相信许多留学生对数学代考都不陌生,国外许多大学都引进了网课的学习模式。网课学业有利有弊,学生不需要到固定的教室学习,只需要登录相应的网站研讨线上课程即可。但也正是其便利性,线上课程的数量往往比正常课程多得多。留学生课业深重,时刻名贵,既要学习知识,又要结束多种类型的课堂作业,physics作业代写,物理代写,论文写作等;网课考试很大程度增加了他们的负担。所以,您要是有这方面的困扰,不要犹疑,订购myassignments-help代考渠道的数学代考服务,价格合理,给你前所未有的学习体会。

我们的数学代考服务适用于那些对课程结束没有掌握,或许没有满足的时刻结束网课的同学。高度匹配专业科目,按需结束您的网课考试、数学代写需求。担保买卖支持,100%退款保证,免费赠送Turnitin检测报告。myassignments-help的Math作业代写服务,是你留学路上忠实可靠的小帮手!


数学代写|变分法代写Calculus of Variations代考|Variational Problems with Fixed Boundaries

The calculus of variations is also called the variational methods or variational calculus, it is a branch of mathematical analysis began to grow at the end of the 17th century, it is a science to study the definite integral type extremum of a functional which depends on some unknown functions. In short, the method to find the extremum of a functional is called the calculus of variations. The problem to find the extremum of a functional is called the variational problem, variation problem or variational principle. On February 5, 1733, Clairaut published the first treatise of the variational methods Sur quelques questions de maximis et minimis. The work published by Euler in 1744 Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solution Problematis Isoperimetrici Latissimo sensu Accepti ( $A$ method of finding curves which have a property of extremes or solution of the isoperimetric problem, if it is understood in the broadest sense of the word) marked the birth of the calculus of variations as a new branch of mathematics. The word variational methods was proposed for the first time by Lagrange in August 1755 in a letter to Euler, He called it the method of variation, while Euler in a paper in 1756 proposed the word the calculus

The calculus of variations is an important part of functional analysis, but calculus of variations appeared first, and the functional analysis appeared later.

This chapter through the examples of several classical variational problems illustrates the concepts of functional and variation. Mainly discuss the first variation of functional, necessary conditions of extremum of a functional, Euler equations, special cases of Euler equations, and solving methods of different types of extremal functions of functionals under the fixed boundary conditions, particularly discuss the variational problems of the complete functional.

数学代写|变分法代写Calculus of Variations代考|Examples of the Classical Variational Problems

The basic problem of variational methods is to find the extremal problems of functionals and the corresponding extremal functions. In order to show the research contents of variational methods, first embark from the several classical variational examples to raise the concept of functional.

Example 2.1.1 The brachistochrone problem, problem of brachistochrone or problem of curve of steepest descent. This is one of the earliest appeared variational problems in the history, which was usually considered the beginning of the history of the variational methods, was also a symbol of the development of the variational methods. It was first proposed by Galileo in 1630, he systematically studied the problem again in 1638 , but at that time he gave the wrong results, he thought this was a circular arc curve. The substantial research of variational method was that John Bernoulli wrote to his brother Jacob Bernoulli an open letter on the Leipziger Acta Eurditorum in the June 1696 issue to ask for the solution to the problem. The formulation of the problem was: Assuming that $A$ and $B$ are the two points which are not in the same vertical straight line in a vertical plane, in all the plane curves joining point $A$ and point $B$, determine a curve, such that the time needed is the shortest when a particle that is acted on only by gravity and the initial velocity is zero moves from point $A$ to point $B$ along the curve. This problem had caused many mathematicians’ interest at that time. After Newton heard the news on January 29, 1697, he solved this problem on the same day. Leibniz, Bernoulli brothers and L’Hospital et al. all studied this problem, they obtained correct results in different ways, among them, Jacob Bernoulli started from geometric intuition, he gave the more general solution, the solution took a big step towards the direction of the variational methods. Except Jacob Bernoulli’s method of solution, others’ methods of solution were published on the Acta eurditorum in the May 1697 issue.

Solution The particle motion time depends not only on the length of the path, but also is associated with the speed. In all the curves joining point $A$ and point $B$, the straight line distance $A B$ is the shortest (see the solution of Example 2.5.11), but it is not necessarily a particle motion time shortest path. Now to establish the mathematical model of this problem. As shown in Fig. 2.1, taking $A$ as the origin of plane rectangular coordinate system, $x$ axis is put in a horizontal position, the direction of $y$ axis is downward. Obviously, the brachistochrone should be in the plane. Thus the coordinate of point $A$ is $(0,0)$. Let the coordinate of point $B$ be $\left(x_1, y_1\right)$, the equation of a curve joining point $A$ and point $B$ is
$$
y=y(x) \quad\left(0 \leq x \leq x_1\right)
$$

数学代写|变分法代写Calculus of Variations代考|МАТH5451

数学代写|变分法代写Calculus of Variations代考|Variational Problems with Fixed Boundaries

变分法又称变分法或变分微积分,是17世纪末开始发展起来的数学分析的一个分支,是研究函数的定积分型极值的一门科学,它依赖于一些未知功能。简而言之,求泛函极值的方法称为变分法。求泛函极值的问题称为变分问题、变分问题或变分原理。1733 年 2 月 5 日,Clairaut 发表了关于变分方法 Sur quelques questions de maximis et minimis 的第一篇论文。Euler 在 1744 Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solution Problematis Isoperimetrici Latissimo sensu Accepti 中发表的作品 (一个寻找具有极值性质的曲线的方法或等周问题的解,如果从最广泛的意义上理解的话)标志着变分法作为一个新的数学分支的诞生。变分法这个词是拉格朗日于 1755 年 8 月在给欧拉的一封信中首次提出的,他称之为变分法,而欧拉在 1756 年的一篇论文中提出了微积分这个词

变分法是泛函分析的重要组成部分,但变分法先出现,泛函分析出现后。

本章通过几个经典变分问题的例子说明泛函和变分的概念。主要讨论泛函的一阶变分、泛函极值的必要条件、欧拉方程组、欧拉方程组的特例、泛函不同类型极值函数在固定边界条件下的求解方法,特别讨论了泛函的变分问题。功能性的。

数学代写|变分法代写Calculus of Variations代考|Examples of the Classical Variational Problems

变分法的基本问题是求泛函的极值问题和对应的极值函数。为了展示变分方法的研究内容,首先从几个经典的变分例子出发,提出泛函的概念。

例 2.1.1 brachistochrone 问题,brachistochrone 问题或最速下降曲线问题。这是历史上最早出现的变分问题之一,通常被认为是变分方法历史的开端,也是变分方法发展的标志。它是伽利略在1630年首次提出的,1638年他又系统地研究了这个问题,但当时他给出了错误的结果,他认为这是一条圆弧曲线。对变分法的实质性研究是约翰·伯努利在 1696 年 6 月的《Leipziger Acta Eurditorum》上给他的兄弟雅各布·伯努利写了一封公开信,要求解决这个问题。问题的表述是:假设一个和乙是在一个垂直平面中不在同一条垂直直线上的两点,在所有平面曲线的连接点一个并指出乙,确定一条曲线,使得仅受重力作用且初速度为零的粒子从点移动所需的时间最短一个指向乙沿着曲线。这个问题在当时引起了很多数学家的兴趣。牛顿在 1697 年 1 月 29 日听到这个消息后,当天就解决了这个问题。Leibniz、Bernoulli 兄弟和 L’Hospital 等人。所有人都研究过这个问题,他们以不同的方式得到了正确的结果,其中,Jacob Bernoulli 从几何直觉出发,给出了更一般的解决方案,该解决方案朝着变分方法的方向迈出了一大步。除了 Jacob Bernoulli 的解法外,其他人的解法都发表在 1697 年 5 月号的 Acta eurditorum 上。

解决方案 质点运动时间不仅取决于路径的长度,还与速度有关。在所有的曲线连接点一个并指出乙, 直线距离一个乙是最短的(见例2.5.11的解法),但不一定是质点运动时间最短路径。现在来建立这个问题的数学模型。如图 2.1 所示,取一个作为平面直角坐标系的原点,X轴放置在水平位置,方向是轴向下。很明显,brachistochrone 应该在平面上。因此点的坐标一个是(0,0). 设点坐标乙是(X1,是1), 曲线连接点的方程一个并指出乙是

是=是(X)(0≤X≤X1)

数学代写|变分法代写Calculus of Variations代考

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址,相关账户,以及课程名称,Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明,让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb,费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵),报价后价格觉得合适,可以先付一周的款,我们帮你试做,满意后再继续,遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款,全款,周付款,周付款一方面方便大家查阅自己的分数,一方面也方便大家资金周转,注意:每周固定周一时先预付下周的定金,不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

留学生代写覆盖学科?

代写学科覆盖Math数学,经济代写,金融,计算机,生物信息,统计Statistics,Financial Engineering,Mathematical Finance,Quantitative Finance,Management Information Systems,Business Analytics,Data Science等。代写编程语言包括Python代写、Physics作业代写、物理代写、R语言代写、R代写、Matlab代写、C++代做、Java代做等。

数学作业代写会暴露客户的私密信息吗?

我们myassignments-help为了客户的信息泄露,采用的软件都是专业的防追踪的软件,保证安全隐私,绝对保密。您在我们平台订购的任何网课服务以及相关收费标准,都是公开透明,不存在任何针对性收费及差异化服务,我们随时欢迎选购的留学生朋友监督我们的服务,提出Math作业代写、数学代写修改建议。我们保障每一位客户的隐私安全。

留学生代写提供什么服务?

我们提供英语国家如美国、加拿大、英国、澳洲、新西兰、新加坡等华人留学生论文作业代写、物理代写、essay润色精修、课业辅导及网课代修代写、Quiz,Exam协助、期刊论文发表等学术服务,myassignments-help拥有的专业Math作业代写写手皆是精英学识修为精湛;实战经验丰富的学哥学姐!为你解决一切学术烦恼!

物理代考靠谱吗?

靠谱的数学代考听起来简单,但实际上不好甄别。我们能做到的靠谱,是把客户的网课当成自己的网课;把客户的作业当成自己的作业;并将这样的理念传达到全职写手和freelancer的日常培养中,坚决辞退糊弄、不守时、抄袭的写手!这就是我们要做的靠谱!

数学代考下单流程

提早与客服交流,处理你心中的顾虑。操作下单,上传你的数学代考/论文代写要求。专家结束论文,准时交给,在此过程中可与专家随时交流。后续互动批改

付款操作:我们数学代考服务正常多种支付方法,包含paypal,visa,mastercard,支付宝,union pay。下单后与专家直接互动。

售后服务:论文结束后保证完美经过turnitin查看,在线客服全天候在线为您服务。如果你觉得有需求批改的当地能够免费批改,直至您对论文满意为止。如果上交给教师后有需求批改的当地,只需求告诉您的批改要求或教师的comments,专家会据此批改。

保密服务:不需求提供真实的数学代考名字和电话号码,请提供其他牢靠的联系方法。我们有自己的工作准则,不会泄露您的个人信息。

myassignments-help擅长领域包含但不是全部:

myassignments-help服务请添加我们官网的客服或者微信/QQ,我们的服务覆盖:Assignment代写、Business商科代写、CS代考、Economics经济学代写、Essay代写、Finance金融代写、Math数学代写、report代写、R语言代考、Statistics统计学代写、物理代考、作业代写、加拿大代考、加拿大统计代写、北美代写、北美作业代写、北美统计代考、商科Essay代写、商科代考、数学代考、数学代写、数学作业代写、physics作业代写、物理代写、数据分析代写、新西兰代写、澳洲Essay代写、澳洲代写、澳洲作业代写、澳洲统计代写、澳洲金融代写、留学生课业指导、经济代写、统计代写、统计作业代写、美国Essay代写、美国代考、美国数学代写、美国统计代写、英国Essay代写、英国代考、英国作业代写、英国数学代写、英国统计代写、英国金融代写、论文代写、金融代考、金融作业代写。