## 计算机代写|计算机图形学代写computer graphics代考|CS4600

2022年12月24日

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

The explicit equation
$$y=3 x^2+2 x+4$$
tells us that the value of $y$ depends on the value of $x$, and not the other way around. For example, when $x=1, y=9$; and when $x=2, y=20$. As $y$ depends upon the value of $x$, it is called the dependent variable; and as $x$ is independent of $y$, it is called the independent variable.
We can also say that $y$ is a function of $x$, which can be written as
$$y=f(x)$$
where the letter ‘ $f$ ‘ is the name of the function, and the independent variable is enclosed in brackets. We could have also written $y=g(x), y=h(x)$, etc.

Eventually, we have to identify the nature of the function, which in this case is
$$f(x)=3 x^2+2 x+4 .$$
Nothing prevents us from writing
$$y=f(x)=3 x^2+2 x+4$$
which means: $y$ equals the value of the function $f(x)$, which is determined by the independent variable $x$ using the expression $3 x^2+2 x+4$.

An equation may involve more than one independent variable, such as the volume of a cylinder:
$$V=\pi r^2 h$$
where $r$ is the radius, and $h$, the height, and is written:
$$V(r, h)=\pi r^2 h .$$

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

An interval is a continuous range of numerical values associated with a variable, which can include or exclude the upper and lower values. For example, a variable such as $x$ is often subject to inequalities like $x \geq a$ and $x \leq b$, which can also be written as
$$a \leq x \leq b$$
and implies that $x$ is located in the closed interval $[a, b]$, where the square brackets indicate that the interval includes $a$ and $b$. For example,
$$1 \leq x \leq 10$$
means that $x$ is located in the closed interval $[1,10]$, which includes 1 and 10 .
When the boundaries of the interval are not included, then we would state $x>a$ and $x<b$, which is written
$$a<x<b$$
and means that $x$ is located in the open interval $] a, b[$, where the reverse square brackets indicate that the interval excludes $a$ and $b$. For example,
$$1<x<10$$
means that $x$ is located in the open interval ]1, 10[, which excludes 1 and 10 .

Closed and open intervals may be combined as follows. If $x \geq a$ and $x<b$ then
$$a \leq x<b$$
and means that $x$ is located in the half-open interval $[a, b[$. For example,
$$1 \leq x<10$$
means that $x$ is located in the half-open interval $[1,10[$, which includes 1 , but not 10 . Similarly, if
$$1<x \leq 10$$
means that $x$ is located in the half-open interval ]1, 10], which includes 10 , but not 1 .
An alternative notation employs parentheses instead of reversed brackets:
\begin{aligned} &] a, b[=(a, b) \ &{[a, b[=[a, b)} \ &] a, b]=(a, b] . \end{aligned}
Figure $3.5$ shows open, closed and half-open intervals diagrammatically.

# 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 Notation

$$y=3 x^2+2 x+4$$

$$y=f(x)$$

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

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

$$V=\pi r^2 h$$

$$V(r, h)=\pi r^2 h$$

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

$$a \leq x \leq b$$

$$1 \leq x \leq 10$$

$$a<x<b$$

$$1<x<10$$

$$a \leq x<b$$

$$1 \leq x<10$$

$$1<x \leq 10$$

$$] a, b[=(a, b) \quad[a, b[=[a, b)] a, b]=(a, b]$$

## 有限元方法代写

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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。