### 数学代写|微积分代写Calculus代写|Algebra Review

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|微积分代写Calculus代写|Algebra Review

A line has one dimension. Lengths or distances are one-dimensional units. We describe the length of a board or the length of a race using units such as feet (ft) or meters (m). A measuring tape used to find lengths or distances is a physical number line. Locations on roads are marked with mile or kilometer markers that essentially turn the road into a physical number line.
A plane has two dimensions. Areas are two-dimensional units. One dimension-a length or distance-is inadequate to describe the size of a field. A rectangular field that is $1 \mathrm{~km}$ long and $100 \mathrm{~m}$ wide is not as large as a rectangular field that is $1 \mathrm{~km}$ long and $1 \mathrm{~km}$ wide; saying that a field is $1 \mathrm{~km}$ long is not a complete description. Areas are given in square units, such as square feet $\left(\mathrm{ft}^{2}\right.$ ) or square kilometers $\left(\mathrm{km}^{2}\right)$. Locations in a plane (or other two-dimensional surface, such as the surface of the earth) are given using two values. We may say “go 1 mile east and 2 miles north” or give a location’s longitude and latitude. Instead of a number line, we need a coordinate plane.

Space has three dimensions. Volumes are three-dimensional units. The same truckload of dirt could be spread thinly over an entire acre or dumped in a pile; neither length nor area gives an adequate description of its size. To say that a rectangular storage bin is $2 \mathrm{~m}$ wide and $1 \mathrm{~m}$ long does not indicate its capacity, for such a bin could be $20 \mathrm{~cm}$ high or it could be $4 \mathrm{~m}$ high. Volumes are measured in cubic units, such as cubic inches $\left(\mathrm{in}^{3}\right.$ ) or cubic meters $\left(\mathrm{m}^{3}\right)$. Locations in space require three values. An airplane’s location is described not just by latitude and longitude, but by altitude as well. Instead of a number line or a coordinate plane, we need a three-dimensional coordinate system.
In the previous section we reviewed one-dimensional algebra using number lines. In this section we review two-dimensional algebra using coordinate planes. Three-dimensional coordinate systems are discussed later in calculus.

## 数学代写|微积分代写Calculus代写|Coordinate plane

One way to describe the location of a point in a plane, which has two dimensions, is to use two number lines placed perpendicularly. We call the horizontal number line the $x$-axis (positive coordinates to the right, negative to the left) and the vertical number line the $y$-axis (positive coordinates up, negative coordinates down), with the axes intersecting at their zero points. We call that intersection the origin. See figure $1 .$

The axes partition the plane into four regions, called quadrants, numbered as in figure 1 . The location of a point is given by the $x$ – and $y$-coordinates. The $x$-coordinate of a point is the number on the $x-$ axis for which the point aligns vertically; the $y$-coordinate of a point is the number on the $y$-axis for which the point aligns horizontally. See figure 2. The coordinates are denoted by a pair of numbers in parentheses, separated by a comma, with the first number being the $x$-coordinate and the second number, the $y$-coordinate. This plane is called the $x y$-plane, the coordinate plane, or the Cartesian plane (in honor of René Descartes). These coordinates are sometimes called rectangular coordinates.

To plot a point means to identify and mark its location in the $x y-$ plane.

## 数学代写|微积分代写Calculus代写|Graphs of equations

The word graph is used as both a noun and a verb. As a noun, it represents a set of points. For instance, the graph of the equation $y=x^{2}-4$ is the set of points
$$\left{(x, y) \mid y=x^{2}-4\right}$$
As a verb, graph means to produce a picture of the graph (the set of points). This picture is also referred to as the graph of the equation. One method of producing such a picture is to plot a few points that are on the graph and connect them as appropriate.
Example 2 Graph the equation $y=x^{2}-4$.
Solution We begin by calculating points to plot. We choose values of the variable $x$ (the independent variable, so called because its values are chosen independently of any other variable) and then use the equation to determine the corresponding value of the variable $y$ (the dependent variable, so called because its value depends on the value of $x$. The values of $x$ and $y$ are the $x$ – and $y$-coordinates of the points to be plotted. We choose the values $x=-3, \ldots, 3$, as shown in Table 1 .

## 数学代写|微积分代写Calculus代写|Graphs of equations

\left{(x, y) \mid y=x^{2}-4\right}\left{(x, y) \mid y=x^{2}-4\right}

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## 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。