For the equations course, I was given a set of unpublished lectures that emphasized existence proofs and uniqueness of solutions to differential equations.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。
Mathematical equations, from simple algebraic ones to the more challenging differential equations, have allowed us to summarize an enormous amount of physical phenomena into a simple format.
数学方程，从简单的代数式到富有挑战性的困难的微分方程，这些简洁的模式都允许我们把一个巨大的物理现象纳入其中。
Ok, we've also seen how to look at equations of lines, and those were of a slightly different nature because we've been doing them as parametric equations.
我们还学过怎样理解直线方程，它们有些特性，因为我们是从参数方程角度理解。
So let's start with a case when we have some number of the equations say n equations and n unknown.
所以让我们从一个例子入手，当我们有一些方程式，假定n个方程，n个未知数。
Slide-shows original equations, then equations re-written as vector analysis, then using the symmetry of special relativity.
麦克斯韦方程组用矢量的形式重新表示，并利用狭义相对论你的对称性。
As for the white board equations in the background that have become a staple of each weekly episode, Saltzberg provided classic diagrams and equations describing magnetic monopoles.
至于背景中白色写字板上的那些公式，已经成为每周新的一集的主要部分，Saltzberg提供了描述磁单极子的经典图像和方程。
There are no mathematical equations in the book (possibly because the 137 pages don't quite allow enough room to fully explain Einstein's equations).
书里面没有数学公式(也许是因为受到137页的篇幅的限制，不能完全解释爱因斯坦的等式)。
Equations are of very great use. We can use equations in many mathematical problems.
方程很有用，可以用它来解决许多实际应用问题。
After solving the system of linear algebraic equations, another problem is induced that requires revising this coefficient matrix in order to get a new system of equations.
在线性代数方程组已解出之后，另一个课题需要修改它的系数矩阵，从而得到一个新的方程组。
In the analysis of very complex systems, the governing equations for the system components form a large set of simultaneous equations.
在非常复杂的系统的分析中，系统组件的控制方程是由一个大的联立方程形成的。
In design of pulsed asynchronous sequential circuits, it will solve for equations of clock and equations of state, on a symbolic Karnaugh map.
在异步时序电路设计中，它将时钟方程和状态方程的求解归在统一的符号卡诺图上进行。
Such equations are deemed to have important application in general ship dynamics and a theorem is established to facilitate the derivation of the equations.
相信一般的船舶动力学中这些方程会有重要的应用。本文建立了一个定理以便于推导这一方程。
The characteristic equations of the two equations are identical.
两方程对应的特征方程是恒等的。
Euler equations of generalized Riemann variable are derived from unsteady primitive variable Euler equations and solved by using two - a point-two-step upwind finite difference method.
该方法将原参数非定常欧拉方程组重新组合成以广义黎曼变量表示的欧拉方程组，再用二点二步迎风格式离散求解。
The coupled boundary integral equations and their reduced forms are deduced for hybrid mode problems, and these equations are discreted into a system of linear algebraic equations by moment method.
导出了关于混合模的耦合边界积分方程组及其退化形式，并用矩量法将之离散为齐次代数方程组，从而得波导的混合模传输常数；
Shallow water waves. Derivation of the equations. Linearization and solution. Radiation conditions. More on characteristics and shocks, now for all Shallow water equations.
浅水波。方程的导出。线性化及其解。辐射过程。所有浅水波方程的特征曲线和激波。
Convergence reliability, computational cost and applicability of different algorithms were compared by testing several classical equations of nonlinear equations.
选择了几个典型非线性方程组，从收敛可靠性、计算成本和适用性等指标分析对比了不同算法。
The equations are extra nonlinear differential equations. the dexter function is not continuous in field of real number .
该方程右边的函数在实数域内不连续，是一个高度非线性微分方程组。
The model includes three parts: equations of the motion for the parachute-store system, equations of the motion for the wake, equations of the momentum transfer between parachute and wake.
建立的尾流再附动力学模型包括：伞系统运动方程、尾流运动方程、伞衣-尾流动量交换方程。
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.
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。
For both simple and complex faults, all voltage equations can be converted to branch voltage equations.
无论是简单故障还是复故障，均可以支路为基础列写电压方程。
These equations are interval linear equations.
该控制方程是线性区间方程组。
Objective :In this study , regression equations (prediction equations) were established for the purpose of accurately predicting the mesiodistal widths of the crowns of unerupted lateral incisors .
目的：建立在混合牙列早期预测恒侧切牙牙冠及恒侧切牙至第二前磨牙冠宽和的回归方程。
We considered the finite volume element methods (FVM) based on circumcenter dual subdivision for the elliptic equations and parabolic equations.
考虑基于外心对偶剖分的椭圆型与抛物型方程的有限体积元法。
The ballistic limit equations, design equations, and application techniques applicable for the multilayer shock shield were summarized from the view of engineering application.
从工程应用角度，总结了适合于多层冲击防护结构的弹道极限方程、设计方程和应用技术。
The boundary value problem of ordinary differential equations is an important domain in differential equations.
常微分方程的边值问题是微分方程的一个重要研究领域。
Utilizing principle of potential energy to obtain governing differential equations, to turn differential equations into state equations by means of state space method.
用最小势能原理得到控制微分方程组，采用状态空间法将微分方程化为状态方程。
Utilizing principle of potential energy to obtain governing differential equations, to turn differential equations into state equations by means of state space method.
用最小势能原理得到控制微分方程组，采用状态空间法将微分方程化为状态方程。
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