首先这个中文摘要要先整理一下
数学分析作为理、工科院校一门重要的基础学科,有其固有的特点,即高度的抽象性、严密的逻辑性和广泛的应用性.它对许多后续课程的学习有直接的影响,因此学好数学分析对我们是相当重要的,但大部分学生对如何学好数学分析,尤其是对其中不等式证明、函数极值问题、函数项级数一致性收敛感到很困惑.不等式的证明是数学分析中的一个常见问题,其证明方法灵活多样,技术性和综合性较强.函数极值问题是一个非常普遍的数学问题,是经典微积分学最成功的应用,不仅在实际问题中占有重要地位,而且也是函数性态的一个重要特征.函数项级数一致性收敛是数分中一个典型的类型,其定义以及相应的证明也较复杂多变 .
本文对数学分析中不等式的证明、函数极值问题、函数项级数一致性收敛进行了综合研究,主要应用了数学分析中的单调性、拉格朗日中值定理、柯西中值定理等相关知识.对于函数极值问题,本文在给出了一元函数极值定义的同时,探讨了一元函数极值和最值的求解方法 .在此基础上,本文给出了多元函数极值存在的充分条件与必要条件,并对结果进行了简要的证明.对函数项级数一致性收敛的研究中,首先进行了概念阐述,然后利用M判别法和Cauchy判别法分别证明了函数项级数一致性收敛的问题.
然后翻译
The mathematical analysis, as one of the important basic disciplines in engineering colleges and universities, has its inherent characteristics. They are the abstract of the height, the strict logic and extensive application. It has direct impact for many subsequent course of study, so learning mathematics analysis well is quite important. However, most students are confused how to study it, especially the Inequation proof, the function extreme value problem and the consistency convergence of the function series. Inequation proof is a common problem of mathematical analysis, the proofs are flexible, technical and more integrated. The function extreme value problem is a very common math problem, which is a successful application of classic calculus. So it has an important position not only in the actual problems but also in the function sex state. Function of consistency is several points series convergence in a typical types, its definition and the corresponding proof is more complicated. The consistency convergence of the function’s series is a typical types and its definition and corresponding proof are complicated.
This article try to do a comprehensive study about the Inequation proof, the function extreme value problem and the consistency convergence of the function series, which applies The monotonicity of mathematical analysis, Lagrange's mean value theorem and Cauchy mid-value theorem and so on. For function extreme problems, this paper gives the definition of a circular function extreme value, and discusses the solutions of the extreme value and most value.On this basis, this paper gives the function extreme value multiple sufficient conditions of the existence of and necessary conditions, and simply proves the results. In the study of the consistency convergence of the function series, it gives the concept firstly, and then proves the problem with M and Cauchy discriminant method. 首先这个中文摘要要先整理一下
数学分析作为理、工科院校一门重要的基础学科,有其固有的特点,即高度的抽象性、严密的逻辑性和广泛的应用性.它对许多后续课程的学习有直接的影响,因此学好数学分析对我们是相当重要的,但大部分学生对如何学好数学分析,尤其是对其中不等式证明、函数极值问题、函数项级数一致性收敛感到很困惑.不等式的证明是数学分析中的一个常见问题,其证明方法灵活多样,技术性和综合性较强.函数极值问题是一个非常普遍的数学问题,是经典微积分学最成功的应用,不仅在实际问题中占有重要地位,而且也是函数性态的一个重要特征.函数项级数一致性收敛是数分中一个典型的类型,其定义以及相应的证明也较复杂多变 .
本文对数学分析中不等式的证明、函数极值问题、函数项级数一致性收敛进行了综合研究,主要应用了数学分析中的单调性、拉格朗日中值定理、柯西中值定理等相关知识.对于函数极值问题,本文在给出了一元函数极值定义的同时,探讨了一元函数极值和最值的求解方法 .在此基础上,本文给出了多元函数极值存在的充分条件与必要条件,并对结果进行了简要的证明.对函数项级数一致性收敛的研究中,首先进行了概念阐述,然后利用M判别法和Cauchy判别法分别证明了函数项级数一致性收敛的问题.
然后翻译
The mathematical analysis, as one of the important basic disciplines in engineering colleges and universities, has its inherent characteristics. They are the abstract of the height, the strict logic and extensive application. It has direct impact for many subsequent course of study, so learning mathematics analysis well is quite important. However, most students are confused how to study it, especially the Inequation proof, the function extreme value problem and the consistency convergence of the function series. Inequation proof is a common problem of mathematical analysis, the proofs are flexible, technical and more integrated. The function extreme value problem is a very common math problem, which is a successful application of classic calculus. So it has an important position not only in the actual problems but also in the function sex state. Function of consistency is several points series convergence in a typical types, its definition and the corresponding proof is more complicated. The consistency convergence of the function’s series is a typical types and its definition and corresponding proof are complicated.
This article try to do a comprehensive study about the Inequation proof, the function extreme value problem and the consistency convergence of the function series, which applies The monotonicity of mathematical analysis, Lagrange's mean value theorem and Cauchy mid-value theorem and so on. For function extreme problems, this paper gives the definition of a circular function extreme value, and discusses the solutions of the extreme value and most value.On this basis, this paper gives the function extreme value multiple sufficient conditions of the existence of and necessary conditions, and simply proves the results. In the study of the consistency convergence of the function series, it gives the concept firstly, and then proves the problem with M and Cauchy discriminant method.