In fact, the problem with relativity wasn't that it involved a lot of differential equations, Lorentz transformations, and other complicated mathematics (though it did-even Einstein needed help with some of it), but that it was just so thoroughly nonintuitive.

实际上，相对论的问题并在于它涉及许多微方程、洛伦兹变换和其他复杂的数学（虽然它确实涉及——有的方面连爱因斯坦也需要别人帮忙），而是在于它是凭直觉所能完全搞懂的。

In this degree, you're gonna have to go through calculus one, calculus two, calculus three, differential equations, a lot of math.

在获取学位的过程中，必须学习微积一，微积二，微积三，微方程，要学习大量的数学知识。

I discover that I'm not very good at geometry, but also that I excel in differential equations.

我发现我长几何，但我长微方程。

You know, it was the old quantum mechanics, solving partial differential equations.

知道，这是旧的量子力学，求解偏微方程。

And so essentially I've got a function here to describe the differential equation.

这里我有一个函数来描述这个微方程。

So all of those things usually center on solving the three-dimensional partial differential equations.

因此，所有这些工作通常都围绕着求解三维偏微方程展开。

But to know the two things in physics to solve a partial differential equation are the initial conditions and the boundary conditions.

但要知道在物理学中求解偏微方程所需的两个要素是初始条件和边界条件。

I saw the differential equations you listed, and I don't think an analytical solution is possible, only a numerical one.

我看了列出的微方程，我认为可能有解析解，只能有数值解。

Then you see that the principle of least action works whenever this differential equation is satisfied.

然后会发现，只要满足这个微方程，最小作用原理就会起作用。

They're not into complex differential equations.

他们长复杂的微方程。

It's a core construct in the theory of probability, they're used a lot in solving differential equations and one context where you've almost certainly seen it if not by this name is multiplying to polynomials together.

它是概率论中的一个核心概念，在求解微方程时经常被使用， 而且如果是通过这个名字来认识它的话， 几乎肯定在多项式的乘法中见过它。

I think I'm stuck in some classical mindset where, to me, the local picture, the differential equation way of thinking about the universe, that that's really what's going on.

- 我想我陷入了一些古典的思维模式，对我而言，局部的图像、用微方程思考宇宙的方式才是真正发生的事情。

And you can change the parameters in there to get different behaviors and stuff, but it's all based on now it's one differential equation that you need to solve.

可以调整其中的参数以获得同的行为和效果，但这一切都基于现在只需解一个微方程。

This system will then be able to carry out the calculations we need and work out those differential equations for predicting the suns' movements.

这个系统将能够执行我们需要的计算，并解决那些用于预测阳运动的微方程。

Using the corrected reaction coefficient of the foundation bed, the differential equation of tunnel deformation was established, and the longitudinal displacement matrix of the tunnel was calculated using the finite difference method.

利用修正后的基床反作用系数，建立隧道变形微方程，采用有限差法计算隧道纵向位移矩阵。

So it matches or tries to imitate what applications do in solving that three-dimensional partial differential equation.

因此，它匹配或试图模仿应用程序在求解三维偏微方程时所执行的操作。

Like I didn't have an ordinary differential equation solver I could just call.

就像我没有一个可以直接调用的常微方程求解器。

What you want to do for the math underlying this is to basically feed some software, a differential equation and an initial condition and just say, how does this initial condition evolve?

想要做的就是给一些软件输入一个微方程和初始条件，然后问，这个初始条件会如何演变？

An ordinary differential equation for the longitudinal deformation of an existing tunnel subjected to ground surcharge was established, and the analytical solution of the longitudinal deformation was obtained.

建立了地基附加作用下既有隧道纵向变形的常微方程，得到了纵向变形的解析解。

There are so many applications for FFTs from solving differential equations to radar and sonar, studying crystal structures, WiFi and 5G.

FFT 的应用非常广泛，从求解微方程到雷达和声纳、研究晶体结构、WiFi 和 5G。