• 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

In various parts of this text, we will need the sum of large numbers of terms. Sometimes we will need the actual total, and then we will have to sum the numbers physically. Other times, however, we will only need to indicate the appropriate sum. An example is a statement, “Yearly expenditures are the sum of weekly expenditures.” Here we are not explicitly calculating the total yearly expenditure but simply indicating that it is the sum of 52 numbers. In cases like this, there is a useful mathematical notation for indicating the appropriate sum.

Consider the case of a teacher who has a list of seven grades and wants their sum. If we denote the first grade as $G_{1}$, the second grade as $G_{2}$, and so on through the seventh grade, which we denote as $G_{7}$, the final sum can be given as
$$\text { Sum }=G_{1}+G_{2}+G_{3}+G_{4}+G_{5}+G_{6}+G_{7}$$
Of course, if we had 52 items to add as opposed to only 7 , writing an expression similar to Equation $1.7$ would be tedious indeed. A more convenient way to represent the right side of Equation $1.7$ symbolically as
$$\sum_{i=1}^{7} G_{i}$$
The capital Greek letter sigma $(\Sigma)$ denotes a sum. The term(s) after the sigma, in this case, the letter $G$, tells us what values are to be added, in this case, we are adding $G$ terms.

The quantity $i=1$ at the bottom of the sigma indicates where the sum is to start from; in this case, the sum starts with $G_{1}$, that is, $G_{i}$, with $i$ replaced with the starting value of 1 . The number at the top of the sigma indicates where the sum is to stop, which in this case is $G_{7}$. Intermediate values in the sum are obtained by replacing the subscript $i$ on individual $G$ terms with consecutive integers between the starting and ending numbers at the bottom and top of the sigma, respectively.
For example, the notation
$$\sum_{i=3}^{8} S_{i}$$
indicates a sum of $S$ terms. The sum starts with $S_{3}$, because the starting $i$ value is given as 3 at the bottom of the sigma sign, and ends at $S_{5}$, because the ending value of $i$ is given as 8 above the sigma sign. Thus, the notation
$$\sum_{i=3}^{s} S_{i}$$
is shorthand for
$$S_{3}+S_{4}+S_{5}+S_{6}+S_{7}+S_{8}$$

## 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。