Einstein's equations showed the universe to be expanding.
爱因斯坦的方程式表明宇宙正在扩大。
You've got to juggle the two equations, multiply that by 4, multiply that by 3, add and subtract and so on.
你必须联立这两个方程，一个乘以4，另一个乘以3，再加减等等。
The method is that designing theory is simpleness and being understood is easy and avoiding complexity computation on state equations and drive equations.
该方法设计理论简单易懂，避免了状态方程和驱动方程的复杂计算。
Einstein discovered to his horror that Hilbert had taken what he had learned from Einstein's lectures and was racing to come up with the correct equations first.
爱因斯坦惊恐地发现，希尔伯特把他从爱因斯坦的讲座中学到的东西都拿来了，而且还在争先恐后地首先提出正确的方程式。
Computers cannot accurately predict climate change unless the mathematical equations fed into them adequately capture the natural meteorological processes they are intended to simulate.
计算机无法准确地预测气候变化，除非输入计算机的数学方程充分地捕捉它们想要模拟的自然气象过程。
In October 1915, Einstein threw himself into a month-long frantic endeavor in which he returned to an earlier mathematical strategy and wrestled with equations, proofs, corrections and updates.
在1915年的10月，爱因斯坦投身于长达一个月的疯狂工作中。在此期间，他回顾了早先的一个数学策略，并且与方程式、证明法、修正法、数据更新等展开了一番搏斗。
At the top of the list is the notion that intelligence is measured by your ability to solve complex problems; to read, write and compute at certain levels; and to resolve abstract equations quickly.
最重要的一点是，智力是通过你解决复杂问题的能力来衡量的；一定的读写和计算能力；能快速解出抽象方程。
Some movements involving primarily vertical or horizontal motions of the body as a whole, in which rotations can be ignored, can be studied using simple equations of linear motion in three dimensions.
有些运动主要涉及整体的垂直或水平运动，其中转动可以忽略，可以用三维线性运动的简单方程来研究。
He was struggling to find the right equations that would describe his new concept of gravity, ones that would define how objects move through space and how space is curved by objects.
他一直在努力寻找合适的方程来描述他的新引力概念，这些方程将定义物体如何在空间中移动，以及物体是如何扭曲空间的。
By 1545, Gerolamo Cardano compiled the works related to the quadratic equations.
到1545年，卡达诺编写了有关二次方程的著作。
Model CR118 has a Fraction to Decimal Conversion Chart and Trigonometric Ratio Equations etched on the front side.
CR118模型的正面刻有一个分数到十进制的转换图和三角比公式。
The equations looked familiar.
这些方程序看起来有些熟悉。
Couple of differential equations.
几个微分方程。
What if these equations are slightly off?
如果这些方程稍微偏离一点会怎么样呢？
I am not going to write parametric equations.
我不准备写参数方程。
Electricity and Magnetism: Maxwell's equations.
电与磁：麦克斯韦方程组。
Listing 7: Retrieving the homework 1 equations.
清单7：检索homework1等式。
Graphically sending equations and receiving answers.
图形式地发送方程序并接收答案。
Now we try to apply our Lagrange multiplier equations.
现在我们来用拉格朗日乘数法方程。
So they're solving the equations represent those laws.
它们实际在解这些定律的方程。
So they’re solving the equations represent those laws.
它们实际在解这些定律的方程。
But matrices can also represent mathematical equations.
然而，矩阵也同样能够用来表示数学方程。
Some of you may already have solved differential equations.
你们有些人也许已经，解出了微分方程。
OK, so if not, let's move on to linear parametric equations.
如果没有的话，我们继续往下，线性参数方程组。
So, today, we'll start by looking at the equations of lines.
今天我们要从学习直线方程开始。
In fact, parametric equations of lines always look like that.
实际上，直线的参数方程总是这个样子的。
You all, I'm sure you've all seen equations about equilibrium.
你们所有人，我相信，都见过了平衡态方程。
Parametric models are built from a set of mathematical equations.
参数的模型是从一组数学公式中被建造出来的。
OK, so we are going to learn about parametric equations of lines.
我们马上就要学习直线的参数方程。
Are there equations of 3d shapes that we should know at this point?
本节是否也有一些3维空间中的方程是我们需要了解的？
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