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# 数学代写|微积分代写Calculus代考|Differentiation

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## 数学代写|微积分代写Calculus代考|Differentiation

Differentiation is the first big idea in calculus. It’s the process of finding a derivative of a curve. And a derivative is just the fancy calculus term for a curve’s slope or steepness.
In algebra, you learned the slope of a line is equal to the ratio of the rise to the run. In other words, Slop $=\frac{\text { rise }}{\text { run }}$. In Figure 1-4, the rise is half as long as the run, so segment $A B$ has a slope of $1 / 2$. On a curve, the slope is constantly changing, so you need calculus to determine its slope.
The slope of segment $A B$ is the same at every point from A to $B$. But the steepness of the curve is changing between A and B. At A, the curve is less steep than the segment, and at $B$ the curve is steeper than the segment. So what do you do if you want the exact slope at, say, point C? You just zoom in. See Figure 1-5.
When you zoom in far enough – actually infinitely far – the little piece of the curve becomes straight, and you can figure the slope the old-fashioned way. That’s how differentiation works.
Integration, the second big idea in calculus, is basically just fancy addition. Integration is the process of cutting up an area into tiny sections, figuring out their areas, and then adding them up to get the whole area. Figure 1-6 shows two area problems – one that you can do with geometry and one where you need calculus.
The shaded area on the left is a simple rectangle, so its area, of course, equals length times width. But you can’t figure the area on the right with regular geometry because there’s no area formula for this funny shape. So what do you do? Why, zoom in, of course. Figure 1-7 shows the top portion of a narrow strip of the weird shape blown up to several times its size.

## 数学代写|微积分代写Calculus代考|Why Calculus Works

The mathematics of calculus works because curves are locally straight; in other words, they’re straight at the microscopic level. The earth is round, but to us it looks flat because we’re sort of at the microscopic level when compared to the size of the earth. Calculus works because when you zoom in and curves become straight, you can use regular algebra and geometry with them. This zooming-in process is achieved through the mathematics of limits.
Limits: Math microscopes
The mathematics of limits is the microscope that zooms in on a curve. Say you want the exact slope or steepness of the parabola $y=x^2$ at the point $(1,1)$. See Figure $1-8$.

With the slope formula from algebra, you can figure the slope of the line between $(1,1)$ and $(2,4)$ – you go over 1 and up 3 , so the slope is $3 / 1$, or 3 . But you can see in Figure 1-8 that this line is steeper than the tangent line at $(1,1)$ that shows the parabola’s steepness at that specific point. The limit process sort of lets you slide the point that starts at $(2,4)$ down toward $(1,1)$ till it’s a thousandth of an inch away, then a millionth, then a billionth, and so on down to the microscopic level. If you do the math, the slopes between $(1,1)$ and your moving point would look something like 2.001, 2.000001, 2.000000001, and so on. And with the almost magical mathematics of limits, you can conclude that the slope at $(1,1)$ is precisely 2 , even though the sliding point never reaches $(1,1)$. (If it did, you’d only have one point left and you need two separate points to use the slope formula.) The mathematics of limits is all based on this zooming-in process, and it works, again, because the further you zoom in, the straighter the curve gets.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。