## 数学代写|偏微分方程代写partial difference equations代考|MAT412

statistics-lab™ 为您的留学生涯保驾护航 在代写偏微分方程partial difference equations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。我们的专家在代写偏微分方程partial difference equations代写方面经验极为丰富，各种代写偏微分方程partial difference equations相关的作业也就用不着说。

## 数学代写|偏微分方程代写partial difference equations代考|Laplace’s Equation

Perhaps the most important of all partial differential equations is
$$\Delta u:=u_{x_1 x_1}+u_{x_2 x_2}+\cdots+u_{x_n x_n}=0,$$
known as Laplace’s equation. You will find applications of it to problems in gravitation, elastic membranes, electrostatics, fluid flow, steady-state heat conduction and many other topics in both pure and applied mathematics.
As the remarks of the last section on ODEs indicated, the choice of boundary conditions is of paramount importance in determining the wellposedness of a given problem. The following two common types of boundary conditions on a bounded domain $\Omega \subset \mathbb{R}^n$ yield well-posed problems and will be studied in a more general context in later chapters.
Dirichlet conditions. Given a function $f: \partial \Omega \rightarrow \mathbb{R}$, we require
$$u(\mathbf{x})=f(\mathbf{x}), \quad \mathbf{x} \in \partial \Omega .$$
In the context of elasticity, $u$ denotes a change of position, so Dirichlet boundary conditions are often referred to as displacement conditions.
Neumann conditions. Given a function $f: \partial \Omega \rightarrow \mathbb{R}$, we require
$$\frac{\partial u}{\partial n}(\mathbf{x})=f(\mathbf{x}), \quad \mathbf{x} \in \partial \Omega .$$
Here $\frac{\partial u}{\partial n}$ is the partial derivative of $u$ with respect to the unit outward normal of $\partial \Omega, \mathbf{n}$. In linear elasticity $\frac{\partial u}{\partial n}(\mathbf{x})=\nabla u(\mathbf{x}) \cdot \mathbf{n}(\mathbf{x})$ can be interpreted as a force, so Neumann boundary conditions are often referred to as traction boundary conditions.

We have been intentionally vague about the smoothness required of $\partial \Omega$ and $f$, and the function space in which we wish $u$ to lie. These are central areas of concern in later chapters.

## 数学代写|偏微分方程代写partial difference equations代考|Solution by separation of variables

The first method we present for solving Laplace’s equation is the most widely used technique for solving partial differential equations: separation of variables. The technique involves reducing a partial differential equation to a system of ordinary differential equations and expressing the solution of the PDE as a sum or infinite series.

Let us consider the following Dirichlet problem on a square in the plane. Let
$$\Omega=\left{(x, y) \in \mathbb{R}^2 \mid 0<x<1, \quad 0<y<1\right} .$$
We wish to find a function $u: \bar{\Omega} \rightarrow \mathbb{R}$ satisfying Laplace’s equation
$$u_{x x}+u_{y y}=0$$

at each point in $\Omega$ and satisfying the boundary conditions
\begin{aligned} & u(0, y)=0, \ & u(1, y)=0, \ & u(x, 0)=0, \ & u(x, 1)=f(x) . \end{aligned}
The key to separation of variables is to look for solutions of (1.36) of the form
$$u(x, y)=X(x) Y(y) .$$
When we put a function of this form into (1.36), the partial derivatives in the differential equation appear as ordinary derivatives on the functions $X$ and $Y$; i.e., (1.36) becomes
$$X^{\prime \prime}(x) Y(y)+X(x) Y^{\prime \prime}(y)=0 .$$
At any point $(x, y)$ at which $u$ is nonzero we can divide this equation by $u$ and rearrange to get
$$\frac{X^{\prime \prime}(x)}{X(x)}=-\frac{Y^{\prime \prime}(y)}{Y(y)} .$$
We now argue as follows: Since the right side of the equation does not depend on the variable $x$, neither can the left side; likewise, since the left side does not depend on $y$, neither does the right side. The only function on the plane that is independent of both $x$ and $y$ is a constant, so we must have
$$\frac{X^{\prime \prime}(x)}{X(x)}=-\frac{Y^{\prime \prime}(y)}{Y(y)}=\lambda .$$
This gives us
\begin{aligned} & X^{\prime \prime}=\lambda X, \ & Y^{\prime \prime}=-\lambda Y . \end{aligned}

# 偏微分方程代写

## 数学代写|偏微分方程代写partial difference equations代考|Laplace’s Equation

$$\Delta u:=u_{x_1 x_1}+u_{x_2 x_2}+\cdots+u_{x_n x_n}=0,$$

$$u(\mathbf{x})=f(\mathbf{x}), \quad \mathbf{x} \in \partial \Omega .$$

$$\frac{\partial u}{\partial n}(\mathbf{x})=f(\mathbf{x}), \quad \mathbf{x} \in \partial \Omega .$$

## 数学代写|偏微分方程代写partial difference equations代考|Solution by separation of variables

$$\Omega=\left{(x, y) \in \mathbb{R}^2 \mid 0<x<1, \quad 0<y<1\right} .$$

$$u_{x x}+u_{y y}=0$$

\begin{aligned} & u(0, y)=0, \ & u(1, y)=0, \ & u(x, 0)=0, \ & u(x, 1)=f(x) . \end{aligned}

$$u(x, y)=X(x) Y(y) .$$

$$X^{\prime \prime}(x) Y(y)+X(x) Y^{\prime \prime}(y)=0 .$$

$$\begin{array}{r} \int_0^{\infty} \int_{-\infty}^{\infty}\left[\mathbf{u}(x, t) \cdot \phi_t(x, t)+\mathbf{f}(\mathbf{u}(x, t)) \cdot \phi_x(x, t)\right] d x d t \ +\int_{-\infty}^{\infty} \mathbf{u}_0(x) \phi(x, 0) d x=0 \end{array}$$

$$C_0^1\left(\mathbb{R}^{2+}\right):=\left{\phi \in C^1\left(\mathbb{R}^{2+}\right) \mid \exists r>0 \text { s.t. } \operatorname{supp} \phi \subset B_r((0,0)) \cap \mathbb{R}^{2+}\right} .$$

## 数学代写|偏微分方程代写partial difference equations代考|The Rankine-Hugoniot Condition

$\mathbf{u}$ 是(3.5)在$N^l$和$N^r$的经典解，

$\mathbf{u}$ 在曲线$C$处经历跳跃不连续$[\mathbf{u}]$，且

$$s[\mathbf{u}]=[\mathbf{f}(\mathbf{u})]$$

$$\mathbf{u}:=\mathbf{u}^r(\mathbf{p})-\mathbf{u}^l(\mathbf{p}):=\lim {\left(x^r, t^r\right) \rightarrow \mathbf{p}} \mathbf{p}\left(x^r, t^r\right)-\lim {\left(x^l, t^l\right) \stackrel{l}{\rightarrow} \mathbf{p}} \mathbf{u}\left(x^l, t^l\right),$$

## 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。

## 数学代写|偏微分方程代写partial difference equations代考|Math3357

statistics-lab™ 为您的留学生涯保驾护航 在代写偏微分方程partial difference equations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。我们的专家在代写偏微分方程partial difference equations代写方面经验极为丰富，各种代写偏微分方程partial difference equations相关的作业也就用不着说。

## 数学代写|偏微分方程代写partial difference equations代考|A PDE without Solutions

Every now and then a paper appears with a title like “A method to solve all partial differential equations.” The content of such papers is always very far from satisfying the claims made in the title. It is rumored that a paper of this kind inspired Lewy to construct his famous example of a linear PDE which has no solutions at all. This example also highlights the importance of analyticity in the Cauchy-Kovalevskaya result.
Theorem 2.25. For a complex-valued function $u(x, y, z)$, let
$$L u=-u_x-i u_y+2 i(x+i y) u_z .$$
Then there is a real-valued function $f(x, y, z)$, of class $C^{\infty}\left(\mathbb{R}^3\right)$, such that the equation
$$L u=f(x, y, z)$$
has no solutions of class $C^1(\Omega)$ in any open subset $\Omega \subset \mathbb{R}^3$.
We note that when $f$ is analytic, the Cauchy-Kovalevskaya theorem applies and noncharacteristic initial-value problems for (2.104) have local solutions. In contrast, for nonanalytic $f$ there may be no solutions, even if no initial conditions are prescribed.

We shall not give a full proof of the theorem, but outline some of the main ideas. First, we shall prove the following lemma.

Lemma 2.26. Let $\psi \in C^{\infty}(\mathbb{R})$ be real-valued and such that $\psi$ is not real analytic at $z_0$. Then the equation
$$L u=\psi^{\prime}(z)$$
has no solution of class $C^1$ in any neighborhood of the point $\left(0,0, z_0\right)$.

Proof. Assume the contrary and let $u$ be a solution in a neighborhood of $\left(0,0, z_0\right)$, say for $x^2+y^2<\epsilon,\left|z-z_0\right|<\epsilon$. We set
$$v(r, \theta, z)=e^{i \theta} \sqrt{r} u(\sqrt{r} \cos \theta, \sqrt{r} \sin \theta, z) .$$
After some algebra, we find that $v$ satisfies the equation
$$-2 v_r-\frac{i}{r} v_\theta+2 i v_z=\psi^{\prime}(z) .$$

## 数学代写|偏微分方程代写partial difference equations代考|An Outline of the Main Idea

Consider a system of linear equations
$$a_{i j}^k(\mathbf{x}) \frac{\partial u_j}{\partial x_k}+b_{i j}(\mathbf{x}) u_j=0, \quad i=1, \ldots, N .$$
Let $\mathbf{u}=\left(u_1, \ldots, u_N\right)$ be a solution in a “lens-shaped” domain $\Omega \subset \mathbb{R}^n$ bounded by two surfaces $S$ and $Z$. Assume that $\mathbf{u}=0$ on $Z$ and that $S$ is noncharacteristic and analytic. We also assume that the coefficients in (2.121) are analytic.

Let $v_i, i=1, \ldots, N$ be arbitrary functions in $C^1(\bar{\Omega})$. We multiply the $i$ th equation of (2.121) by $v_i$, sum over $i$, and integrate over $\Omega$. This yields
\begin{aligned} 0 & =\int_{\Omega} v_i(\mathbf{x}) a_{i j}^k(\mathbf{x}) \frac{\partial u_j}{\partial x_k}(\mathbf{x})+v_i(\mathbf{x}) b_{i j}(\mathbf{x}) u_j(\mathbf{x}) d \mathbf{x} \ & =\int_{\Omega}-\frac{\partial}{\partial x_k}\left[v_i(\mathbf{x}) a_{i j}^k(\mathbf{x})\right] u_j(\mathbf{x})+v_i(\mathbf{x}) b_{i j}(\mathbf{x}) u_j(\mathbf{x}) d \mathbf{x} \ & +\int_{\partial \Omega} a_{i j}^k(\mathbf{x}) v_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S, \end{aligned}
where $\mathbf{n}$ is the outer normal to $\partial \Omega$.
Assume now that $\mathbf{v}$ satisfies the “adjoint” system of PDEs,
$$-\frac{\partial}{\partial x_k}\left(a_{i j}^k v_i\right)+b_{i j} v_i=0, \quad j=1, \ldots, N,$$
with initial conditions
$$v_i=f_i$$
on $S$. Then $(2.122)$ reduces to
$$0=\int_S a_{i j}^k(\mathbf{x}) f_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S .$$

Assume now that $\mathbf{v}$ satisfies the “adjoint” system of PDEs,
$$-\frac{\partial}{\partial x_k}\left(a_{i j}^k v_i\right)+b_{i j} v_i=0, \quad j=1, \ldots, N,$$
with initial conditions
$$v_i=f_i$$
on $S$. Then (2.122) reduces to
$$0=\int_S a_{i j}^k(\mathbf{x}) f_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S .$$

# 偏微分方程代写

## 数学代写|偏微分方程代写partial difference equations代考|A PDE without Solutions

$$L u=-u_x-i u_y+2 i(x+i y) u_z .$$

$$L u=f(x, y, z)$$

$$L u=\psi^{\prime}(z)$$

$$v(r, \theta, z)=e^{i \theta} \sqrt{r} u(\sqrt{r} \cos \theta, \sqrt{r} \sin \theta, z) .$$

$$-2 v_r-\frac{i}{r} v_\theta+2 i v_z=\psi^{\prime}(z) .$$

## 数学代写|偏微分方程代写partial difference equations代考|An Outline of the Main Idea

$$a_{i j}^k(\mathbf{x}) \frac{\partial u_j}{\partial x_k}+b_{i j}(\mathbf{x}) u_j=0, \quad i=1, \ldots, N .$$

\begin{aligned} 0 & =\int_{\Omega} v_i(\mathbf{x}) a_{i j}^k(\mathbf{x}) \frac{\partial u_j}{\partial x_k}(\mathbf{x})+v_i(\mathbf{x}) b_{i j}(\mathbf{x}) u_j(\mathbf{x}) d \mathbf{x} \ & =\int_{\Omega}-\frac{\partial}{\partial x_k}\left[v_i(\mathbf{x}) a_{i j}^k(\mathbf{x})\right] u_j(\mathbf{x})+v_i(\mathbf{x}) b_{i j}(\mathbf{x}) u_j(\mathbf{x}) d \mathbf{x} \ & +\int_{\partial \Omega} a_{i j}^k(\mathbf{x}) v_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S, \end{aligned}

$$-\frac{\partial}{\partial x_k}\left(a_{i j}^k v_i\right)+b_{i j} v_i=0, \quad j=1, \ldots, N,$$

$$v_i=f_i$$

$$0=\int_S a_{i j}^k(\mathbf{x}) f_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S .$$

$$-\frac{\partial}{\partial x_k}\left(a_{i j}^k v_i\right)+b_{i j} v_i=0, \quad j=1, \ldots, N,$$

$$v_i=f_i$$

$$0=\int_S a_{i j}^k(\mathbf{x}) f_i(\mathbf{x}) u_j(\mathbf{x}) n_k d S .$$

## 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。

## 数学代写|常微分方程代写ordinary differential equation代考|MATH-UA262

statistics-lab™ 为您的留学生涯保驾护航 在代写常微分方程ordinary differential equation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。我们的专家在代写常微分方程ordinary differential equation代写方面经验极为丰富，各种代写常微分方程ordinary differential equation相关的作业也就用不着说。

## 数学代写|常微分方程代写ordinary differential equation代考|Preliminaries to Existence and Uniqueness of Solutions

So far, mostly we have engaged ourselves in solving DEs, tacitly assuming that there always exists a solution. However, the theory of existence and uniqueness of solutions of the initial value problems is quite complex. We begin to develop this theory for the initial value problem
$$y^{\prime}=f(x, y), \quad y\left(x_0\right)=y_0,$$
where $f(x, y)$ will be assumed to be continuous in a domain $D$ containing the point $\left(x_0, y_0\right)$. By a solution of (7.1) in an interval $J$ containing $x_0$, we mean a function $y(x)$ satisfying (i) $y\left(x_0\right)=y_0$, (ii) $y^{\prime}(x)$ exists for all $x \in J$, (iii) for all $x \in J$ the points $(x, y(x)) \in D$, and (iv) $y^{\prime}(x)=f(x, y(x))$ for all $x \in J$.

For the initial value problem (7.1) later we shall prove that the continuity of the function $f(x, y)$ alone is sufficient for the existence of at least one solution in a sufficiently small neighborhood of the point $\left(x_0, y_0\right)$. However, if $f(x, y)$ is not continuous, then the nature of the solutions of $(7.1)$ is quite arbitrary. For example, the initial value problem
$$y^{\prime}=\frac{2}{x}(y-1), \quad y(0)=0$$
has no solution, while the problem
$$y^{\prime}=\frac{2}{x}(y-1), \quad y(0)=1$$
has an infinite number of solutions $y(x)=1+c x^2$, where $c$ is an arbitrary constant.

The use of integral equations to establish existence theorems is a standard device in the theory of DEs. It owes its efficiency to the smoothening properties of integration as contrasted with coarsening properties of differentiation. If two functions are close enough, their integrals must be close enough, whereas their derivatives may be far apart and may not even exist. We shall need the following result to prove the existence, uniqueness, and several other properties of the solutions of the initial value problem (7.1).

Theorem 7.1. Let $f(x, y)$ be continuous in the domain $D$, then any solution of (7.1) is also a solution of the integral equation
$$y(x)=y_0+\int_{x_0}^x f(t, y(t)) d t$$
and conversely.
Proof. Any solution $y(x)$ of the $\mathrm{DE} y^{\prime}=f(x, y)$ converts it into an identity in $x$, i.e., $y^{\prime}(x)=f(x, y(x))$. An integration of this equality yields
$$y(x)-y\left(x_0\right)=\int_{x_0}^x f(t, y(t)) d t .$$
Conversely, if $y(x)$ is any solution of $(7.2)$ then $y\left(x_0\right)=y_0$ and since $f(x, y)$ is continuous, differentiating (7.2) we find $y^{\prime}(x)=f(x, y(x))$.

## 数学代写|常微分方程代写ordinary differential equation代考|Picard’s Method of Successive Approximations

We shall solve the integral equation (7.2) by using the method of successive approximations due to Picard. For this, let $y_0(x)$ be any continuous function (we often pick $y_0(x) \equiv y_0$ ) which we assume to be the initial approximation of the unknown solution of (7.2), then we define $y_1(x)$ as
$$y_1(x)=y_0+\int_{x_0}^x f\left(t, y_0(t)\right) d t$$
We take this $y_1(x)$ as our next approximation and substitute this for $y(x)$ on the right side of (7.2) and call it $y_2(x)$. Continuing in this way, the $(m+1)$ st approximation $y_{m+1}(x)$ is obtained from $y_m(x)$ by means of the relation
$$y_{m+1}(x)=y_0+\int_{x_0}^x f\left(t, y_m(t)\right) d t, \quad m=0,1,2, \ldots$$
If the sequence $\left{y_m(x)\right}$ converges uniformly to a continuous function $y(x)$ in some interval $J$ containing $x_0$ and for all $x \in J$ the points $\left(x, y_m(x)\right) \in D$, then using Theorem 7.8 we may pass to the limit in both sides of (8.1), to obtain
$$y(x)=\lim {m \rightarrow \infty} y{m+1}(x)=y_0+\lim {m \rightarrow \infty} \int{x_0}^x f\left(t, y_m(t)\right) d t=y_0+\int_{x_0}^x f(t, y(t)) d t,$$
so that $y(x)$ is the desired solution.

# 常微分方程代写

## 数学代写|常微分方程代写ordinary differential equation代考|Preliminaries to Existence and Uniqueness of Solutions

$$y^{\prime}=f(x, y), \quad y\left(x_0\right)=y_0,$$

$$y^{\prime}=\frac{2}{x}(y-1), \quad y(0)=0$$

$$y^{\prime}=\frac{2}{x}(y-1), \quad y(0)=1$$

$$y(x)=y_0+\int_{x_0}^x f(t, y(t)) d t$$

$$y(x)-y\left(x_0\right)=\int_{x_0}^x f(t, y(t)) d t .$$

## 数学代写|常微分方程代写ordinary differential equation代考|Picard’s Method of Successive Approximations

$$y_1(x)=y_0+\int_{x_0}^x f\left(t, y_0(t)\right) d t$$

$$y_{m+1}(x)=y_0+\int_{x_0}^x f\left(t, y_m(t)\right) d t, \quad m=0,1,2, \ldots$$

$$y(x)=\lim {m \rightarrow \infty} y{m+1}(x)=y_0+\lim {m \rightarrow \infty} \int{x_0}^x f\left(t, y_m(t)\right) d t=y_0+\int_{x_0}^x f(t, y(t)) d t,$$

## 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。