微积分网课代修|常微分方程代写Ordinary Differential Equation代考|MATH350 Existence and Uniqueness

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|MATH350 Existence and Uniqueness

简单的说,学好微积分(数学分析)是一个毁灭自己的先天直觉然后重新塑造一个后天直觉。

转变思维永远不是简单,但是不转变,贪图一时的捷径只是饮鸩止渴罢了。高中的时候,我一个同学很背单词的时候喜欢用汉字去拼那些单词的发音,还喜欢学各种解题技巧,这个时候我和他的成绩是一样的。

国外的老师较为看重学生homework的完成情况,对于同学们来说,完成一门科目作业并获得不错的成绩是尤为重要的事情。但对于不少同学来说,在自身英语说存在局限的情况下,当数学基础较为薄弱时,微积分作业的难度一下子就提升了,很难独立完成微积分作业。Calculus-do™提供的专业微积分代写能为大家解决所有的学术困扰,我们不仅会帮大家完成作业,还提供相应的数学知识辅导课程,以此来提高同学们学习能力。

我们提供的econ代写服务范围广, 其中包括但不限于:

  • 单变量微积分
  • 多变量微积分
  • 傅里叶级数
  • 黎曼积分
  • ODE
  • 微分学
微积分网课代修|常微分方程代写Ordinary Differential Equation代考|MATH350 Existence and Uniqueness

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|Existence and Uniqueness

Let $J \subseteq \mathbb{R}, U \subseteq \mathbb{R}^{n}$, and $\Lambda \subseteq \mathbb{R}^{k}$ be open subsets, and suppose that $f: J \times U \times \Lambda \rightarrow \mathbb{R}^{n}$ is a smooth function. Here the term “smooth” means that the function $f$ is continuously differentiable. An ordinary differential equation (ODE) is an equation of the form
$$
\dot{x}=f(t, x, \lambda)
$$
where the dot denotes differentiation with respect to the independent variable $t$ (usually a measure of time), the dependent variable $x$ is a vector of state variables, and $\lambda$ is a vector of parameters. As convenient terminology,especially when we are concerned with the components of a vector differential equation, we will say that equation (1.1) is a system of differential equations. Also, if we are interested in changes with respect to parameters, then the differential equation is called a family of differential equations.

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|Types of Differential Equations

Differential equations may be classified in several different ways. In this section we note that the independent variable may be implicit or explicit, and that higher order derivatives may appear.
An autonomous differential equation is given by
$$
\dot{x}=f(x, \lambda), \quad x \in \mathbb{R}^{n}, \quad \lambda \in \mathbb{R}^{k} ;
$$
that is, the function $f$ does not depend explicitly on the independent variable. If the function $f$ does depend explicitly on $t$, then the corresponding differential equation is called nonautonomous.

In physical applications, we often encounter equations containing second, third, or higher order derivatives with respect to the independent variable. These are called second order differential equations, third order differential equations, and so on, where the the order of the equation refers to the order of the highest order derivative with respect to the independent variable that appears explicitly. In this hierarchy, a differential equation is called a first order differential equation.

Recall that Newton’s second law-the rate of change of the linear momentum acting on a body is equal to the sum of the forces acting on the body-involves the second derivative of the position of the body with respect to time. Thus, in many physical applications the most common differential equations used as mathematical models are second order differential equations. For example, the natural physical derivation of van der Pol’s equation leads to a second order differential equation of the form
$$
\ddot{u}+b\left(u^{2}-1\right) \dot{u}+\omega^{2} u=a \cos \Omega t .
$$

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|MATH350 Existence and Uniqueness

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|Existence and Uniqueness


让 $J \subseteq \mathbb{R}, U \subseteq \mathbb{R}^{n}$ ,和 $\Lambda \subseteq \mathbb{R}^{k}$ 是开放子集,并假设 $f: J \times U \times \Lambda \rightarrow \mathbb{R}^{n}$ 是一 个平滑函数。这里的“平滑”是指函数 $f$ 是连续可微的。常微分方程 (ODE) 是以下形式的 方程
$$
\dot{x}=f(t, x, \lambda)
$$
其中点表示相对于自变量的微分 $t$ (通常是时间的度量),因变量 $x$ 是状态变量的向量, 并且 $\lambda$ 是参数向量。作为一个方便的术语,特别是当我们关心向量微分方程的分量时, 我们会说方程 (1.1) 是一个微分方程组。此外,如果我们对参数的变化感兴趣,则微分 方程称为微分方程族。


微积分网课代修|常微分方程代写Ordinary Differential Equation代考|Types of Differential Equations


微分方程可以以几种不同的方式分类。在本节中,我们注意到自变量可能是隐式的或显
式的,并且可能会出现高阶导数。
一个自治微分方程由下式给出
$$
\dot{x}=f(x, \lambda), \quad x \in \mathbb{R}^{n}, \quad \lambda \in \mathbb{R}^{k} ;
$$
也就是函数 $f$ 不明确依赖于自变量。如果函数 $f$ 确实明确地取决于 $t$ ,则对应的微分方程 称为非自治的。
在物理应用中,我们经常遇到包含关于自变量的二阶、三阶或更高阶导数的方程。这些 被称为二阶微分方程、三阶微分方程等,其中方程的阶是指关于显式出现的自变量的最 高阶导数的阶。在这种层次结构中,微分方程称为一阶微分方程。
回想一下牛顿第二定律一一作用在物体上的线性动量的变化率等于作用在物体上的力的 总和一一涉及物体位置对时间的二阶导数。因此,在许多物理应用中,用作数学模型的 最常见的微分方程是二阶微分方程。例如,范德波尔方程的自然物理推导导致了形式为 的二阶微分方程
$$
\ddot{u}+b\left(u^{2}-1\right) \dot{u}+\omega^{2} u=a \cos \Omega t .
$$

微积分网课代修|常微分方程代写Ordinary Differential Equation代考|MATH350 Existence and Uniqueness
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