英语翻译摘要近些年来对闭合积分的研究已经越来越深入，闭合积分由空间闭曲线积分到空间闭曲面积分已经有很多的解决方法出现了，如高斯公式，格林公式等，对于解决围道积分的此类

英语翻译摘要近些年来对闭合积分的研究已经越来越深入，闭合积分由空间闭曲线积分到空间闭曲面积分已经有很多的解决方法出现了，如高斯公式，格林公式等，对于解决围道积分的此类
英语翻译
摘要
近些年来对闭合积分的研究已经越来越深入，闭合积分由空间闭曲线积分到空间闭曲面积分已经有很多的解决方法出现了，如高斯公式，格林公式等，对于解决围道积分的此类方法都有很广泛的应用。由此我们很容易知道围道积分的研究意义，所以我们确定了本文的研究方向。
本文对围道积分的发展历程进行了研究和概括，接着我们对围道积分中的柯西积分定理运用了新方法进行证明，而后对定理进行了推广，研究了柯西积分定理的推广意义。而后，我们将柯西积分定理在定积分和数理方程上进行应用，研究了利用柯西积分定理和留数定理解决数学和物理问题的方法，并给出相应的例子，使这些定理在应用上可以更简单的被理解。
同时，本文也将柯西积分定理和留数定理与级数展开相结合，研究他们在解决实际问题上的使用，本文具体研究了多元傅里叶级数的使用，并利用级数和柯西积分定理求解相应的积分问题。
本文的主要研究内容是围绕柯西积分定理和留数定理展开的，所以本文对围道积分的研究可以转化为对复积分的研究。

英语翻译摘要近些年来对闭合积分的研究已经越来越深入，闭合积分由空间闭曲线积分到空间闭曲面积分已经有很多的解决方法出现了，如高斯公式，格林公式等，对于解决围道积分的此类
Summary in recent years,research has become more of a closed score,points from
closed curves in space points to the closed space closed surface integral has
many solutions appear,such as the Gauss formula green formula for solving
contour integral which have a very wide range of applications.It is easy to
know the significance of contour integral,we determine the direction of this
article.This contour integral conducted research and provides an overview of
the history,then our contour integrals of Cauchy integral theorem using new
methods to prove that,then the theorem was promoted significance research on
generalization of the Cauchy integral theorem.Then,we will be in definite
integrals and Cauchy integral theorem of mathematical equations to be applied,
studied using residue theorem and Cauchy integral theorem to solve problems of
mathematics and physics,and gives you the appropriate examples,making these
theorems in the application can be simple to understand.At the same time,also
the residue theorem and Cauchy integral theorem combined with the series
expansion,study their use in solving the practical problems,this article
examined the use of multiple Fourier series,and used progression and integrals
of Cauchy integral theorem problem.Main research contents of this article are
organized around the residue theorem and Cauchy integral theorem,so this study
on contour integral can be converted into a study of complex integration.

In recent years has become increasingly in-depth study of closed integral, closed by space closed curve integral to space has a lot of closed surface integral solution emerged, such as gauss formula, ...

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In recent years has become increasingly in-depth study of closed integral, closed by space closed curve integral to space has a lot of closed surface integral solution emerged, such as gauss formula, green's theorem, etc. To solve this kind of method of contour integral has a wide range of applications. Thus we can easily know the contour integral research significance, so we determine the research direction in this paper.
In this paper, the developing course of contour integral is studied and summarized, then the cauchy integral theorem of contour integral using the new method are verified, and then to promote theorem, cauchy integral theorem is studied in the promotion of significance. We will then go on to cauchy integral theorem application in definite integral and the mathematical equation, studied the use of residue theorem and cauchy integral theorem to solve the problems of the mathematics and physics method, and gives the corresponding examples, make on the application of the theorem can be more simple to be understood.
At the same time, this article will also be residue theorem and cauchy integral theorem and the combination of series expansion, study their use in solving practical problems, this paper studies the multiple use of Fourier series, and using series and cauchy integral theorem to solve the corresponding integral problem.
This article main research content is around the residue theorem and cauchy integral theorem, so in this paper, the study of contour integral can be converted into the study of double integral.

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如需编辑回答或插入图片，请点击标题到问题详情页Abstract
In recent years, research on closed integral has been more and more in-depth, closed integral by a closed space curve integral to the closed space curve area has ma...

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如需编辑回答或插入图片，请点击标题到问题详情页Abstract
In recent years, research on closed integral has been more and more in-depth, closed integral by a closed space curve integral to the closed space curve area has many solutions emerged, such as Gauss formula, Green formula, are widely used for solving this kind of contour integration method. It's very easy to know the meaning of the contour integral, so we determine the research direction of this paper.
In this paper, the development course of the contour integral is studied and summarized, then we on the contour integral of the Cauchy integral theorem by using the new method to prove, then the theorem is generalized, the Cauchy integral theorem popularization significance. Then, we will Cauchy integral theorem in integral and mathematical equations on the application of the method, using the Cauchy integral theorem and the residue theorem in solving mathematical and physical problems, and given some examples, the theorem in the application can be more easily understood.
At the same time, this paper will also Cauchy integral theorem and the theorem of residue and the combination of series expansion, their use in solving practical problems, this paper studies the use of multiple Fourier series, and the integration of series and Cauchy integral theorem for the corresponding.
The main content of this paper is around the Cauchy integral theorem and the residue theorem to launch, so this paper to study the contour integral is transformed into the study of the complex integral.

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