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。
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。
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。
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。
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。
So now you have two equations.
所以现在有俩等式。
别看方程。
Couple of differential equations.
几个微分方程。
For him, equations were beautiful.
对他来说，方程才是最美的。
所以如果我有两个方程。
The equations are basically the same.
等式也基本是相同的。
Those are the equations we have to solve.
这就是我们要解的方程组。
What if these equations are slightly off?
如果这些方程稍微偏离一点会怎么样呢？
The equations have the same equation form.
方程式的形式相同。
So take an example: 2 equations 2 unknowns.
所以，让我们来举一个例子：两个方程两个未知数。
I am not going to write parametric equations.
我不准备写参数方程。
Ok, can I move to 3 equations and 3 unknowns?
好了，我能够转向三个方程三个未知数了么？
Electricity and Magnetism: Maxwell's equations.
电与磁：麦克斯韦方程组。
And, we know what equations of planes look like.
我们已经知道了平面方程是怎样的。
You don't have to write everything in equations.
你没有必要把所有东西都写成方程式。
The equations that you get are very complicated.
你得到的方程会极其复杂。
All it could do, though, was solve those equations.
它所能做的就是解决这些方程组问题。
Now we try to apply our Lagrange multiplier equations.
现在我们来用拉格朗日乘数法方程。
But matrices can also represent mathematical equations.
然而，矩阵也同样能够用来表示数学方程。
In your equations, it's the same thermodynamic picture.
在方程里面，基本是相同的热力学图像。
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。
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。
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