### 数学代写|多变量微积分代写multivariable calculus代考|МАTH263

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|多变量微积分代写multivariable calculus代考|Introduction to sets

It is not possible to provide a picture of $\boldsymbol{x} \in \mathbb{R}^n$ for $n>3$ (nor $\mathbb{R}^n$ itself). However, there should be no cause for concern as points in $\mathbb{R}^n$ behave the same as points in $\mathbb{R}^2$ and $\mathbb{R}^3$. That is, they follow the same set of rules. So it is enough to be familiar with points and point operations in $\mathbb{R}^2$ and $\mathbb{R}^3$, and then being able to generalize their properties. The most important point operations are listed below.
Vector algebra laws.
Let $\boldsymbol{x}, \boldsymbol{y} \in \mathbb{R}^n$ and $\lambda \in \mathbb{R}$.
At its most. basic description, $\mathbb{R}^n$ is an example of a linear vector space which is characterized by the two properties of addition and scalar multiplication:

(a) $\boldsymbol{x}+\boldsymbol{y}=\left(x_1+y_1, x_2+y_2, \ldots, x_n+y_n\right) \in \mathbb{R}^n$.
(b) $\lambda \boldsymbol{x}=\left(\lambda x_1, \lambda x_2, \ldots, \lambda x_n\right) \in \mathbb{R}^n$.
As a direct generalization of the scalar product of $2(\mathrm{c})$, points in $\mathbb{R}^n$ satisfy the so-called inner product,
(c) $\boldsymbol{x} \cdot \boldsymbol{y}=x_1 y_1+\ldots+x_n y_n \in \mathbb{R} \quad-\mathbb{R}^n$ is called an inner product space.
Finally, there are the following generalizations to $\mathbb{R}^n$ of the two fundamental geometric measures:
(d) $|x|=\sqrt{\boldsymbol{x} \cdot \boldsymbol{x}}=\sqrt{x_1^2+\cdots+x_n^2}$

• the length of $\boldsymbol{x}$.
(e) $|\boldsymbol{x}-\boldsymbol{y}|=\sqrt{\left(x_1-y_1\right)^2+\cdots+\left(x_n-y_n\right)^2}$
• the distance between points.
With this distance property $\mathbb{R}^n$ is also a so-called metric space, since the distance between points is one measure or metric that allows a geometric characterization of a space.

## 数学代写|多变量微积分代写multivariable calculus代考|Real-valued functions

In Chapters 2,3 , and 4 , we focus attention almost exclusively on scalarvalued functions of many variables, while in Chapter 5 we extend the ideas to vector-valued functions. In both contexts the following introduction to fundamental properties of multi-valued functions is invaluable. To start, we introduce some more notation and a pictorial view of what functions do.
In single-variable calculus we have the following scenario:
Let $y=f(x)$. The “graph” of $f$ is the set of ordered pairs ${(x, f(x))} \in \mathbb{R}^2$. This is shown graphically in Figure $1.11$ where the independent variable $x$ and dependent variable $y$ are plotted on mutually orthogonal axes.

This way of visualizing functions of one variable was introduced in the early $17^{\text {th }}$ century by René Descartes [17], and is named the Cartesian representa tion in recognition. It is quite a useful means of illustrating function dependence and function properties, especially for functions of one or two variables.
It ceases to be as useful, however, for functions of more than two variables. For the latter cases one resorts to simply considering a set-mapping picture. For the case $y=f(x)$ this is a simple interval-to-interval map as shown in Figure $1.12$.

# 多变量微积分代写

## 数学代写|多变量微积分代写multivariable calculus代考|Introduction to sets

(一个) $\boldsymbol{x}+\boldsymbol{y}=\left(x_1+y_1, x_2+y_2, \ldots, x_n+y_n\right) \in \mathbb{R}^n$.
(二) $\lambda \boldsymbol{x}=\left(\lambda x_1, \lambda x_2, \ldots, \lambda x_n\right) \in \mathbb{R}^n$.

(c) $\boldsymbol{x} \cdot \boldsymbol{y}=x_1 y_1+\ldots+x_n y_n \in \mathbb{R} \quad-\mathbb{R}^n$ 称为内积空间。

(d) $|x|=\sqrt{\boldsymbol{x} \cdot \boldsymbol{x}}=\sqrt{x_1^2+\cdots+x_n^2}$

• 的长度 $x$ 囯
(和) $|\boldsymbol{x}-\boldsymbol{y}|=\sqrt{\left(x_1-y_1\right)^2+\cdots+\left(x_n-y_n\right)^2}$
• 点之间的距离。
有了这个距离属性 $\mathbb{R}^n$ 也是所谓的度量空间，因为点之间的距离是允许对空间进行几何表征的一种度量或 度量。

## 有限元方法代写

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## MATLAB代写

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