## 计算机代写|计算机图形学代写computer graphics代考|COS426

2022年12月24日

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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
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## 计算机代写|计算机图形学代写computer graphics代考|Function Domains and Ranges

The following descriptions of domains and ranges only apply to functions with one independent variable: $f(x)$.
Returning to the above function:
$$y=f(x)=3 x^2+2 x+4$$
the independent variable $x$, can take on any value from $-\infty$ to $\infty$, which is called the domain of the function. In this case, the domain of $f(x)$ is the set of real numbers

$\mathbb{R}$. The notation used for intervals, is also used for domains, which in this case is
$$]-\infty, \infty[$$
and is open, as there are no precise values for $-\infty$ and $\infty$.
As the independent variable takes on different values from its domain, so the dependent variable, $y$ or $f(x)$, takes on different values from its range. Therefore, if the domain of the linear function $f(x)=3 x+4$ is $[-4,4]$, the range of $f(x)$ is calculated by finding $f(-4)$ and $f(4)$ :
$$\begin{gathered} f(-4)=-12+4=-8 \ f(4)=12+4=16 \end{gathered}$$
and the range is $[-4,4]$.
Although calculating the range of linear functions is simple, other types of functions require a knowledge of calculus.
The domain of $\log x$ is
$$] 0, \infty[$$
which is open, because $x \neq 0$. Whereas, the range of $\log x$ is
$$]-\infty, \infty[\text {. }$$
The domain of $\sqrt{x}$ is
$$[0, \infty[$$
which is half-open, because $\sqrt{0}=0$, and $\infty$ has no precise value.

## 计算机代写|计算机图形学代写computer graphics代考|Units of Angular Measurement

The measurement of angles is at the heart of trigonometry, and today two units of angular measurement are part of modern mathematics: degrees and radians. The degree (or sexagesimal) unit of measure derives from defining one complete rotation as $360^{\circ}$. Each degree divides into $60 \mathrm{~min}$, and each minute divides into $60 \mathrm{~s}$. The number 60 has survived from Mesopotamian days and appears rather incongruous when used alongside today’s decimal system-nevertheless, it is still convenient to work with degrees even though the radian is a natural feature of mathematics.
The radian of angular measure does not depend upon any arbitrary constant, and is often defined as the angle created by a circular arc whose length is equal to the circle’s radius. And because the perimeter of a circle is $2 \pi r, 2 \pi$ rad correspond to one complete rotation. As $360^{\circ}$ corresponds to $2 \pi \mathrm{rad}, 1 \mathrm{rad}$ equals $180^{\circ} / \pi$, which is approximately $57.3^{\circ}$. The following relationships between radians and degrees are worth remembering:
\begin{aligned} \frac{\pi}{2}[\mathrm{rad}] & \equiv 90^{\circ}, & \pi[\mathrm{rad}] \equiv 180^{\circ} \ \frac{3 \pi}{2}[\mathrm{rad}] & \equiv 270^{\circ}, & 2 \pi[\mathrm{rad}] \equiv 360^{\circ} . \end{aligned}
To convert $x^{\circ}$ to radians:
$$\frac{\pi x^{\circ}}{180}[\mathrm{rad}] .$$
To convert $x$ [rad] to degrees:
$$\frac{180 x}{\pi} \text { [degrees]. }$$
For those readers wishing to know the background to radians we need to use power series. We start with the power series for $\mathrm{e}^\theta, \sin \theta$ and $\cos \theta$ :
\begin{aligned} \mathrm{e}^\theta & =1+\frac{\theta^1}{1 !}+\frac{\theta^2}{2 !}+\frac{\theta^3}{3 !}+\frac{\theta^4}{4 !}+\frac{\theta^5}{5 !}+\frac{\theta^6}{6 !}+\frac{\theta^7}{7 !}+\frac{\theta^8}{8 !}+\frac{\theta^9}{9 !}+\cdots \ \sin \theta & =\theta-\frac{\theta^3}{3 !}+\frac{\theta^5}{5 !}-\frac{\theta^7}{7 !}+\frac{\theta^9}{9 !}+\cdots \ \cos \theta & =1-\frac{\theta^2}{2 !}+\frac{\theta^4}{4 !}-\frac{\theta^6}{6 !}+\frac{\theta^8}{8 !}+\cdots . \end{aligned}
Euler proved that these three power series are related, and when $\theta=\pi, \sin \theta=0$, and $\cos \theta=-1$. Figure $4.1$ shows curves of the sine power series for $3,5,7$ and 9 terms, and when $\theta=2 \pi$, the graph reaches zero.

# 计算机图形学代考

## 计算机代写|计算机图形学代写computer graphics代考|Function Domains and Ranges

$$y=f(x)=3 x^2+2 x+4$$

$\mathbb{R}$. 用于间隔的符号也用于域，在这种情况下是
$$]-\infty, \infty[$$

$$f(-4)=-12+4=-8 f(4)=12+4=16$$

$$] 0, \infty[$$

$$]-\infty, \infty[$$

$$[0, \infty[$$

## 计算机代写|计算机图形学代写computer graphics代考|Units of Angular Measurement

$$\frac{\pi}{2}[\mathrm{rad}] \equiv 90^{\circ}, \quad \pi[\mathrm{rad}] \equiv 180^{\circ} \frac{3 \pi}{2}[\mathrm{rad}] \equiv 270^{\circ}, \quad 2 \pi[\mathrm{rad}]$$

$$\frac{\pi x^{\circ}}{180}[\mathrm{rad}] .$$

$$\frac{180 x}{\pi} \text { [degrees]. }$$

$$\mathrm{e}^\theta=1+\frac{\theta^1}{1 !}+\frac{\theta^2}{2 !}+\frac{\theta^3}{3 !}+\frac{\theta^4}{4 !}+\frac{\theta^5}{5 !}+\frac{\theta^6}{6 !}+\frac{\theta^7}{7 !}+\frac{\theta^8}{8 !}+\frac{\theta^9}{9 !}+$$

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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。