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数学代写|常微分方程代写ordinary differential equation代考|MATH3331

Posted on 2023年1月6日2023年1月6日 by statistics-lab

如果你也在怎样代写常微分方程ordinary differential equation这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

常微分方程是为一个或多个独立变量的函数及其导数定义的方程。y’=x+1是一个常微分方程的例子。

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我们提供的常微分方程ordinary differential equation及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

数学代写|常微分方程代写ordinary differential equation代考|MATH3331

数学代写|常微分方程代写ordinary differential equation代考|Separation of variables

Consider the ODE of the form
$$
\frac{d}{d x} y(x)=\frac{f(x)}{g(y(x))} .
$$
We assume that $f:\left(a_0, a_1\right) \rightarrow \mathbb{R}$ and $g:\left(b_0, b_1\right) \rightarrow(0, \infty)$ are continuous functions. Wè also assume that there exists $y_0$ in the interval $\left(b_0, b_1\right)$ such that
$$
g\left(y_0\right) \neq 0 .
$$
We define a function $F:\left(a_0, a_1\right) \times\left(b_0, b_1\right) \rightarrow \mathbb{R}$ by
$$
F(x, y)=\int_{y_0}^y g(\xi) d \xi-\int_{x_0}^x f(s) d s, x \in\left(a_0, a_1\right), y \in\left(b_0, b_1\right) .
$$
Since $f$ and $g$ are continuous, $F$ is a $C^1$-function. Moreover for every $x_0 \in$ $\left(a_0, a_1\right)$ we have
$$
\frac{\partial F}{\partial y}\left(x_0, y_0\right)=g\left(y_0\right) \neq 0 \text {. }
$$

Therefore by the implicit function theorem (see Appendix C) there exists $\delta>0$ and a $C^1$-function $\phi:\left(x_0-\delta, x_0+\delta\right) \rightarrow \mathbb{R}$ such that
$$
F(x, \phi(x))=\int_{y_0}^{\phi(x)} g(\xi) d \xi-\int_{x_0}^x f(s) d s=F\left(x_0, y_0\right), x \in\left(x_0-\delta, x_0+\delta\right) .
$$
One can easily prove that $\phi$ is a solution to (2.1). For, on differentiating (2.3) with respect to $x$ (using the Leibniz rule of differentiation ${ }^1$ ) we get
$$
\phi^{\prime}(x) g(\phi(x))-f(x)=0, x \in\left(x_0-\delta, x_0+\delta\right) .
$$
This proves that the function $\phi$ which is implicitly given by the relation $F(x, y)=F\left(x_0, y_0\right)$, is a solution to (2.1). In other words, the relation
$$
\int^y g(y) d y=\int^x f(x) d x+c, c \in \mathbb{R},
$$
where the above integrals are indefinite integrals, defines a solution to (2.1). We now present some examples where this technique is demonstrated.

数学代写|常微分方程代写ordinary differential equation代考|Exact cquations

In this subsection, we present another special form of differential equations called exact equations which can be solved easily. Let $M, N$ be continuous functions in a rectangle
$$
R=\left{(x, y):\left|x-x_0\right| \leq a,\left|y-y_0\right| \leq b\right},
$$
and $N$ does not vanish in $R$. An ODE of the form
$$
N(x, y(x)) y^{\prime}(x)+M(x, y(x))=0,
$$
is said to be exact if there exists a $C^1$-function $F: R \rightarrow \mathbb{R}$ such that
$$
\frac{\partial F}{\partial x}(x, y)=M(x, y), \quad \frac{\partial F}{\partial y}(x, y)=N(x, y),(x, y) \in R .
$$
Example 2.1.8. Show that $y(x) y^{\prime}(x)+x=0$ is an exact equation.
Solution. In order to prove this, we first compare the given equation with (2.18) to get $M(x, y)=x$ and $N(x, y)=y$. It is easy to verify that

$$
F(x, y)=\frac{x^2+y^2}{2},
$$
satisfies (2.19). Hence the given equation is exact.
We now establish the connection between $F$ and the solutions to (2.18). To this end, we suppose (2.18) is exact and $F$ is known to us. We observe that $\frac{\partial F}{\partial y}=N \neq 0$, in $R$. Let $(\tilde{x}, \tilde{y}) \in \mathbb{R}^2$ satisfy $\left|x_0-\tilde{x}\right|<a$ and $\left|y_0-\tilde{y}\right|<b$. Then by the implicit function theorem there exists an interval $(\tilde{x}-\delta, \tilde{x}+\delta)$, which is denoted by $J$, and a $C^1$-function $\phi: J \rightarrow \mathbb{R}$ such that
$$
F(x, \phi(x))=F(\tilde{x}, \tilde{y}), x \in J .
$$
Claim. The function $\phi$ is a solution to (2.18).
For, on differentiating (2.20) with respect to $x$ we get
$$
\frac{\partial F}{\partial x}(x, \phi(x))+\frac{\partial F}{\partial y}(x, \phi(x)) \phi^{\prime}(x)=0, x \in J .
$$
Thus we have
$$
M(x, \phi(x))+N(x, \phi(x)) \phi^{\prime}(x)=0, x \in J,
$$
which proves that $\phi$ is a solution to (2.18). Hence the claim is proved.
Now, we shall revisit Example 2.1.8 and solve the ODE therein.

常微分方程代写

数学代写|常微分方程代写ordinary differential equation代考|Separation of variables

考虑形式的 ODE
$$
\frac{d}{d x} y(x)=\frac{f(x)}{g(y(x))}
$$
我们假设 $f:\left(a_0, a_1\right) \rightarrow \mathbb{R}$ 和 $g:\left(b_0, b_1\right) \rightarrow(0, \infty)$ 是连续函数。我们还假设存在 $y_0$ 在区间 $\left(b_0, b_1\right)$ 这样
$$
g\left(y_0\right) \neq 0 .
$$
我们定义一个函数 $F:\left(a_0, a_1\right) \times\left(b_0, b_1\right) \rightarrow \mathbb{R}$ 经过
$$
F(x, y)=\int_{y_0}^y g(\xi) d \xi-\int_{x_0}^x f(s) d s, x \in\left(a_0, a_1\right), y \in\left(b_0, b_1\right) .
$$
自从 $f$ 和 $g$ 是连续的， $F$ 是一个 $C^1$-功能。此外对于每一个 $x_0 \in\left(a_0, a_1\right)$ 我们有
$$
\frac{\partial F}{\partial y}\left(x_0, y_0\right)=g\left(y_0\right) \neq 0 .
$$
因此根据隐函数定理 (见附录 C) 存在 $\delta>0$ 和一个 $C^1$-功能 $\phi:\left(x_0-\delta, x_0+\delta\right) \rightarrow \mathbb{R}$ 这样
$$
F(x, \phi(x))=\int_{y_0}^{\phi(x)} g(\xi) d \xi-\int_{x_0}^x f(s) d s=F\left(x_0, y_0\right), x \in\left(x_0-\delta, x_0+\delta\right)
$$
可以很容易地证明 $\phi$ 是 (2.1) 的解。因为，关于微分 (2.3) 关于 $x$ (使用莱布尼兹微分法则 ${ }^1$ ) 我们得到
$$
\phi^{\prime}(x) g(\phi(x))-f(x)=0, x \in\left(x_0-\delta, x_0+\delta\right) .
$$
这证明了函数 $\phi$ 这是由关系隐式给出的 $F(x, y)=F\left(x_0, y_0\right)$ ，是 (2.1) 的解。换句话说，关系
$$
\int^y g(y) d y=\int^x f(x) d x+c, c \in \mathbb{R}
$$
其中上述积分是不定积分，定义了 (2.1) 的解。我们现在提供一些演示此技术的示例。

数学代写|常微分方程代写ordinary differential equation代考|Exact cquations

在本小节中，我们介绍另一种特殊形式的微分方程，称为精确方程，它很容易求解。让 $M, N$ 是矩形内的连续函数
和 $N$ 不会消失 $R$. 形式的 $\mathrm{ODE}$
$$
N(x, y(x)) y^{\prime}(x)+M(x, y(x))=0,
$$
如果存在 $C^1$-功能 $F: R \rightarrow \mathbb{R}$ 这样
$$
\frac{\partial F}{\partial x}(x, y)=M(x, y), \quad \frac{\partial F}{\partial y}(x, y)=N(x, y),(x, y) \in R .
$$
示例 2.1.8。显示 $y(x) y^{\prime}(x)+x=0$ 是一个精确方程。
解决方案。为了证明这一点，我们首先将给定的方程与 (2.18) 进行比较得到 $M(x, y)=x$ 和 $N(x, y)=y$. 很容易验证
$$
F(x, y)=\frac{x^2+y^2}{2}
$$
满足 (2.19)。因此给定的方程是精确的。
我们现在建立之间的连接 $F$ 以及 (2.18) 的解。为此，我们假设 (2.18) 是精确的并且 $F$ 为我们所熟知。我们观察到 $\frac{\partial F}{\partial y}=N \neq 0$ ，在 $R$. 让 $(\tilde{x}, \tilde{y}) \in \mathbb{R}^2$ 满足 $\left|x_0-\tilde{x}\right|<a$ 和 $\left|y_0-\tilde{y}\right|<b$. 则由隐函数定理存在区间 $(\tilde{x}-\delta, \tilde{x}+\delta)$ ，表示为 $J$ ，和一个 $C^1$-功能 $\phi: J \rightarrow \mathbb{R}$ 这样
$$
F(x, \phi(x))=F(\tilde{x}, \tilde{y}), x \in J .
$$
宣称。功能 $\phi$ 是 (2.18) 的解。
因为，关于微分 $(2.20)$ 关于 $x$ 我们得到
$$
\frac{\partial F}{\partial x}(x, \phi(x))+\frac{\partial F}{\partial y}(x, \phi(x)) \phi^{\prime}(x)=0, x \in J .
$$
因此我们有
$$
M(x, \phi(x))+N(x, \phi(x)) \phi^{\prime}(x)=0, x \in J,
$$
这证明 $\phi$ 是 (2.18) 的解。因此，索赔得到证明。
现在，我们将重新审视示例 $2.1 .8$ 并求解其中的 ODE。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|常微分方程代写ordinary differential equation代考|MATH53

Posted on 2023年1月6日2023年1月6日 by statistics-lab

如果你也在怎样代写常微分方程ordinary differential equation这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

常微分方程是为一个或多个独立变量的函数及其导数定义的方程。y’=x+1是一个常微分方程的例子。

我们提供的常微分方程ordinary differential equation及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

数学代写|常微分方程代写ordinary differential equation代考|MATH53

数学代写|常微分方程代写ordinary differential equation代考|Ordinary differential equations

The term ‘equatio differentialis’ (differential equations) was first used by Leibniz in 1676 to denote a relationship between the differentials of two variables. Very soon, this restricted usage was abandoned. Roughly speaking, differential equations are the equations involving one or more dependent variables (unknowns) and their derivatives/partial derivatives. If the unknown in the differential equation is a function of only one variable, then such differential equation is called an ordinary differential equation (ODE).
Notation: Unless specified otherwise, the unknown in the differential equation is denoted by $y$. Let $\mathbb{R}$ denote the set of real numbers, and $J$ be an open interval in $\mathbb{R}$. Throughout the book we denote the derivative of the function $y: J \rightarrow \mathbb{R}$ with respect to $x$ by either
$$
\frac{d}{d x} y(x) \text { or } \frac{d y}{d x}(x) \text { or } y^{\prime}(x) .
$$
When there is no ambiguity regarding the argument in the function $y$, we denote the derivative simply with $\frac{d y}{d x}$ or $y^{\prime}$. Similarly, let $y^{\prime \prime}$ and $y^{\prime \prime \prime}$ denote the second and the third derivative of $y$, respectively. In general, for $k \in \mathbb{N}$, $y^{(k)}$ or $\frac{d^k y}{d x^k}$ denotes the $k$-th order derivative of $y$.
With this notation, examples of ODEs are
$$
\begin{gathered}
\frac{d}{d x} y(x)=\left(\frac{d^2}{d x^2} y(x)\right)^5+y^2(x), x \in(0,1), \
y^{\prime}=3 y^2+(\sin x) y+\log \left(\cos ^2 y\right), x \in \mathbb{R} .
\end{gathered}
$$
The order of an ODE is the largest number $k$ such that the $k$-th order derivative of the unknown is present in the ODE. For example, the order of (1.1) is two.
At the beginning, it may look like tools from the integral calculus are sufficient to study ODEs. But very soon one realizes that to develop methods to solve or analyze them, one needs notions from subjects like analysis, linear algebra, etc. In fact, the study of differential equations motivated crucial development of many areas of mathematics: the theory of Fourier series and more general orthogonal expansions, integral transformations, Hilbert spaces, and Lebesgue integration to name a few.

数学代写|常微分方程代写ordinary differential equation代考|Applications of ODEs

Many laws in physics, chemistry, biology etc., can be easily expressed using differential equations. One of the reasons for this is the following. The quantity $y^{\prime}(x)$ can be interpreted as the rate of change of the quantity $y$ with respect to the quantity $x$. In many natural phenomena, there is a relationship between the unknowns (which are relatively difficult to measure), the rate of change of the unknowns with respect to a known quantity, and the other known quantities (which are easy to measure) that govern the process. When this relationship is expressed in mathematics, it turns out to be a (system of) differential equation(s). Therefore the study of ODEs is crucial in understanding physical sciences. In fact, much of the theory developed in ODEs owes to the questions/situations raised in the study of subjects like mechanics, astronomy, electronics etc.
Listing all the available ODE models in any branch of science is an impossible task. Therefore in this chapter, we present a few ODE models which arise from physics and biology which can be solved or analyzed using the material in the book. We begin with models from physics.

Example 1.2.1 (Radioactivity and half-life). Let $N(t)$ denote the number of radioactive active atoms in a substance of a fixed quantity at time $t$. Then a model for the decay of the number of radioactive atoms is
$$
\begin{gathered}
\frac{d}{d t} N(t)=-k N(t), t>0, \
N\left(t_0\right)=N_0,
\end{gathered}
$$
where $k>0$. Equation (1.3b) is known as the initial condition. This kind of models are studied in detail in Chapter 2, Subsection 2.1.3. One can easily verify that the solution to (1.3a) is
$$
N(t)=N_0 e^{-k\left(t-t_0\right)}, t>t_0 .
$$
The half-life of a specific radioactive isotope is defined as the time taken for half of its radioactive atoms to decay. In fact, the half-life is independent of the quantity of the radioactive material. We now calculate the half-life of an isotope using (1.3a) if $k$ is known explicitly. For, it is enough to find $T$ at which $N(T)=\frac{N_0}{2}$. From (1.4) we have
$$
N(T)=N_0 e^{-k\left(T-t_0\right)}=\frac{N_0}{2}
$$

常微分方程代写

数学代写|常微分方程代写ordinary differential equation代考|Ordinary differential equations

莱布尼茨于 1676 年首次使用术语“equatio differentialis”（微分方程）来表示两个变量的微分之间的关系。很快，这种限制性使用被放弃了。粗略地说，微分方程是涉及一个或多个因变量（末知数）及其导数/偏导数的方程。如果微分方程中的末知数是只有一个变量的函数，则这样的微分方程称为常微分方程 (ODE)。
符号: 除非另有说明，微分方程中的末知数表示为 $y$. 让 $\mathbb{R}$ 表示实数集，并且 $J$ 是一个开区间 $\mathbb{R}$. 在整本书中，我们表示函数的导数 $y: J \rightarrow \mathbb{R}$ 关于 $x$ 通过任何一个
$$
\frac{d}{d x} y(x) \text { or } \frac{d y}{d x}(x) \text { or } y^{\prime}(x) .
$$
当函数中的参数没有歧义时 $y$ ，我们简单地用导数表示 $\frac{d y}{d x}$ 要么 $y^{\prime}$. 同样，让 $y^{\prime \prime}$ 和 $y^{\prime \prime \prime}$ 表示的二阶和三阶导数 $y$ ，分别。一般来说，对于 $k \in \mathbb{N}, y^{(k)}$ 要么 $\frac{d^k y}{d x^k}$ 表示 $k$-th阶导数 $y$.
使用这种表示法， ODE 的示例是
$$
\frac{d}{d x} y(x)=\left(\frac{d^2}{d x^2} y(x)\right)^5+y^2(x), x \in(0,1), y^{\prime}=3 y^2+(\sin x) y+\log \left(\cos ^2 y\right), x \in \mathbb{R}
$$
$\mathrm{ODE}$ 的阶数是最大数 $k$ 这样的 $k \mathrm{ODE}$ 中存在末知数的 -th 阶导数。例如，(1.1) 的阶数为二。
开始，积分学中的工具似乎足以研究 $\mathrm{ODE}$ 。但很快人们就会意识到，要开发解决或分析它们的方法，需要来自分析、线性代数等学科的概念。事实上，微分方程的研究推动了数学许多领域的重要发展：傅立叶级数理论以及更一般的正交展开、积分变换、莃尔伯特空间和勒贝格积分等等。

数学代写|常微分方程代写ordinary differential equation代考|Applications of ODEs

物理、化学、生物等领域的许多定律，都可以很容易地用微分方程来表达。其原因之一如下。数量 $y^{\prime}(x)$ 可以解释为数量的变化率 $y$ 关于数量 $x$. 在许多自然现象中，末知数（相对难以测量）、末知数相对于已知量的变化率和其他已知量 (易于测量) 之间存在关系过程。当这种关系用数学表达时，它就是一个 (系统) 微分方程。因此，ODE 的研究对于理解物理科学至关重要。事实上，在 ODE 中发展的大部分理论都归功于在力学、天文学、电子学等学科的研究中提出的问题/情况。
列出任何科学分支中所有可用的 ODE 模型是一项不可能完成的任务。因此，在本章中，我们介绍了一些源自物理学和生物学的 ODE 模型，可以使用本书中的材料对其进行求解或分析。我们从物理学模型开始。
示例 1.2.1 （放射性和半衰期）。让 $N(t)$ 表示某一时刻一定数量的物质中放射性活性原子的数量 $t$. 那么放射性原子数量衰减的模型是
$$
\frac{d}{d t} N(t)=-k N(t), t>0, N\left(t_0\right)=N_0,
$$
在哪里 $k>0$. 方程 (1.3b) 称为初始条件。此类模型在第 2 章 $2.1 .3$ 小节中进行了详细研究。可以很容易地验证 (1.3a) 的解是
$$
N(t)=N_0 e^{-k\left(t-t_0\right)}, t>t_0 .
$$
特定放射性同位素的半衰期定义为其放射性原子衰变一半所需的时间。事实上，半衰期与放射性物质的数量无关。我们现在使用 (1.3a) 计算同位素的半衰期，如果 $k$ 明确知道。因为，找到就足够了 $T$ 在哪个 $N(T)=\frac{N_0}{2}$. 从 (1.4) 我们有
$$
N(T)=N_0 e^{-k\left(T-t_0\right)}=\frac{N_0}{2}
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|宏观经济学代写Macroeconomics代考|ECON1120

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写宏观经济学Macroeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

宏观经济学，对国家或地区经济整体行为的研究。它关注的是了解整个经济的事件，如商品和服务的生产总量、失业水平和价格的一般行为。

statistics-lab™ 为您的留学生涯保驾护航在代写宏观经济学Macroeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宏观经济学Macroeconomics代写方面经验极为丰富，各种代写宏观经济学Macroeconomics相关的作业也就用不着说。

我们提供的宏观经济学Macroeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and the Lambert Function

In his 1931 article on the “Shipbuilding cycle,” Tinbergen was interested in the increase of tonnage that followed the building of ships with a lag of about one year due to the construction period. From this connection a relation emerged between the increase of total tonnage and the volume of total tonnage two years before (Tinbergen, 1959: 2). Tinbergen proposed to model this relation as a differential equation with a delay, of the form:
$$
\dot{f}(t)=-a f(t-\theta),
$$
where $f(t)$ is the tonnage as a function of time, $\theta$ represents the delay between the tonnage and its increase in $t$, and $a$ is the intensity of the relation, the volume of increase above the trend (Tinbergen, 1959: 3). Tinbergen assumed a solution to his equation of the form $f(t)=C e^{\lambda t}$, which, inserted into the equation above yields $\lambda=-a e^{-\lambda \theta}$, once we have simplified the $C$ which only depends on the initial conditions. $\lambda$ can be a real or complex number, but because it appears both in the exponential function and alone this equation is transcendental. Now, “transcendental” means that usually the answer will only be found “experimentally” as Tinbergen put it. Indeed a transcendental equation is periodic, in the same sense that the exponential function with an imaginary argument traces a circle repeating itself as the argument increases. To find a general solution, Tinbergen (and after him Frisch and Kalecki) separated the real and the imaginary part of this equation and solved for one of the two in terms of trigonometric functions; for instance Tinbergen obtained the equation:
$$
b \frac{\sin (y)}{y}=e^{-\frac{y}{\tan (y)}},
$$
where $b=a \theta$ and $\lambda=x+i y, i=\sqrt{-1}$. To find the solutions for $y$ of this type of equations, they took the same approach of plotting both sides and looking for points of intersection, before improving on this solution with simple algorithms. Figure $2.4$ shows in the solid red lines the right hand side of the Eq. $2.2$, while the dashed lines are the left hand side, for three different values of $b$ and both as a function of $y$.

经济代写|宏观经济学代写Macroeconomics代考|From Natural Sciences to Economics

Hamburger claimed that it was only with new mathematical tools that economists would be able to account quantitatively and qualitatively for economic processes. Ultimately, the aim was to transform economics into a science similar to biology, ${ }^5 \mathrm{a}$ science capable of understanding the operation of social organisms beset by recurrent “pathologies.” It should be noted that Hamburger was not the only economist interested in business cycles who was showing some discontent with a mechanical analogy. Ernst Wagemann, the German head of the imperial statistical office and of the business cycle research institute of Berlin, in a book published in 1928, called as well for a biological metaphor.

Although Wagemann wrote in German, his book met enough success to warrant its translation in English only two years later under the title Economic Rhythm: A Theory of Business Cycles, with a prefatory note from Wesley C. Mitchell (Wagemann, 1930). In the preface to the English edition, Wagemann presented his contribution as a small step “toward the repayment of the debt which Europe owes to America in the field of research into economic dynamics” (Wagemann, 1930: v). However, the type of dynamics that was applied remained very empirical; although Wagemann was searching for a theory, he steered resolutely away from abstract constructions which were heavily criticized. His review of existing theories led him to propose that “while the American methods are those of engineering, and the Russian those of astronomy, the German institute represents the medical, or, better, the organicbiological point of view” (1930: 10). The “organic-biological principle” which he described (with reference to Menger) was meant to capture both the interconnection of the separate parts of an (economic) organism as well as “a peculiarity which may be defined as consisting in the power to regulate its own movement” (1930: 11), an approach which he emphasized as “anything but mechanical” (1930: 11).

Another radical opinion on the business cycle was that it was only a “myth.” This opinion was shared among American economists and statisticians, such as Carl Snyder (1930) and Irving Fisher (1925). ${ }^6$ While the former based his claim on the fact that compared to the growth of the economy, the amplitude of fluctuations remained within certain limits, the second doubted that “inherent” cyclical regularity in business could be detected. For Fisher, even if there existed a simple self-generating cycle similar to that of a pendulum swinging under the influence of the force of gravity, its tendency to materialize would be necessarily “defeated in practice”

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and the Lambert Function

在他 1931 年关于“造船周期”的文章中，Tinbergen 对船舶建造后吨位的增加感兴趣，由于建造周期的原因，滞后大约一年。由此可见，总吨位的增加与两年前的总吨位体积之间存在一种关系 (Tinbergen， 1959：2）。Tinbergen 建议将这种关系建模为具有延迟的微分方程，形式如下:
$$
\dot{f}(t)=-a f(t-\theta),
$$
在哪里 $f(t)$ 吨位是时间的函数， $\theta$ 代表吨位与其增加量之间的延迟 $t$ ，和 $a$ 是关系的强度，高于趋势的增加量 (Tinbergen, 1959: 3)。Tinbergen 假设了他的方程式的解 $f(t)=C e^{\lambda t}$ ，揷入到上面的等式中得到 $\lambda=-a e^{-\lambda \theta}$ ，一旦我们简化了 $C$ 这仅取决于初始条件。 $\lambda$ 可以是实数或复数，但因为它既出现在指数函数中又单独出现，这个方程是超越的。现在，”先验”意味着答案通常只能像丁伯根所说的那样”通过实验” 找到。事实上，超越方程是周期性的，就像具有虚参数的指数函数跟踪一个随着参数增加而重复自身的圆圊一样。为了找到一个通解，Tinbergen（以及在他之后的 Frisch 和 Kalecki) 将这个方程的实部和虚部分开，并根据三角函数求解其中一个；例如 Tinbergen 获得了等式:
$$
b \frac{\sin (y)}{y}=e^{-\frac{y}{\tan (y)}},
$$
在哪里 $b=a \theta$ 和 $\lambda=x+i y, i=\sqrt{-1}$. 寻找解决方案 $y$ 对于此类方程式，他们采用相同的方法绘制两边并寻找交点，然后使用简单的算法改进此解决方案。数字 $2.4$ 以红色实线显示等式的右侧。2.2，而虚线是左侧，对于三个不同的值 $b$ 两者都作为函数 $y$.

经济代写|宏观经济学代写Macroeconomics代考|From Natural Sciences to Economics

Hamburger 声称，只有使用新的数学工具，经济学家才能对经济过程进行定量和定性分析。最终，目标是将经济学转变为类似于生物学的科学，5一种能够理解被反复出现的“病态”困扰的社会有机体运作的科学。应该指出的是，汉堡并不是唯一对商业周期感兴趣并对机械类比表示不满的经济学家。德国帝国统计局局长兼柏林商业周期研究所所长恩斯特·瓦格曼 (Ernst Wagemann) 在 1928 年出版的一本书中也呼吁使用生物学隐喻。

尽管 Wagemann 用德语写作，但他的书取得了足够的成功，仅在两年后就被翻译成英文，标题为“经济节奏：商业周期理论”，并附有 Wesley C. Mitchell 的序言（Wagemann，1930 年）。在英文版的序言中，Wagemann 将他的贡献描述为“朝着偿还欧洲在经济动态研究领域欠美国的债务”迈出的一小步（Wagemann，1930：v）。然而，所应用的动力类型仍然非常经验主义；尽管 Wagemann 正在寻找一种理论，但他坚决避开了受到严厉批评的抽象结构。他对现有理论的回顾使他提出“虽然美国的方法是工程学的方法，而俄罗斯的方法是天文学的方法，德国研究所代表了医学，或者更确切地说，有机生物学的观点”（1930：10）。他描述的“有机生物学原理”（参考门格尔）旨在捕捉（经济）有机体各个部分之间的相互联系以及“可以定义为存在于调节能力中的特性”它自己的运动”（1930：11），他强调这种方法“绝不是机械的”（1930：11）。

另一种关于商业周期的激进观点是，它只是一个“神话”。这一观点在美国经济学家和统计学家之间得到了认同，例如卡尔·斯奈德 (Carl Snyder) (1930) 和欧文·费雪 (Irving Fisher) (1925)。6前者的主张基于这样一个事实，即与经济增长相比，波动幅度保持在一定限度内，而第二个则怀疑是否可以检测到商业中“固有的”周期性规律。在费舍尔看来，即使存在类似于钟摆在重力作用下摆动的简单自生循环，其实现的趋势也必然会“在实践中被击败”

经济代写|宏观经济学代写Macroeconomics代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|宏观经济学代写Macroeconomics代考|ECON6002

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写宏观经济学Macroeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

宏观经济学，对国家或地区经济整体行为的研究。它关注的是了解整个经济的事件，如商品和服务的生产总量、失业水平和价格的一般行为。

我们提供的宏观经济学Macroeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|宏观经济学代写Macroeconomics代考|Supply Lags and Market Movements

Tinbergen proposed a supply lag scheme as early as 1928 , in a paper published in $D e$ Socialistische Gids. The paper was rather long considering that the journal usually published articles of only a dozen pages, and most of it was concerned with problems of exchange related to Cournot’s theories of competition. Incidentally, Tinbergen deplored the fact that Cournot’s work had remained mostly ignored, adding that the mathematical form in which it was published (in 1838) was probably to blame for this (Tinbergen, 1928: 543). ${ }^{14}$

The last part of this paper was concerned with the problem of the temporal element in his analysis, recognizing that this influence was mostly ignored in the previous sections. Tinbergen studied a problem of fluctuations around an equilibrium and based his discussion on a mechanical analogy: solving the “dynamic problem” meant that “as in mechanical dynamics, further data is needed, data which we can denote by inertia and delay, the inertia being related to the effort, the delay to the time of displacement” (Tinbergen, 1928: 544). Tinbergen then proposed to observe the behavior of one market where supply would adjust with a lag, while “demand adapts to supply without delay” (Tinbergen, 1928: 544). Although he did not explicitly present the equations behind his scheme, he did propose a numerical example with a figure of the temporal evolution of the quantities exchanged of a good, which took the form of damped oscillations that were in fact the result of a cobweb mechanism (reproduced in Fig. 2.2).

Obviously this example showed somewhat trivial oscillations from a high point to a low point each period, the only kind allowed by a first-order difference equation. ${ }^{15}$ This did not prevent him from discussing the conclusions one could draw from such a model for the economy as a whole and the observed cycles of three to four years or the longer cycles of seven to ten years, and the problems they posed for the social welfare of workers. Tinbergen also touched upon the problem of the damping of those oscillations, in connection with similar problems in physical system, and briefly considered the case where “the deviations are getting bigger (as in cases of unstable equilibrium),” but he added that these fluctuations could occur “only occasionally” (Tinbergen, 1928: 547).

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and Mixed Equations

In the introduction of his 1931 paper “Ein Problem der Dynamik,” when Tinbergen distinguished several lines of research that expanded “the static theory of social economy,” he finished his review by remarking that no one had yet tried to combine time derivatives and lags into a “systematic design of the dynamic theory” (Tinbergen, 1931a: 169). A scheme was proposed in the paper but it was still floundering; nevertheless, that same year, Tinbergen proposed a straightforward combination of time derivatives and lags, through his model of the shipbuilding cycle.

The choice of shipbuilding was not anecdotal; in a paper published in De Nederlandsche Conjunctuur, the journal of the Centraal Bureau voor de Statistiek (CBS) where he was working at the time, Tinbergen explained that “[t]he branch of industry concerned with shipbuilding has a number of peculiarities which make a study of the relationship between the business cycle and this branch of industry of great importance, especially for shipbuilding itself and for shipping companies” (Tinbergen, 1931c: 14). Shipbuilding was one of the biggest branches of activity in the Netherlands, and Tinbergen saw at least three characteristics that made its study worthwhile: the Iong production process of building ships, the strong fluctuations in its activity, and the long life of its means of production. This meant that the shipbuilding industry was quite different from the agricultural markets that had spurred the cobweb models of Moore, Schultz, Ricci and Tinbergen. Clearly, trying to explain the fluctuations of a market of durable instead of perishable goods led Tinbergen to important new ideas.

The first study that he published on the question (Tinbergen, 1931c) was very empirical as he tried to determine the lifespan of ships and other characteristics of the cycle. Nevertheless, he was also clearly searching for an explanation of the cycle, for a mechanism that would explain the fluctuations he had found empirically. He argued that a causal mechanism existed in particular between tonnage and its own increase: “[t]here is indeed a clear interaction between tonnage and increase in tonnage, an interaction which will be referred to in the remainder of this article as the ‘own mechanism’ of the development of tonnage” (Tinbergen, 1931c: 17). But he did not try in this paper to give a more mathematical form to this finding, which he reserved for a paper written in German for the Weltwirtschaftliches Archiv, the journal of the Kiel group of economists (Tinbergen 1931b, which was translated in Tinbergen 1959 from which we quote hereafter). ${ }^{24}$

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Supply Lags and Market Movements

Tinbergen 早在 1928 年就在一篇发表于丁和Socialistische Gids。考虑到该杂志通常发表的文章通常只有十几页，而且大部分都是与古诺竞争理论相关的交流问题，所以这篇论文相当长。顺便说一句，Tinbergen 对古诺的工作几乎一直被忽视这一事实感到遗憾，并补充说它出版时所用的数学形式（1838 年）可能是造成这种情况的原因（Tinbergen，1928：543）。14

本文的最后一部分在他的分析中关注时间因素的问题，认识到这种影响在前几节中大多被忽略了。丁伯根研究了围绕平衡的波动问题，并将他的讨论基于机械类比：解决“动态问题”意味着“在机械动力学中，需要更多数据，我们可以用惯性和延迟表示的数据，惯性是与努力有关，延迟与流离失所的时间有关”（Tinbergen，1928：544）。Tinbergen 随后提议观察一个市场的行为，在该市场中，供应会滞后调整，而“需求会立即适应供应”（Tinbergen，1928：544）。尽管他没有明确提出他的方案背后的方程式，

显然，这个例子显示了每个周期从高点到低点的轻微振荡，这是一阶差分方程唯一允许的振荡。15这并没有阻止他讨论人们可以从这样一个模型中得出的结论，该模型适用于整个经济和观察到的三到四年或七到十年的更长周期，以及它们对社会福利提出的问题工人。丁伯根还谈到了与物理系统中类似问题相关的这些振荡的阻尼问题，并简要考虑了“偏差越来越大（如不稳定平衡的情况）”的情况，但他补充说，这些波动可能“只是偶尔”发生（Tinbergen，1928：547）。

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and Mixed Equations

在他 1931 年的论文“Ein Problem der Dynamik”的引言中，当 Tinbergen 区分了扩展“社会经济的静态理论”的几条研究路线时，他在结束评论时说，还没有人试图将时间导数和滞后结合起来进入“动态理论的系统设计”（Tinbergen，1931a：169）。论文中提出了一个方案，但仍在挣扎；尽管如此，同年，丁伯根通过他的造船周期模型提出了时间导数和滞后的直接组合。

造船的选择不是轶事。在他当时工作的中央统计局 (CBS) 期刊 De Nederlandsche Conjunctuur 上发表的一篇论文中，Tinbergen 解释说，“与造船业有关的行业有许多特点，这使得研究商业周期与这个非常重要的行业分支之间的关系，特别是对于造船业本身和航运公司”（Tinbergen，1931c：14）。造船业是荷兰最大的活动分支之一，丁伯根至少看到了三个值得研究的特点：造船的生产过程很长，活动波动很大，生产资料的使用寿命很长. 这意味着造船业与刺激了摩尔、舒尔茨、里奇和丁伯根蜘蛛网模型的农业市场截然不同。显然，试图解释耐用品而非易腐烂商品市场的波动使丁伯根产生了重要的新想法。

他发表的关于这个问题的第一项研究（Tinbergen，1931c）非常注重经验，因为他试图确定船舶的寿命和周期的其他特征。尽管如此，他显然也在寻找周期的解释，寻找一种机制来解释他凭经验发现的波动。他认为，特别是在吨位与其自身增长之间存在因果机制：“[t]吨位与吨位增长之间确实存在明显的相互作用，这种相互作用将在本文的其余部分称为“自身”吨位发展的机制”（Tinbergen，1931c：17）。但他并没有在这篇论文中尝试为这一发现提供更多的数学形式，他将其保留在用德语为 Weltwirtschaftliches Archiv 撰写的论文中，24

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|宏观经济学代写Macroeconomics代考|ECOS3007

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写宏观经济学Macroeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

宏观经济学，对国家或地区经济整体行为的研究。它关注的是了解整个经济的事件，如商品和服务的生产总量、失业水平和价格的一般行为。

我们提供的宏观经济学Macroeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|宏观经济学代写Macroeconomics代考|Economic Barometers and “Cumulation”

The hunt for mechanisms responsible for cyclical fluctuations was clearly visible in Tinbergen’s first published article, where he recognized the importance of Aftalion’s theory of crisis, one of the few that was able, in his view, to account for the fact that “in each cycle there is already the seed for the next one” (Tinbergen, 1927: 715). But Tinbergen did not build a model of the economy in this article, which was aimed at the readers of De Economist to inform them of the latest developments in statistical and mathematical economics and business cycle analysis. At this time, what this covered was essentially the latest debates around the barometers, and the critiques they were subjected to.

One debate in particular interested Tinbergen, it was the “new interpretation” of Karl Karsten which had been discussed-among others -by Warren Persons and Alvin Hansen. Karsten was the main proponent in the 1920s of the “quadrature theory,” which had been developed by Charles Edge in 1908 (Karsten, 1924: 14). Being in “quadrature,” a term borrowed from electrical engineering, meant that the fluctuations of one curve corresponded to the fluctuations of the cumulation of another curve, or in other terms, its integral. ${ }^2$ For Karsten, the main advantage of this approach was to show how to obtain cycles of different length or amplitude: “By the quadrature theory, it seems possible to interpret the various phases of the economic cycle as entirely orderly and in accordance with theory, and yet wholly irregular in point of time” (Karsten, 1924: 16).

It was on the basis of this theory that Karsten suggested a new interpretation of the Harvard Business Index in Karsten (1926). While in the “official” interpretation of the barometer, the A curve (speculation) preceded and caused the B curve (production), Karsten thought that the second curve was in fact the causal predecessor of the first and the real driver of the cycle. His theoretical argument was that what counted was not so much business conditions represented by the B curve but the flow of money into the markets that accompanied poor business conditions and inversely the flow of money toward business when it was booming; in terms of “cumulation,” the A curve, representing the prices of securities, “shows the cumulative effects of the flow of money (into the market out of business, or out of the market into business)” (Karsten, 1926: 406). This led him to argue that the B curve was plotted upside down, and he showed that he could obtain a much larger correlation coefficient by following his theory.

经济代写|宏观经济学代写Macroeconomics代考|Time Derivatives and the Theories of Maximum Production

By the time he defended his thesis in 1929 , Tinbergen had already published at least two papers in De Economist and one in De Socialistische Gids. The economic appendix of his thesis, which he wrote up under the direction of renowned physicist Paul Ehrenfest, was published the same year in German in the Archiv für Sozialwissenschaft und Sozialpolitik, and the contents of his thesis were reviewed for $D e$

Economist by Ludwig Hamburger (see Chap. 3). This was a strong start for the 26-year-old Tinbergen, although those works bear little resemblance to the large macroeconometric models that he later developed and became known for. In fact, the thesis was taking an approach wholly different from what was hinted at in Tinbergen’s earlier article on barometers, but it opened a research program that he pursued for several years and that connected him to many other researchers in Europe and the USA.

The thesis title was “Minimum problems in physics and in the economy,” although Tinbergen warned from the beginning that the economic problems were only pointed out in the appendix. The title was also misleading in that the object of the work was not so much “minimum problems” but problems involving stationarity, neglecting the problem of knowing whether the solution obtained was a maximum or a minimum, and the latter term was used in this general meaning. Tinbergen argued that he was merely interested in the “formal analogy” between a number of problems that could be represented under this form of a “minimum problem.” This allowed him to avoid the treacherous question of the teleological aspect of such an idea, although he was inclined to think that the “striving for a minimum” was something that lied in the nature of an economic system (Tinbergen, 1929:2), something he shared with Evans, one of the main proponents of maximum principles. ${ }^6$

The thesis was mostly concerned with the demonstration that much of contemporary physics could be derived from extremal principles, Tinbergen taking throughout his work examples of mechanical motions, thermodynamics, optics, electrostatics and electrodynamics. Historically, minimum principles had been developed in optics and mechanics, and had first culminated in the middle of the eighteenth century with Maupertuis’ principle of least action. Maupertuis saw in his principle the proof that God existed and had built the world according to an harmonious principle, a Leibnizian idea that was the subject of Voltaire’s derision in Candide ${ }^7$ While these teleological aspects marked the developments of the idea, the most important works on the question became those that managed to keep a safe distance from it, first in Euler’s work and especially in Lagrange’s analytical mechanics. The works of the latter two formed the basis of the calculus of variation, and the solutions of such problems are still called today Euler-Lagrange equations.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Economic Barometers and “Cumulation”

在 Tinbergen 发表的第一篇文章中清楚地看到了对周期性波动机制的寻找，他认识到 Aftalion 危机理论的重要性，在他看来，这是少数能够解释“在每个周期中”这一事实的理论之一已经有了下一个种子”（Tinbergen，1927：715）。但丁伯根在这篇文章中并没有建立经济模型，其目的是为了让《经济学人》的读者了解统计和数理经济学以及商业周期分析的最新进展。此时，它所涵盖的基本上是围绕晴雨表的最新辩论，以及它们受到的批评。

Tinbergen 特别感兴趣的一场辩论是 Warren Persons 和 Alvin Hansen 讨论过的 Karl Karsten 的“新解释”。Karsten 是 1920 年代“正交理论”的主要支持者，该理论由 Charles Edge 于 1908 年提出 (Karsten, 1924: 14)。处于“正交”（从电气工程中借用的一个术语）意味着一条曲线的波动对应于另一条曲线的累积波动，或者换句话说，它的积分。2对于 Karsten 来说，这种方法的主要优点是展示了如何获得不同长度或幅度的周期：“通过正交理论，似乎可以将经济周期的各个阶段解释为完全有序且符合理论，并且但在时间点上完全不规则”（Karsten，1924：16）。

正是基于这一理论，Karsten 在 Karsten (1926) 中提出了对哈佛商业指数的新解释。虽然在晴雨表的“官方”解释中，A 曲线（投机）先于并导致 B 曲线（生产），但 Karsten 认为第二条曲线实际上是第一条曲线的因果前身，也是周期的真正驱动因素。他的理论论点是，重要的不是 B 曲线所代表的商业状况，而是伴随着商业状况不佳而流入市场的资金流量，以及相反的资金流向繁荣时期的业务；就“累积”而言，代表证券价格的 A 曲线“显示了资金流动的累积效应（进入市场的业务，或退出市场的业务）”（Karsten，1926：406 ).

经济代写|宏观经济学代写Macroeconomics代考|Time Derivatives and the Theories of Maximum Production

到 1929 年为论文答辩时，丁伯根已经在《经济学人》上发表了至少两篇论文，在《社会主义未来》上发表了一篇论文。他在著名物理学家保罗·埃伦费斯特 (Paul Ehrenfest) 的指导下撰写的论文的经济附录于同年以德文发表在 Archiv für Sozialwissenschaft und Sozialpolitik 上，他论文的内容被丁和

Ludwig Hamburger 的经济学家（见第 3 章）。对于 26 岁的 Tinbergen 来说，这是一个良好的开端，尽管这些作品与他后来开发并成名的大型宏观计量模型几乎没有相似之处。事实上，这篇论文采用的方法与 Tinbergen 早期关于气压计的文章中暗示的方法完全不同，但它开启了一个他追求了数年的研究计划，并将他与欧洲和美国的许多其他研究人员联系起来。

论文题目是“物理学和经济中的最小问题”，尽管丁伯根从一开始就警告经济问题只在附录中指出。标题也具有误导性，因为该工作的对象与其说是“最小问题”，不如说是涉及平稳性的问题，而忽略了知道所获得的解决方案是最大值还是最小值的问题，而后一个术语在本文中使用意义。Tinbergen 争辩说，他只对可以用这种“最小问题”形式表示的许多问题之间的“形式类比”感兴趣。这让他避免了这种想法的目的论方面的危险问题，6

这篇论文主要关注的是证明当代物理学的大部分内容都可以从极值原理中推导出来，丁伯根在他的整个工作中都采用了机械运动、热力学、光学、静电学和电动力学的例子。从历史上看，最小值原理是在光学和力学领域发展起来的，并在 18 世纪中叶以莫佩尔蒂的最小作用原理首次达到顶峰。莫佩尔蒂在他的原则中看到了上帝存在并根据和谐原则建造世界的证据，莱布尼茨的思想是伏尔泰在《老实人》中嘲笑的主题7虽然这些目的论方面标志着这个想法的发展，但关于这个问题的最重要的工作变成了那些设法与它保持安全距离的工作，首先是欧拉的工作，尤其是拉格朗日的分析力学。后两者的工作构成了变分法的基础，这些问题的解在今天仍被称为欧拉-拉格朗日方程。

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金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|微观经济学代写Microeconomics代考|ECON20002

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写微观经济学Microeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

微观经济学是研究稀缺性及其对资源的使用、商品和服务的生产、生产和福利的长期增长的影响，以及对社会至关重要的其他大量复杂问题的研究。

statistics-lab™ 为您的留学生涯保驾护航在代写微观经济学Microeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics相关的作业也就用不着说。

我们提供的微观经济学Microeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|微观经济学代写Microeconomics代考|Criteria for classification of consumer goods

simple demand price elasticities:
$E_{i i}\left(p_1, p_2, I\right)>0, \quad i=1,2$-Giffen goods or Veblen goods, ${ }^{28}$ (an increase in the price of a given good results in an increase in the demand for this good).
$E_{i i}\left(p_1, p_2, I\right)<0, \quad i=1,2$-ordinary goods, (an increase in the price of a given good results in a decrease in the demand for this good).
cross price elasticities of demand:
$E_{i j}\left(p_1, p_2, I\right)>0, \quad i, j=1,2, i \neq j$ 一substitute goods, (an increase in the price of $j$-th commodity results in an increase in the demand for $i$-th good),
$E_{i j}\left(p_1, p_2, I\right)=0, \quad i, j=1,2, i \neq j$-independent goods, (an increase in the price of $j$-th good does not affect the demand for $i$-th good),
$E_{i j}\left(p_1, p_2, I\right)<0, \quad i, j=1,2, \quad i \neq j$-complementary goods, (an increase in the price of $j$-th good results in a decrease in the demand for $i$-th good).
income elasticity of demand
$E_i\left(p_1, p_2, I\right)>0, \quad i=1,2$-normal goods, (an increase in a consumer’s income results in an increase in the demand for $i$-th good).
$E_i\left(p_1, p_2, I\right)<0, \quad i=1$, 2-inferior goods, (an increase in a consumer’s income results in a decrease in the demand for $i$-th good). ${ }^{29}$

Note 2.26 If an increase in the price of an inferior good results in an increase in the demand for this good, then it is called a Giffen good. On the other hand, when an increase in the price of a normal good results in an increase in the demand for this good, then it is called a Veblen good.
Note 2.27 Let us notice that:
(2.122) $\quad E_{i j}\left(p_1, p_2, I\right)=P_{i j}\left(p_1, p_2, I\right) \frac{p_j}{\varphi_i\left(p_1, p_2, I\right)}, \quad i, j=1,2$,
(2.123) $\quad E_i\left(p_1, p_2, I\right)=P_i\left(p_1, p_2, I\right) \frac{I}{\varphi_i\left(p_1, p_2, I\right)}, \quad i=1,2$.
The price and income elasticities of demand have the same sign as the marginal demand for $i$-th good with respect to prices of goods or with respect to a consumer’s income because prices and the demand for consumer goods are positive.

经济代写|微观经济学代写Microeconomics代考|Dynamic Approach

Let us introduce a notation $t$ of the time. In a discrete version of a dynamic consumers problem the time changes in jumps, that is we consider the values of the analysed functions in subsequent periods $t=0,1,2, \ldots, T$, where $T$ means a time horizon. For example, assuming we treat periods as months, when $T=30$, this means the time horizon of $2.5$ years. In a continuous version of a dynamic consumer’s problem the time $t \in[0 ; T]$ changes continuously, that is we consider the values of the analysed functions at any moment of the considered time horizon. As in the static approach, we assume that we are interested in bundles composed of two consumer goods ${ }^{30}$ :
$\mathbf{p}(t)=\left(p_1(t), p_2(t)\right) \geq 0$ — a vector of time-varying prices of goods,
$I(t) \geq 0$-a consumer’s income changing over time,
$\mathbf{x}(t)=\left(x_1(t), x_2(t)\right) \geq 0$-a bundle of goods that a consumer is willing to purchase at period/moment $t$ at prices $\mathbf{p}(t)$.

When choosing a bundle $\mathbf{x}(t)$ the consumer takes into account her/his preferences towards bundles of goods, described by a utility function $u(\mathbf{x}(t))$. Over time, it is not the consumer’s preferences that change, but only the bundle of goods that the consumer is willing to buy. This change occurs due to changes over time in the prices of goods and in the consumer’s income.
The consumption utility maximization problem has a form:
$$
u(\mathbf{x}(t)) \mapsto \max
$$
$$
p_1(t) x_1(t)+p_2(t) x_2(t) \leq I(t)
$$
$$
\mathbf{x}(t) \geq \mathbf{0} .
$$

If we assume that an insatiability phenomenon occurs (utility functions are increasing in quantities of goods in a consumption bundle), then as a budget constraint, instead of the inequality of the budget set, we can use the budget line equation:
$$
p_1(t) x_1(t)+p_2(t) x_2(t)=I(t) .
$$

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|Criteria for classification of consumer goods

简单的需求价格弹性:
$E_{i i}\left(p_1, p_2, I\right)>0, \quad i=1,2$ – 吉芬商品或凡勃伦商品，
28 (给定商品价格的上涨导致对该商品的需求增加）。
$E_{i i}\left(p_1, p_2, I\right)<0, \quad i=1,2$-普通商品，（给定商品价格的上涨导致对该商品的需求减少)。
需求的交叉价格弹性:
$E_{i j}\left(p_1, p_2, I\right)>0, \quad i, j=1,2, i \neq j$ 一替代品，（价格上涨 $j$-th商品导致需求增加 $i$-好)，
$E_{i j}\left(p_1, p_2, I\right)=0, \quad i, j=1,2, i \neq j$ – 独立商品，（价格上涨 $j$-th 商品不影响需求 $i$ – 好)，
$E_{i j}\left(p_1, p_2, I\right)<0, \quad i, j=1,2, \quad i \neq j$ – 互补品，（价格上涨 $j$ – 良好的结果导致对需求的减少 $i$-很好)。
需求收入弹性
$E_i\left(p_1, p_2, I\right)>0, \quad i=1,2$ – 正常商品，（消费者收入的增加导致对商品的需求增加 $i$-很好)。
$E_i\left(p_1, p_2, I\right)<0, \quad i=1$ ，2-劣质品，(消费者收入的增加导致对 $i$-很好)。 ${ }^{29}$
注释 $2.26$ 如果劣质商品价格上涨导致对该商品的需求增加，则它被称为吉芬商品。另一方面，当一种正常商品的价格上涨导致对该商品的需求增加时，它被称为凡勃伦商品。
注释 $2.27$ 让我们注意到:
(2.122) $\quad E_{i j}\left(p_1, p_2, I\right)=P_{i j}\left(p_1, p_2, I\right) \frac{p_j}{\varphi_i\left(p_1, p_2, I\right)}, \quad i, j=1,2$ ，
(2.123) $\quad E_i\left(p_1, p_2, I\right)=P_i\left(p_1, p_2, I\right) \frac{I}{\varphi_i\left(p_1, p_2, I\right)}, \quad i=1,2$.
需求的价格弹性和收入弹性与边际需求的符号相同 $i$ – 与商品价格或消费者收入相关的商品，因为价格和对消费品的需求是正的。

经济代写|微观经济学代写Microeconomics代考|Dynamic Approach

让我们引入一个符号 $t$ 的时间。在动态消费者问题的离散版本中，时间在跳跃中变化，即我们考虑后续期间分析函数的值 $t=0,1,2, \ldots, T$ ，在哪里 $T$ 表示时间范围。例如，假设我们将期间视为月份，当 $T=30$ ，这意味着时间范围 $2.5$ 年。在动态消费者问题的连续版本中 $t \in[0 ; T]$ 不断变化，也就是说，我们在所考虑的时间范围内的任何时刻考虑分析函数的值。与静态方法一样，我们假设我们对由两种消费品组成的捆绑包感兴趣 30 :
$\mathbf{p}(t)=\left(p_1(t), p_2(t)\right) \geq 0$ – 随时间变化的商品价格向量，
$I(t) \geq 0$-消费者的收入随时间变化，
$\mathbf{x}(t)=\left(x_1(t), x_2(t)\right) \geq 0$ – 消费者愿意在一段时间/时刻购买的一览子商品 $t$ 按价格 $\mathbf{p}(t)$.
选择捆绑包时 $\mathbf{x}(t)$ 消费者考虑她/他对商品组合的偏好，用效用函数描述 $u(\mathbf{x}(t))$. 随着时间的推移，改变的不是消费者的偏好，而是消费者愿意购买的商品组合。这种变化是由于商品价格和消费者收入随时间的变化而发生的。
消费效用最大化问题有一个形式:
$$
\begin{gathered}
p_1(t) x_1(t)+p_2(t) x_2(t) \leq I(t) \
\mathbf{x}(t) \geq \mathbf{0}
\end{gathered}
$$
如果我们假设发生了无法满足的现象（效用函数在消费束中的商品数量增加），那么作为预算约束，我们可以用预算线方程代替预算集的不等式:
$$
p_1(t) x_1(t)+p_2(t) x_2(t)=I(t)
$$

经济代写|微观经济学代写Microeconomics代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|微观经济学代写Microeconomics代考|PACC6007

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写微观经济学Microeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

微观经济学是研究稀缺性及其对资源的使用、商品和服务的生产、生产和福利的长期增长的影响，以及对社会至关重要的其他大量复杂问题的研究。

我们提供的微观经济学Microeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|微观经济学代写Microeconomics代考|Substitute, Independent and Complementary Goods

The substitutability concerns only these consumption bundles $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}_{+}^2$ whose utility is the same.

Any two goods are called substitute goods (substitutes) if in order to keep some given level of utility of a consumption bundle $\mathbf{x} \in \mathbb{R}_{+}^2$ when quantity of one of the goods is reduced (raised) one needs to compensate this change by appropriate increase (decrease) in quantity of the other good in a consumption bundle $\mathbf{x}$.

If in order to keep some given level of utility of a consumption bundle $\mathbf{x} \in \mathbb{R}_{+}^2$ when quantity of one of the goods is reduced (raised) one does need to compensate for this change by any increase (decrease) in quantity of the other good in a consumption bundle $\mathbf{x}$, then such two consumer goods are called independent goods.

Any two goods are called complementary goods (complements) if in order to change the utility of a given consumption bundle $\mathbf{x} \in \mathbb{R}_{+}^2$ one needs to simultaneously raise or reduce quantities of both goods in the bundle.

Note 2.11 When classifying consumption bundles in substitutes or independent goods one takes into account only these goods which are considered in bundles with the same utility level (bundles indifferent to each other).

Note 2.12 To state if any two goods in a consumption bundle $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}{+}^2$ are complements to each other one needs to determine whether an increase (decrease) in the utility of this bundle requires a simultaneous raise (reduction) in quantities of both goods. If there is no such need then the goods are called not complementary. Let us define measures of the substitutability of consumer goods. For this purpose let us assume that we are given: (1) a differentiable utility function $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}$,

(2) an indifference curve – a set
$$
G(u)=\left{\mathbf{x} \in \mathbb{R}_{+}^2 \mid u(\mathbf{x})=u=\text { const. }>0\right} .
$$
of all bundles with the same reference utility $u=$ const. $>0$.

经济代写|微观经济学代写Microeconomics代考|Marshallian Demand Function

Let us consider a market for two consumer goods where:
$i=1,2$ – consumer goods (products and services),
$X=\mathbb{R}{+}^2-$ a goods space, $\mathbf{p}=\left(p_1, p_2\right) \in \mathbb{R}{+}^2$-a vector of prices of consumer goods,
$\mathbf{x}=\left(x_1, x_2\right) \in B \subset \mathbb{R}{+}^2-$ a bundle of goods that the consumer wants to purchase (a consumption bundle), $B=\left{\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}{+}^2 \mid x_1 \leq b_1, x_2 \leq b_2\right}$-a supply set,
$b_i, i=1,2$-supply of $i$-th consumer good, ${ }^{22}$
$I \in$ int $\mathbb{R}{+}-$a consumer’s income, ${ }^{23}$ $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}-$ a utility function describing the preferences of a consumer (describing a relation of consumer preference).
$D(\mathbf{p}, I)=\left{\mathbf{x} \in \mathbb{R}{+}^2 \mid p_1 x_1+p_2 x_2 \leq I\right} \subset X=\mathbb{R}{+}^2-$ a set of all consumption bundles whose value is not greater than the consumer’s income (a budget set),
Definition 2.26 A bundle $\mathbf{x}$ is called a limit of a sequence $\left{\mathbf{x}^i\right}_{i=1}^{+\infty}$ if a limit of sequence of metric values $\lim {i \rightarrow+\infty} d\left(\mathbf{x}^i, \mathbf{x}\right)=0$, which can be written as $$ \lim {i \rightarrow+\infty} \mathbf{x}^i=\mathbf{x} \text { or } \quad \mathbf{x}^i \rightarrow_{i \rightarrow+\infty} \mathbf{x} .
$$
Definition 2.27 The budget set $D(\mathbf{p}, I) \subset X=\mathbb{R}{+}^2$ is a closed set because: (2.38) $\forall \mathbf{x}^i \in D(\mathbf{p}, I) \lim {i \rightarrow+\infty} \mathbf{x}^i=\mathbf{x} \Rightarrow \mathbf{x} \in D(\mathbf{p}, I)$.
Definition $2.28$ The budget set $D(\mathbf{p}, I) \subset X=\mathbb{R}_{+}^2$ is a bounded set because:
$$
\forall \mathbf{x}^1, \mathbf{x}^2 \in D(\mathbf{p}, I) \quad \exists \mathrm{N}>0 \quad d\left(\mathbf{x}^1, \mathbf{x}^2\right)<N
$$

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|Substitute, Independent and Complementary Goods

可替代性只涉及这些消费束 $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}{+}^2$ 谁的效用是一样的。任何两种商品都被称为替代商品 (substitutes)，如果为了保持消费束的某个给定效用水平 $\mathbf{x} \in \mathbb{R}{+}^2$ 当一种商品的数量减少 (增加) 时，需要通过适当增加 (减少) 消费束中另一种商品的数量来补偿这种变化 $\mathbf{x}$.
如果为了保持某个给定水平的消费束效用 $\mathbf{x} \in \mathbb{R}{+}^2$ 当其中一种商品的数量减少 (增加）时，确实需要通过消费束中另一种商品数量的增加 (减少) 来补偿这种变化 $\mathbf{x}$ ，则称这两种消费品为独立品。如果为了改变给定消费束的效用，任何两种商品都称为互补品 (complements) $\mathbf{x} \in \mathbb{R}{+}^2$ 需要同时增加或减少捆绑包中两种商品的数量。
注释 $2.11$ 在将消费束分类为替代品或独立商品时，仅考虑这些商品，这些商品被视为具有相同效用水平的消费束（彼此无关的消费束）。
注 $2.12$ 说明消费束中是否有任何两种商品 $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}+{ }^2$ 是互补的，因此需要确定增加（减少) 这一束的效用是否需要同时增加 (减少) 两种商品的数量。如果没有这种需要，则该商品称为非互补商品。让我们定义消费品可替代性的衡量标准。为此，让我们假设给定: (1)一个可微的效用函数 $u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$
(2) 一条无差异曲线一一一个集合
$G(u)=\backslash$ left $\left{\backslash m a t h b f{x} \backslash\right.$ in $\backslash m a t h b b{R}_{-}{+}^{\wedge} 2 \backslash$ mid $u(\backslash \operatorname{mathbf}{x})=u=\backslash \operatorname{text}{$ 常数。 $}>0 \backslash$ 右 $}$
具有相同参考效用的所有束 $u=$ 常量。 $>0$.

经济代写|微观经济学代写Microeconomics代考|Marshallian Demand Function

让我们考虑两种消费品的市场，其中:
$i=1,2$ – 消费品（产品和服务)，
$X=\mathbb{R}+{ }^2$ 一货品空间， $\mathbf{p}=\left(p_1, p_2\right) \in \mathbb{R}+{ }^2$-消费品价格的向量，
$\mathbf{x}=\left(x_1, x_2\right) \in B \subset \mathbb{R}+{ }^2$ 一消费者想要购买的一束商品（消费束），
$B=\backslash$ left $\left{\backslash\right.$ mathbf ${x}=\backslash \operatorname{left}\left(x_{-} 1, x_{-} \backslash \backslash\right.$ ight $) \backslash$ in $\backslash m a t h b b{R}{+}^{\wedge} 2 \backslash m i d x_{-} 1 \backslash$ leq b_1, $x_{-} 2 \backslash$ leq b_2\right } } \text { – 一套补给 }
品，
$b_i, i=1,2$-供应 $i$-i肖费品， 22
$I \in$ 整数 $\mathbb{R}+$ 一消费者的收入， ${ }^{23} u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$ 一描述消费者偏好的效用函数（描述消费者偏好的关
系)。
一组所有消费束，其价值不大于消费者的收入 (预算集)，
$\lim i \rightarrow+\infty d\left(\mathbf{x}^i, \mathbf{x}\right)=0$, 可以写成
$$
\lim i \rightarrow+\infty \mathbf{x}^i=\mathbf{x} \text { or } \quad \mathbf{x}^i \rightarrow_{i \rightarrow+\infty} \mathbf{x}
$$
定义 $2.27$ 预算集 $D(\mathbf{p}, I) \subset X=\mathbb{R}+{ }^2$ 是闭集因为: $\forall \mathbf{x}^i \in D(\mathbf{p}, I) \lim i \rightarrow+\infty \mathbf{x}^i=\mathbf{x} \Rightarrow \mathbf{x} \in D(\mathbf{p}, I)$
定义 $2.28$ 预算设定 $D(\mathbf{p}, I) \subset X=\mathbb{R}_{+}^2$ 是有界集因为:
$$
\forall \mathbf{x}^1, \mathbf{x}^2 \in D(\mathbf{p}, I) \quad \exists \mathrm{N}>0 \quad d\left(\mathbf{x}^1, \mathbf{x}^2\right)<N
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|微观经济学代写Microeconomics代考|ECON2516

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写微观经济学Microeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

微观经济学是研究稀缺性及其对资源的使用、商品和服务的生产、生产和福利的长期增长的影响，以及对社会至关重要的其他大量复杂问题的研究。

我们提供的微观经济学Microeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

经济代写|微观经济学代写Microeconomics代考|Preliminary Terms

For the sake of simplicity we consider rational choices ${ }^4$ made by an individual consumer on a market of two consumer goods ${ }^5$ denoted by subscript $i=1,2$.
Let us introduce basic terms which set the frame of an analysis we conduct in this chapter and Chap. 3.

Definition 2.1 A bundle of consumer goods (a consumption bundle) is a vector $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}_{+}^2$, in which $i$-th component $x_i \geq 0, i=1,2$ indicates a nonnegative expressed in physical units amount of $i$-th good in the consumption bundle $\mathbf{x}$.

Definition 2.2 A consumer goods space is a set $X=\mathbb{R}{+}^2$ of all bundles of goods available on the market along with a metric specified on it ${ }^6$ : (2.1) $\quad d_E\left(\mathbf{x}^1, \mathbf{x}^2\right)=\sqrt{\sum{i=1}^2\left(x_i^1-x_i^2\right)^2}=\sqrt{\left(x_1^1-x_1^2\right)^2+\left(x_2^1-x_2^2\right)^2}$, or
(2.2) $\quad d\left(\mathbf{x}^1, \mathbf{x}^2\right)=\max {i=1,2}\left{\left|x_i^1-x_i^2\right|\right}=\max {i=1,2}\left{\left|x_1^1-x_1^2\right|,\left|x_2^1-x_2^2\right|\right}$
being a measure of distance between two consumption bundles. ${ }^7$
Definition 2.3 A Cartesian product determined on the goods space $X=\mathbb{R}_{+}^2$ is such a set:
$$
X \times X=\left{\left(\mathbf{x}^1, \mathbf{x}^2\right) \mid \mathbf{x}^1 \in X, \mathbf{x}^2 \in X\right},
$$
of all ordered pairs of consumption bundles in which both bundles (the first one and the second one in the pair) belong to the goods space.

经济代写|微观经济学代写Microeconomics代考|Utility Function

Definition 2.12 A consumer’s utility function (defined on the goods space $X=$ $\mathbb{R}{+}^2$ ) is a mapping $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}$ such that
$$
\begin{aligned}
& \forall \mathbf{x}^1, \mathbf{x}^2 \in X=\mathbb{R}{+}^2 \quad \mathbf{x}^1 \succsim \mathbf{x}^2 \Leftrightarrow u\left(\mathbf{x}^1\right) \geq u\left(\mathbf{x}^2\right), \ & \forall \mathbf{x}^1, \mathbf{x}^2 \in X=\mathbb{R}{+}^2 \quad \mathbf{x}^1 \succ \mathbf{x}^2 \Leftrightarrow u\left(\mathbf{x}^1\right)>u\left(\mathbf{x}^2\right), \
& \forall \mathbf{x}^1, \mathbf{x}^2 \in X=\mathbb{R}{+}^2 \quad \mathbf{x}^1 \sim \mathbf{x}^2 \Leftrightarrow u\left(\mathbf{x}^1\right)=u\left(\mathbf{x}^2\right) . \end{aligned} $$ Some properties of the utility function Definition 2.13 A utility function $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}$ is called continuous at point $\mathbf{x} \in \mathbb{R}{+}^2$ if for any sequence $\left{\mathbf{x}^i\right}{i=1}^{+\infty}$, where $\mathbf{x}^i \in X=\mathbb{R}{+}^2$, it is satisfied: $$ \lim {i \rightarrow+\infty} \mathbf{x}^i=\mathbf{x} \Rightarrow \lim {i \rightarrow+\infty} u\left(\mathbf{x}^i\right)=u(\mathbf{x}) . $$ Definition 2.14 A utility function $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}$ is called continuous on the goods space $X=\mathbb{R}_{+}^2$ if it is continuous at every point of this space.

Definition 2.15 A utility function $u: \mathbb{R}{+}^2 \rightarrow \mathbb{R}$ is called differentiable on the goods space $X=\mathbb{R}{+}^2$ if its partial first-order derivatives:
$$
\begin{aligned}
& \frac{\partial u\left(x_1, x_2\right)}{\partial x_1}=\lim {\Delta x_1 \rightarrow 0} \frac{u\left(x_1+\Delta x_1, x_2\right)-u\left(x_1, x_2\right)}{\Delta x_1}, \ & \frac{\partial u\left(x_1, x_2\right)}{\partial x_2}=\lim {\Delta x_2 \rightarrow 0} \frac{u\left(x_1, x_2+\Delta x_2\right)-u\left(x_1, x_2\right)}{\Delta x_2}
\end{aligned}
$$
are continuous on this space.
Definition 2.16 A marginal utility of $\boldsymbol{i}$-th good in a consumption bundle $\mathbf{x}=$ $\left(x_1, x_2\right) \in \mathbb{R}_{+}^2$ is a partial first-order derivative of the utility function:
$$
\frac{\partial u\left(x_1, x_2\right)}{\partial x_i} \quad i=1,2,
$$ which describes by approximately how many units the utility of a consumption bundle $\mathbf{x} \in \mathbb{R}_{+}^2$ changes when quanity of $i$-th good increases by one (notional) unit and quantity of the other good in the bundle does not change.

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|Preliminary Terms

为了简单起见，我们考虑理性选择 ${ }^4$ 由个人消费者在两种消费品市场上制造的 ${ }^5$ 用下标表示 $i=1,2$. 让我们介绍一些基本术语，这些术语为我们在本章和第 1 章中进行的分析设定了框架。3.
定义 $2.1$ 一束消费品 (a consumption bundle) 是一个向量 $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}{+}^2$ ，其中 $i$-th 组件 $x_i \geq 0, i=1,2$ 表示以物理单位量表示的非负数 $i$ – 消费束中的第一种商品 $\mathbf{x}$. 定义 $2.2$ 一个消费品空间是一个集合 $X=\mathbb{R}+^2$ 市场上所有可用商品的捆绑包及其上指定的指标 ${ }^6:(2.1)$ $d_E\left(\mathbf{x}^1, \mathbf{x}^2\right)=\sqrt{\sum i=1^2\left(x_i^1-x_i^2\right)^2}=\sqrt{\left(x_1^1-x_1^2\right)^2+\left(x_2^1-x_2^2\right)^2}$, 或 (2.2) 是衡量两个消费束之间距离的指标。 ${ }^7$ 定义 $2.3$ 在商品空间上确定的笛卡尔积 $X=\mathbb{R}{+}^2$ 是这样一个集合:
所有有序的消费束对，其中两个束（对中的第一个和第二个）都属于商品空间。

经济代写|微观经济学代写Microeconomics代考|Utility Function

定义 $2.12$ 消费者的效用函数 (定义在商品空间 $X=\mathbb{R}+{ }^2$ ) 是一个映射 $u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$ 这样
$$
\forall \mathbf{x}^1, \mathbf{x}^2 \in X=\mathbb{R}+^2 \quad \mathbf{x}^1 \succsim \mathbf{x}^2 \Leftrightarrow u\left(\mathbf{x}^1\right) \geq u\left(\mathbf{x}^2\right), \quad \forall \mathbf{x}^1, \mathbf{x}^2 \in X=\mathbb{R}+{ }^2 \quad \mathbf{x}^1 \succ \mathbf{x}^2 \Leftrightarrow \imath
$$
效用函数的一些性质定义 $2.13$ 效用函数 $u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$ 在点上称为连续的 $\mathbf{x} \in \mathbb{R}+{ }^2$ 如果对于任何序列 left{\mathbffx}^^i|right $\left{[i=1}^{\prime}{+\right.$ linfty $}$, 在哪里 $\mathbf{x}^i \in X=\mathbb{R}+^2$ ，满足:
$$
\lim i \rightarrow+\infty \mathbf{x}^i=\mathbf{x} \Rightarrow \lim i \rightarrow+\infty u\left(\mathbf{x}^i\right)=u(\mathbf{x})
$$
定义 $2.14$ 效用函数 $u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$ 在商品空间上称为连续的 $X=\mathbb{R}{+}^2$ 如果它在这个空间的每一点都是连续的。定义 $2.15$ 效用函数 $u: \mathbb{R}+{ }^2 \rightarrow \mathbb{R}$ 在商品空间上称为可微分的 $X=\mathbb{R}+{ }^2$ 如果它的偏一阶导数： $$ \frac{\partial u\left(x_1, x_2\right)}{\partial x_1}=\lim \Delta x_1 \rightarrow 0 \frac{u\left(x_1+\Delta x_1, x_2\right)-u\left(x_1, x_2\right)}{\Delta x_1}, \quad \frac{\partial u\left(x_1, x_2\right)}{\partial x_2}=\lim \Delta x_2 \rightarrow 0 $$ 在这个空间上是连续的。定义 $2.16$ 的边际效用 $\boldsymbol{i}$ – 消费束中的第一种商品 $\mathbf{x}=\left(x_1, x_2\right) \in \mathbb{R}{+}^2$ 是效用函数的偏一阶导数:
$$
\frac{\partial u\left(x_1, x_2\right)}{\partial x_i} \quad i=1,2,
$$
它描述了消费束的效用大约有多少个单位 $\mathbf{x} \in \mathbb{R}_{+}^2$ 当数量发生变化时 $i$ – 第一种商品增加一个 (名义上的) 单位，而捆绑中其他商品的数量不变。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|线性代数代写linear algebra代考|MTH2106

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写线性代数linear algebra这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

线性代数是平坦的微分几何，在流形的切线空间中服务。时空的电磁对称性是由洛伦兹变换表达的，线性代数的大部分历史就是洛伦兹变换的历史。

statistics-lab™ 为您的留学生涯保驾护航在代写线性代数linear algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写线性代数linear algebra代写方面经验极为丰富，各种代写线性代数linear algebra相关的作业也就用不着说。

我们提供的线性代数linear algebra及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

数学代写|线性代数代写linear algebra代考|ROW REDUCTION AND ECHELON FORMS

This section refines the method of Section $1.1$ into a row reduction algorithm that will enable us to analyze any system of linear equations. ${ }^1$ By using only the first part of the algorithm, we will be able to answer the fundamental existence and uniqueness questions posed in Section 1.1.

The algorithm applies to any matrix, whether or not the matrix is viewed as an augmented matrix for a linear system. So the first part of this section concerns an arbitrary rectangular matrix and begins by introducing two important classes of matrices that include the “triangular” matrices of Section 1.1. In the definitions that follow, a nonzero row or column in a matrix means a row or column that contains at least one nonzero entry; a leading entry of a row refers to the leftmost nonzero entry (in a nonzero row).

An echelon matrix (respectively, reduced echelon matrix) is one that is in echelon form (respectively, reduced echelon form). Property 2 says that the leading entries form an echelon (“steplike”) pattern that moves down and to the right through the matrix. Property 3 is a simple consequence of property 2 , but we include it for emphasis.
The “triangular” matrices of Section 1.1, such as
$$
\left[\begin{array}{rrrc}
2 & -3 & 2 & 1 \
0 & 1 & -4 & 8 \
0 & 0 & 0 & 5 / 2
\end{array}\right] \text { and }\left[\begin{array}{lllr}
1 & 0 & 0 & 29 \
0 & 1 & 0 & 16 \
0 & 0 & 1 & 3
\end{array}\right]
$$
are in echelon form. In fact, the second matrix is in reduced echelon form. Here are additional examples.

EXAMPLE 1 The following matrices are in echelon form. The leading entries ( $\boldsymbol{)}$ ) may have any nonzero value; the starred entries $(*)$ may have any value (including zero).

数学代写|线性代数代写linear algebra代考|Solutions of Linear Systems

The row reduction algorithm leads directly to an explicit description of the solution set of a linear system when the algorithm is applied to the augmented matrix of the system.
Suppose, for example, that the augmented matrix of a linear system has been changed into the equivalent reduced echelon form
$$
\left[\begin{array}{rrrr}
1 & 0 & -5 & 1 \
0 & 1 & 1 & 4 \
0 & 0 & 0 & 0
\end{array}\right]
$$
There are three variables because the augmented matrix has four columns. The associated system of equations is
$$
\begin{array}{r}
x_1-5 x_3=1 \
x_2+x_3=4 \
0=0
\end{array}
$$
The variables $x_1$ and $x_2$ corresponding to pivot columns in the matrix are called basic variables. ${ }^2$ The other variable, $x_3$, is called a free variable.

Whenever a system is consistent, as in (4), the solution set can be described explicitly by solving the reduced system of equations for the basic variables in terms of the free variables. This operation is possible because the reduced echelon form places each basic variable in one and only one equation. In (4), solve the first equation for $x_1$ and the second for $x_2$. (Ignore the third equation; it offers no restriction on the variables.)
$$
\left{\begin{array}{l}
x_1=1+5 x_3 \
x_2=4-x_3 \
x_3 \text { is free }
\end{array}\right.
$$
The statement ” $x_3$ is free” means that you are free to choose any value for $x_3$. Once that is done, the formulas in (5) determine the values for $x_1$ and $x_2$. For instance, when $x_3=0$, the solution is $(1,4,0)$; when $x_3=1$, the solution is $(6,3,1)$. Each different choice of $x_3$ determines a (different) solution of the system, and every solution of the system is determined by a choice of $x_3$.

线性代数代考

数学代写|线性代数代写linear algebra代考|ROW REDUCTION AND ECHELON FORMS

本节细化Section的方法 1.1到行缩减算法中，使我们能够分析任何线性方程组。 ${ }^1$ 通过仅使用算法的第一部分，我们将能够回答第 $1.1$ 节中提出的基本存在性和唯一性问题。
该算法适用于任何矩阵，无论该矩阵是否被视为线性系统的增广矩阵。因此，本节的第一部分涉及任意矩形矩阵，并首先介绍两类重要的矩阵，其中包括 $1.1$ 节中的“三角”矩阵。在下面的定义中，矩阵中的非零行或列表示包含至少一个非零项的行或列；行的前导条目指的是最左边的非零条目（在非零行中）。
阶梯矩阵 (分别称为简化阶梯矩阵) 是阶梯形式的矩阵 (分别称为简化阶梯形式) 。属性 2 表示领先的条目形成梯人 (“阶梯状”) 模式，在矩阵中向下和向右移动。属性 3 是属性 2 的简单结果，但我们将其包含在内是为了强调。
$1.1$ 节的“三角”矩阵，如
呈梯队形式。事实上，第二个矩阵是简化的阶梯形式。以下是其他示例。
示例 1 以下矩阵为梯形矩阵。主要条目 ()$)$ 可能有任何非零值；加星标的条目 $(*)$ 可以有任何值（包括

数学代写|线性代数代写linear algebra代考|Solutions of Linear Systems

当该算法应用于系统的增广矩阵时，行约简算法直接导致对线性系统解集的显式描述。例如，假设线性系统的增广矩阵已变为等效的简化阶梯形式
$$
\left[\begin{array}{llllllllllll}
1 & 0 & -5 & 1 & 0 & 1 & 1 & 4 & 0 & 0 & 0 & 0
\end{array}\right]
$$
有三个变量，因为增广矩阵有四列。相关联的方程组是
$$
x_1-5 x_3=1 x_2+x_3=40=0
$$
变量 $x_1$ 和 $x_2$ 对应于矩阵中主元列的变量称为基本变量。 ${ }^2$ 另一个变量， $x_3$ ，称为自由变量。
只要系统是一致的，如 (4) 中所示，就可以通过根据自由变量求解基本变量的简化方程组来明确描述解集。这一操作是可能的，因为简化的阶梯形式将每个基本变量放在一个且只有一个方程中。在 (4) 中，求解第一个方程为 $x_1$ 第二个是 $x_2$. (忽略第三个等式；它对变量没有限制。) $\$ \$$
Veft {
$$
x_1=1+5 x_3 x_2=4-x_3 x_3 \text { is free }
$$
正确的。 $\$ \$$
声明” $x_3$ 是免费的”意味着您可以自由选择任何值 $x_3$. 完成后，(5) 中的公式确定 $x_1$ 和 $x_2$. 例如，当 $x_3=0$ ，解是 $(1,4,0)$ ；什么时候 $x_3=1$ ，解是 $(6,3,1)$. 每个不同的选择 $x_3$ 确定系统的 (不同的) 解决方案，并且系统的每个解决方案都由选择 $x_3$.

数学代写|线性代数代写linear algebra代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|线性代数代写linear algebra代考|MATH1051

Posted on 2023年1月5日2023年1月5日 by statistics-lab

如果你也在怎样代写线性代数linear algebra这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

线性代数是平坦的微分几何，在流形的切线空间中服务。时空的电磁对称性是由洛伦兹变换表达的，线性代数的大部分历史就是洛伦兹变换的历史。

我们提供的线性代数linear algebra及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
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

数学代写|线性代数代写linear algebra代考|Solving a Linear System

This section and the next describe an algorithm, or a systematic procedure, for solving linear systems. The basic strategy is to replace one system with an equivalent system (i.e., one with the same solution set) that is easier to solve.

Roughly speaking, use the $x_1$ term in the first equation of a system to eliminate the $x_1$ terms in the other equations. Then use the $x_2$ term in the second equation to eliminate the $x_2$ terms in the other equations, and so on, until you finally obtain a very simple equivalent system of equations.

Three basic operations are used to simplify a linear system: Replace one equation by the sum of itself and a multiple of another equation, interchange two equations, and multiply all the terms in an equation by a nonzero constant. After the first example, you will see why these three operations do not change the solution set of the system.

Row operations can be applied to any matrix, not merely to one that arises as the augmented matrix of a linear system. Two matrices are called row equivalent if there is a sequence of elementary row operations that transforms one matrix into the other.
It is important to note that row operations are reversible. If two rows are interchanged, they can be returned to their original positions by another interchange. If a row is scaled by a nonzero constant $c$, then multiplying the new row by $1 / c$ produces the original row. Finally, consider a replacement operation involving two rows -say, rows 1 and 2 -and suppose that $c$ times row 1 is added to row 2 to produce a new row 2. To “reverse” this operation, add $-c$ times row 1 to (new) row 2 and obtain the original row 2. See Exercises $29-32$ at the end of this section.

At the moment, we are interested in row operations on the augmented matrix of a system of linear equations. Suppose a system is changed to a new one via row operations. By considering each type of row operation, you can see that any solution of the original system remains a solution of the new system. Conversely, since the original system can be produced via row operations on the new system, each solution of the new system is also a solution of the original system. This discussion justifies the following statement.

数学代写|线性代数代写linear algebra代考|Existence and Uniqueness Questions

Section $1.2$ will show why a solution set for a linear system contains either no solutions, one solution, or infinitely many solutions. Answers to the following two questions will determine the nature of the solution set for a linear system.

To determine which possibility is true for a particular system, we ask two questions.

These two questions will appear throughout the text, in many different guises. This section and the next will show how to answer these questions via row operations on the augmented matrix.
EXAMPLE 2 Determine if the following system is consistent:
$$
\begin{aligned}
x_1-2 x_2+x_3 & =0 \
2 x_2-8 x_3 & =8 \
5 x_1-5 x_3 & =10
\end{aligned}
$$
SOLUTION This is the system from Example 1. Suppose that we have performed the row operations necessary to obtain the triangular form
$$
\begin{aligned}
x_1-2 x_2+x_3 & =0 \
x_2-4 x_3 & =4 \
x_3 & =-1
\end{aligned} \quad\left[\begin{array}{rrrr}
1 & -2 & 1 & 0 \
0 & 1 & -4 & 4 \
0 & 0 & 1 & -1
\end{array}\right]
$$ At this point, we know $x_3$. Were we to substitute the value of $x_3$ into equation 2 , we could compute $x_2$ and hence could determine $x_1$ from equation 1 . So a solution exists; the system is consistent. (In fact, $x_2$ is uniquely determined by equation 2 since $x_3$ has only one possible value, and $x_1$ is therefore uniquely determined by equation 1 . So the solution is unique.)

线性代数代考

数学代写|线性代数代写linear algebra代考|Solving a Linear System

本节和下一节描述用于求解线性系统的算法或系统过程。基本策略是用更容易解决的等效系统（即具有相同解集的系统）替换一个系统。

粗略地说，使用X1在一个系统的第一个方程中消除项X1其他方程中的项。然后使用X2第二个方程中的项以消除X2其他方程中的项，依此类推，直到您最终获得一个非常简单的等效方程组。

三个基本运算用于简化线性系统：将一个方程式替换为其自身和另一个方程式的倍数之和，交换两个方程式，以及将一个方程式中的所有项乘以一个非零常数。在第一个示例之后，您将看到为什么这三个操作不会改变系统的解决方案集。

行运算可以应用于任何矩阵，而不仅仅是作为线性系统的增广矩阵出现的矩阵。如果存在将一个矩阵转换为另一个矩阵的一系列基本行操作，则两个矩阵称为行等价矩阵。
重要的是要注意行操作是可逆的。如果两行互换，它们可以通过另一个互换返回到它们的原始位置。如果一行按非零常量缩放C，然后将新行乘以1/C产生原始行。最后，考虑涉及两行的替换操作——比如第 1 行和第 2 行——并假设C将第 1 行添加到第 2 行以生成新的第 2 行的次数。要“反转”此操作，请添加−C将第 1 行乘以（新）第 2 行并获得原始第 2 行。参见练习29−32在本节末尾。

目前，我们感兴趣的是对线性方程组的增广矩阵进行行运算。假设通过行操作将一个系统更改为一个新系统。通过考虑每种类型的行操作，您可以看到原始系统的任何解决方案仍然是新系统的解决方案。反之，由于原系统可以通过对新系统的行操作产生，所以新系统的每一个解也是原系统的一个解。该讨论证明了以下陈述。

数学代写|线性代数代写linear algebra代考|Existence and Uniqueness Questions

部分 $1.2$ 将说明为什么线性系统的解集包含无解、一个解或无限多个解。以下两个问题的答案将决定线性系统解集的性质。
为了确定对于特定系统哪种可能性为真，我们提出两个问题。
这两个问题将以多种不同的形式出现在全文中。本节和下一节将展示如何通过对增广矩阵进行行操作来回答这些问题。
示例 2 确定以下系统是否一致:
$$
x_1-2 x_2+x_3=02 x_2-8 x_3 \quad=85 x_1-5 x_3=10
$$
解决方案这是示例 1 中的系统。假设我们已经执行了获得三角形所需的行操作
$$
x_1-2 x_2+x_3=0 x_2-4 x_3 \quad=4 x_3=-1 \quad\left[\begin{array}{llllllllllll}
1 & -2 & 1 & 0 & 0 & 1 & -4 & 4 & 0 & 0 & 1 & -1
\end{array}\right]
$$
此时，我们知道 $x_3$. 如果我们用 $x_3$ 代入等式 2 ，我们可以计算 $x_2$ 因此可以确定 $x_1$ 从等式 1 。所以存在解决方案；该系统是一致的。（实际上， $x_2$ 由等式 2 唯一确定，因为 $x_3$ 只有一个可能的值，并且 $x_1$ 因此由等式 1 唯一确定。所以解是唯一的。)

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写