计结合了微分几何理论及变结构控制理论。
Design of these controllers combines the differential geometry theory with the variable structure control theory.
因此，研究倒向随机微分方程具有重要的理论意义和应用价值。
Therefore, the research on backward stochastic differential equation is of considerable theoretical significance and practical value.
微分方程是一门表述自然法则的语言。
Differential Equations are the language in which the laws of nature are expressed.
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.
微分代数是带电粒子光学中新近出现的一个很有前途的数学工具。
Differential algebra is a new mathematical method and a promising tool in charged particle optics.
在这种方法中，我们可以在对常微分方程进行积分的过程中自由选择步长。
In this approach we have the freedom in the choice of step size during the integration of the ordinary differential equation.
在接下来的一年里我不得不上额外的几门课程，我选择在接下来的暑假修完近世代数和微分方程。
I had to take a few extra courses during the next year, and I chose reading courses in modern algebra and differential equations for the summer afterwards.
他记得30年前，华尔街的公司发现一些物理学家懂微分方程，于是乎招他们来，有做分析员的也有做交易员的。
Thirty years ago, he says, Wall Street firms realised that some physicists could work out differential equations and recruited them to become “quants”, analysts and traders.
所有中国人都应该为中国数学家在微分几何领域所取得的成就，和对庞加莱猜测的贡献而感到骄傲。
All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare conjecture.
自动微分(AD)技术以非标准分析为理论基础，是计算机数值计算领域中的一种很有前途的方法。
Automatic differentiation (AD), based on the nonstandard analysis theory, is a new technique in computer numerical analysis.
自动微分技术能以较低的成本精确计算中大规模问题函数的导数，在科学计算、工程计算及其应用领域中有着广泛的应用。
Automatic differentiation, by which the derivatives of the function can be evaluated both exactly and economically, is applied to the field of scientific and engineering computation extensively.
当你试图接住一个飞行中的球时，是否会通过解微分方程来确定自己的位置？
Do you position yourself to catch a ball by solving differential equations in your head, on the fly?
这个例子展示了lsode的用法，这是一个常见的微分方程解算器。
This example demonstrates the use of lsode, an ordinary differential equation solver.
然而，在确定所需DB 2许可数量时，需要理解和考虑微分区的优点。
However, you need to understand and account for the benefits of micro-partitioning when determining the number of DB2 licenses you need.
有限的微分区——t1上4个，t2上8个。
Limited micro-partitioning - Four partitions on T1, 8 on t2.
这是整个机理的完整的微分方程，不是它的一部分。
This is the full differential equation for the full mechanism. Not just one part of it.
微分区是一个强大的特性，它允许您最大效率地利用处理器资源。
Micro-partitioning is a powerful feature that allows you to leverage your processor resources with maximum efficiency.
我已经讨论了POWER5的一些虚拟化功能，其中包括微分区和Hypervisor。
I've discussed some of the virtualization features of POWER5, including Micro-Partitioning and the Hypervisor.
脚微微分开，伸展，双手和视线往上，看向天花板。在伸展的时候感觉到延伸的感觉并深深呼吸。
Feet slightly apart, reach and look up towards the ceiling with your arms and eyes. Feel the stretch and take in a deep breath as you reach up.
自动微分技术为带电粒子光学中的任意高阶像差分析与校正提供了一个很有效的工具。
It presents an effective and elegant tool for the analysis and correction of arbitrary order aberrations of charged particle optical systems.
这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。
The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.
运用不动点定理，研究一类具状态依赖时滞的微分方程周期正解的存在性。
By applying a fixed point theorem, the authors study the existence of positive periodic solutions to a class of differential equations with stated-dependent delay.
因为，如果这些收入或效用的增加可以化为无穷小，那我们既能使用符号表示，也能利用微分学强大的操作了。
For if these increases of income or utility are reduced to being infinitesimal, one can use both the symbolism and the powerful manipulations of the differential calculus.
在方程课上，我听了一系列未公开的演讲，强调的是微分方程的解的存在证明及其唯一性。
For the equations course, I was given a set of unpublished lectures that emphasized existence proofs and uniqueness of solutions to differential equations.
在方程课上，我听了一系列未公开的演讲，强调的是微分方程的解的存在证明及其唯一性。
For the equations course, I was given a set of unpublished lectures that emphasized existence proofs and uniqueness of solutions to differential equations.
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