## 微积分代写Calculus代考2023

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## 微积分代写Calculus代考

#### 偏微分方程Partial Differential Equations代写代考

• 常微分方程Ordinary Differential Equations
• 微分几何学Differential Geometry

## 微积分Calculus近代史

In Europe, Bonaventure Cavalieri laid the foundations of differential and integral calculus by discussing in his dissertation the method of determining the area and volume as the sum of the areas and volumes of very fine regions.

His work on the formulation of the calculus led to the combination of Cavalieri’s calculus with the finite difference method, which appeared in Europe at about the same time. This integration was carried out by John Wallis, Isaac Barrow, and James Gregory, with Barrow and Gregory proving the Second Theorem of the Fundamental Theorem of Calculus around 1675.

Isaac Newton introduced the concepts of the law of product differentiation, the chain rule, higher-order differential notation, Taylor series, and analytic functions in a unique notation, and used them to solve problems in mathematical physics. At the time of publication, Newton replaced differentiation with equivalent geometric subjects to accommodate the mathematical terminology of the time and to avoid censure. In Mathematical Principles of Natural Philosophy, Newton used differential and integral methods to discuss a variety of problems, including the orbits of celestial bodies, the shapes of the surfaces of rotating fluids, the eccentricity of the earth, and the motion of a heavy object sliding on a pendulum. In addition to this, Newton developed the series expansion of functions, and it is clear that he understood the principles of Taylor’s series.

Gottfried Leibniz was initially suspected of plagiarizing Newton’s unpublished papers, but is now recognized as one of the original contributors to the development of calculus.
It was Gottfried Leibniz who systematized these ideas and established calculus as a rigorous discipline. At the time, he was accused of plagiarizing Newton, but today he is recognized as one of the original contributors to the establishment and development of differential and integral calculus. Leibniz explicitly defined the rules for the operation of differentials, made possible the computation of second- and higher-order derivatives, and defined Leibniz’s law and the chain rule. Unlike Newton, Leibniz was very much a formalist and spent many days agonizing over what symbols to use for each concept.

## 微积分Calculus的重难点

\begin{aligned} x_t & =f_t\left(x_{t-1}, v_t\right) \ y_t & =h_t\left(x_t, w_t\right) \end{aligned}

\begin{aligned} & x_t=F_t x_{t-1}+G_t v_t \ & y_t=H_t x_t+w_t \end{aligned}

• Exploratory data analysis探索性数据分析
• Curve fitting曲线拟合

## 时间序列分析Time Series Analysis定义

• $Y_1$：1981 年第一季度末的国内生产总值（193 505）；
• $Y_{12}$：1983 年第 4 季度末的本地生產總值 (215 584)；
• $Y_{55}$：1994 年第三季度末的本地生產總值（263 660）。

## 时间序列分析Time Series Analysis的重难点

$$f(x)=f(a)+f^{\prime}(a)(x-a)+R_2$$

$$f(x) \approx f(a)+f^{\prime}(a)(x-a)$$

$$f(x) \approx f(a)$$

$$\int_C f(z) d z=\int_{C_R} f(z) d z .$$
Thus
$$\lim {R \rightarrow \infty} \int_C f(z) d z=\lim {R \rightarrow \infty} \int_{C_R} f(z) d z=0 .$$
Hence
$$\int_C f(z) d z=0 .$$

Let $C_1$ denote the positively oriented boundary of the curve given by $|x|+|y|=2$ and $C_2$ be the positively oriented circle $|z|=4$. Apply Cauchy Integral Theorem to show that
$$\int_{C_1} f(z) d z=\int_{C_2} f(z) d z$$
when
(a) $f(z)=\frac{z+1}{z^2+1}$;
(b) $f(z)=\frac{z+2}{\sin (z / 2)}$;
(c) $f(z)=\frac{\sin (z)}{z^2+6 z+5}$.

Solution. By Cauchy Integral Theorem, $\int_{C_1} f(z) d z=\int_{C_2} f(z) d z$ if $f(z)$ is analytic on and between $C_1$ and $C_2$. Hence it is enough to show that $f(z)$ is analytic in ${|x|+|y| \geq 2,|z| \leq 4}$.
(a) $f(z)$ is analytic in ${z \neq \pm i}$. Since $\pm i \in{|x|+|y|<2}, f(z)$ is analytic in ${|x|+|y| \geq 2,|z| \leq 4}$. (b) $f(z)$ is analytic in ${z: \sin (z / 2) \neq 0}={z \neq 2 n \pi: n \in \mathbb{Z}}$. Since $2 n \pi \in{|x|+$ $|y|<2}$ for $n=0$ and $|2 n \pi|>4$ for $n \neq 0$ and $n \in \mathbb{Z}, f(z)$ is analytic in ${|x|+|y| \geq 2,|z| \leq 4}$.
(c) $f(z)$ is analytic in ${z \neq-1,-5}$. Since $-1 \in{|x|+|y|<2}$ for $n=0$ and $|-5|>4, f(z)$ is analytic in ${|x|+|y| \geq 2,|z| \leq 4}$.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## MAST20022｜Group Theory and Linear Algebra群论与线性代数 墨尔本大学

statistics-labTM为您墨尔本大学The University of Melbourne，简称UniMelb，中文简称“墨大”）Group Theory and Linear Algebra群论与线性代数澳洲代写代考辅导服务！

This subject introduces the theory of groups, which is at the core of modern algebra, and which has applications in many parts of mathematics, chemistry, computer science and theoretical physics. It also develops the theory of linear algebra, building on material in earlier subjects and providing both a basis for later mathematics studies and an introduction to topics that have important applications in science and technology.

Topics include: modular arithmetic and RSA cryptography; abstract groups, homomorphisms, normal subgroups, quotient groups, group actions, symmetry groups, permutation groups and matrix groups; theory of general vector spaces, inner products, linear transformations, spectral theorem for normal matrices, Jordan normal form.

## Group Theory and Linear Algebra群论与线性代数案例

Let $\mathbf{A}$ be a $n$ by $n$ matrix, then the following 4 statements are equivalent:
(a) The matrix $\mathbf{A}$ is invertible (non-singular).
(b) The linear system $\mathbf{A x}=\mathbf{O}$ only has the trivial solution $\mathbf{x}=\mathbf{O}$.

(c) The reduced row echelon form of the matrix $\mathbf{A}$ is the identity matrix $\mathbf{I}$.
(d) $\mathbf{A}$ is a product of elementary matrices.

We show (a) implies (b) and (b) implies (c) and (c) implies (d) and (d) implies (a). In symbolic notation, this is (a) $\Rightarrow(b) \Rightarrow(c) \Rightarrow(d) \Rightarrow(a)$. We first prove (a) implies (b).
For $(\mathbf{a}) \Rightarrow(\mathbf{b})$ :
We assume statement (a) to be true and deduce statement (b).
By assuming $\mathbf{A}$ is an invertible matrix we need to show that the linear system $\mathbf{A x}=\mathbf{O}$ only has the trivial solution $\mathbf{x}=\mathbf{O}$. Consider the linear system $\mathbf{A x}=\mathbf{O}$, because $\mathbf{A}$ is invertible, therefore there is a unique matrix $\mathbf{A}^{-1}$ such that $\mathbf{A}^{-1} \mathbf{A}=\mathbf{I}$. Multiplying both sides of $\mathbf{A x}=\mathbf{O}$ by $\mathbf{A}^{-1}$ yields
\begin{aligned} & \underbrace{\mathbf{A}^{-1} \mathbf{A} \mathbf{x}}_{=\mathbf{I}}=\mathbf{A}^{-1} \mathbf{O} \ & \qquad \mathbf{I x}=\mathbf{A}^{-1} \mathbf{O}=\mathbf{O} \ & \mathbf{I x}=\mathbf{O} \text { which gives } \mathbf{x}=\mathbf{O} \quad[\text { because } \mathbf{I x}=\mathbf{x}] \end{aligned}
The answer $\mathbf{x}=\mathbf{O}$ means that we only have the trivial solution $\mathbf{x}=\mathbf{O}$. Hence we have shown (a) $\Rightarrow$ (b). Next we prove (b) implies (c).
For $(b) \Rightarrow(c)$ :
The procedure to prove (b) $\Rightarrow$ (c) is to assume statement (b) and deduce (c). This time we assume that $\mathbf{A x}=\mathbf{O}$ only has the trivial solution $\mathbf{x}=\mathbf{O}$ and, by using this, prove that the reduced row echelon form of the matrix $\mathbf{A}$ is the identity matrix $\mathbf{I}$.

The reduced row echelon form of matrix A cannot have a row (equation) of zeros, otherwise we would have $n$ unknowns but less than $n$ non-zero rows (equations), which means that by Proposition (1.31): if $r<n$ then the linear system $\mathbf{A x}=\mathbf{O}$ has an infinite number of solutions.

We would have an infinite number of solutions. However, we only have a unique solution to $\mathbf{A x}=\mathbf{O}$, therefore there are no zero rows.

Question (7) of Exercises 1.7 claims: the reduced row echelon form of a matrix is either the identity $\mathbf{I}$ or it contains a row of zeros.
Hence the reduced row echelon form of $\mathbf{A}$ is the identity matrix. We have (b) $\Rightarrow$ (c). For $(c) \Rightarrow$ (d):
In this case, we assume part (c), that is ‘the reduced row echelon form of the matrix $\mathbf{A}$ is the identity matrix I’, which means that the matrix $\mathbf{A}$ is row equivalent to the identity matrix I. By definition (1.33):
$\mathbf{B}$ is row equivalent to a matrix $A$ if and only if $\mathbf{B}=\mathbf{E}n \mathbf{E}{n-1} \cdots \mathbf{E}2 \mathbf{E}_1 \mathbf{A}$. There are elementary matrices $\mathbf{E}_1, \mathbf{E}_2, \mathbf{E}_3, \ldots$ and $\mathbf{E}_k$ such that \begin{aligned} \mathbf{A} & =\mathbf{E}_k \mathbf{E}{k-1} \cdots \mathbf{E}2 \mathbf{E}_1 \mathbf{I} \ & =\mathbf{E}_k \mathbf{E}{k-1} \cdots \mathbf{E}_2 \mathbf{E}_1 \end{aligned}
[because $\mathbf{A}$ is row equivalent to $\mathbf{I}$ ]

This shows that matrix $\mathbf{A}$ is a product of elementary matrices. We have (c) $\Rightarrow$ (d). For $(\mathbf{d}) \Rightarrow$ (a):
In this last case, we assume that matrix $\mathbf{A}$ is a product of elementary matrices and deduce that matrix A is invertible. By Proposition (1.34): an elementary matrix is invertible.

We know that elementary matrices are invertible (have an inverse) and therefore the matrix multiplication $\mathbf{E}k \mathbf{E}{k-1} \cdots \mathbf{E}2 \mathbf{E}_1$ is invertible. In fact, we have \begin{aligned} \mathbf{A}^{-1} & =\left(\mathbf{E}_k \mathbf{E}{k-1} \cdots \mathbf{E}2 \mathbf{E}_1\right)^{-1} \ & =\mathbf{E}_1^{-1} \mathbf{E}_2^{-1} \cdots \mathbf{E}{k-1}^{-1} \mathbf{E}_k^{-1} \quad\left[\text { because }(\mathbf{X Y Z})^{-1}=\mathbf{Z}^{-1} \mathbf{Y}^{-1} \mathbf{X}^{-1}\right] \end{aligned}
Hence the matrix $\mathbf{A}$ is invertible, which means that we have proven (d) $\Rightarrow$ (a). We have shown (a) $\Rightarrow$ (b) $\Rightarrow$ (c) $\Rightarrow$ (d) $\Rightarrow$ (a) which means that the four statements (a), (b), (c) and (d) are equivalent.

The proof of this result can be made a lot easier if we understand some mathematical logic. Generally to prove a statement of the type $P \Leftrightarrow Q$ we assume $P$ to be true and then deduce $Q$. Then we assume $Q$ to be true and deduce $P$.
However, in mathematical logic this can also be proven by showing:
$$(\operatorname{Not} P) \Leftrightarrow(\operatorname{Not} Q)$$
Means that $(\operatorname{Not} P) \Rightarrow(\operatorname{Not} Q)$ and $(\operatorname{Not} Q) \Rightarrow(\operatorname{Not} P)$. This is because statements $P \Leftrightarrow Q$ and $(\operatorname{Not} P) \Leftrightarrow($ Not $Q)$ are equivalent. See website for more details.
The following demonstrates this proposition.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。