### 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|UCASF3F5

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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

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Control Structures

The computation of the orbital velocity of Earth in the previous section is a very simple example for the implementation of a numerical algorithm in Python. ${ }^9$ It involves the following steps:

1. Initialisation of all data needed to perform the following computation.
2. An exactly defined sequence of computational rules (usually based on mathematical formulas), unambiguously producing a result in a finite number of steps given the input from step 1.
3. Output of the result.
In our example, the definition of the variables radius and period provides the input, the expression for the orbital velocity is a computational rule, and the result assigned to the variable velocity is printed as output.

A common generalization of this simple scheme is the repeated execution of the same computational rule in a sequence of steps, where the outcome of one step is used as input for the next step. This is called iteration and will be explained in the remainder of this section. The independent application of the same operations to multiple elements of data is important when working with arrays, which will be introduced in Chap. 2.

Iteration requires a control structure for repeating the execution of a block of statements a given number of times or until a certain condition is met and the iteration terminates. Such a structure is called a loop. For example, let us consider the problem of summing up the first 100 natural numbers (this is a special case of an arithmetic series, in which each term differs by the previous one by a constant):
$$s_n \equiv \sum_{k=1}^n k=1+2+3+\ldots+n$$ The keywords for and in indicate that the loop counter $\mathrm{k}$ runs through all integers defined by range $(1, n+1)$, which means the sequence $1,2,3, \ldots, n$ in mathematical notation. It is a potential source of confusion that Python includes the start value 1 , but excludes the stop value $n+1$ in range $(1, n+1) .{ }^{10}$

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Working with Modules and Objects

Python offers a collection of useful tools in the Python Standard Library (see docs.python.org/3/library). Functions such as print () are part of the Standard Library. They are called built-in functions. Apart from that, many more optional

libraries (also called packages) are available. Depending on the Python distribution you use, you will find that some libraries are included and can be imported as shown below, while you might need to install others. ${ }^{16}$ Python libraries have a hierarchical modular structure. This means that you do not necessarily have to load a complete library, but you can access some part of a library, which can be a module, a submodule (i.e. a module within a module) or even individual names defined in a module. To get started, it will be sufficient to consider a module as a collection of definitions. By importing a module, you can use variables, functions, and classes (see below) defined in the module.

For example, important physical constants and conversion factors are defined in the constants module of the SciPy library (for more information, see www.scipy.org/about.html). A module can be loaded with the import command:
|import scipy.constants
To view an alphabetically ordered list of all names defined in this module, you can invoke dir (scipy. constants) (this works only after a module is imported). By scrolling through the list, you might notice the entry ‘gravitational_constant’. As the name suggests, this is the gravitational constant $G$. Try
2 print(scipy.constants.gravitational_constant)
which displays the value of $G$ in SI units:
$$6.67408 e-11$$
The same value is obtained via scipy.constants.G. Even so, an identifier composed of a library name in conjunction with a module and a variable name is rather cumbersome to use in programs. Alternatively, a module can be accessed via an alias: also displays the value of $G$. Here, const is a user-defined nickname for scipy. constants.

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Control Structures

1. 初始化执行以下计算所需的所有数据。
2. 一个精确定义的计算规则序列（通常基于数学公式），在给定步骙 1 的输入的情况下，在有限的步 骤中明确地产生一个结果。
3. 结果的输出。
在我们的示例中，变量半径和周期的定义提供了输入，轨道速度的表达式是计算规则，分配给变量 速度的结果作为输出打印。
这个简单方案的一个常见概括是在一系列步㡜中重复执行相同的计算规则，其中一步的结果用作下一步的 输入。这称为迭代，将在本节的其余部分进行解释。在使用数组时，将相同的操作独立应用于多个数据元 素非常重要，这将在第 1 章中介绍。2.
迭代需要一个控制结构来重复执行一个语句块给定的次数，或者直到满足某个条件并且迭代终止。这样的 结构称为循环。例如，让我们考虑对前 100 个自然数求和的问题（这是算术级数的特例，其中每一项与 前一项相差一个常数）：
$$s_n \equiv \sum_{k=1}^n k=1+2+3+\ldots+n$$
for和in关键字表示循环计数器k遍历范围定义的所有整数 $(1, n+1)$ ，这意味着序列 $1,2,3, \ldots, n$ 在数 学符号中。Python 包括起始值 1 但不包括停止值，这是一个潜在的混洧来源 $n+1$ 在范围内 $(1, n+1){ }^{10}$

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Working with Modules and Objects

Python 在 Python 标准库中提供了一系列有用的工具 (请参阅 docs.python.org/3/library) 。print() 等 函数是标准库的一部分。它们被称为内置函数。除此之外还有很多可选的

| import scipy.constants

2 print(scipy.constants.gravitational_constant)

$$6.67408 e-11$$

## 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。