共查询到20条相似文献，搜索用时 187 毫秒
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本文针对初等代数研究中的均值不等式的几个定理,做了些应用性研究。对竞赛数学中,均值不等式的应用具有指导意义。 相似文献
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赫尔德（Hǒlder）不等式,柯西（Cauchy）不等式,闵可夫斯基（Minkowski）不等式以及均值不等式都是数学中重要的不等式,这些不等式在传统的证明中,要么太过繁琐并缺乏联系,要幺起点太高过于抽象。本文以一元函数的微分中值定理为起点,系统地演绎了这些不等式。 相似文献
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均值不等式在中学数学中是非常重要的不等式。本文通过对均值不等式在求函数最值中的应用进行分析,开辟了求函数最值的新途径,给求函数最值问题注入了新的生机和活力。对于某些题目可以直接利用公式求解,但是有些题目必须进行巧妙变形后才能利用均值不等式解决。本文通过一些具体的实例来说明均值不等式在求函数最值中的巧妙应用。 相似文献
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数学问题的解决关键在于对待数学题的方法,在学习数学的过程中,有意识地将数学问题系列化,解决数学问题的方法化。在数学的学习中,不等式的证明是可以作为一个系列问题来看待的,不等式的证明是数学的重要内容之一,数学分析中的不等式的应用占有很重要的地位,其证明与很多知识相联系,本文主要研究利用如：函数单调性、凸凹性等,解决不等式问题。证明方法极其广泛,颇难对其结构作系统归纳。研究如何巧妙地利用数分知识,探讨其不同证法,从而开阔思路,提高整体能力,有利于掌握数学分析中的基本理论。 相似文献
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在数学新课标中,强调要让学生领会数学的美学价值,因此数学教学过程中适时渗透数学美的知识和进行数学审美教学是很有必要的.不等式教学是高中数学中比较重要的部分,利用数学美的对称性、简单性、统一性和奇异性能很巧妙解决不等式的有关问题. 相似文献
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证明不等式是高等数学中常见的问题,在数学的每个分支中均涉及.而证明不等式的方法很多,本文列举了用定理来证明不等式的方法和例子,谈谈不等式的几种证明方法以及如何把握问题的实质并熟练运用各种证明技巧.另外对常见的不等式证明方法也做了简单的补充。 相似文献
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在数学新课标中，强调要让学生领会数学的美学价值，因此数学教学过程中适时渗透数学美的知识和进行数学审美教学是很有必要的。不等式教学是高中数学中比较重要的部分，利用数学美的对称性、简单性、统一性和奇异性能很巧妙解决不等式的有关问题。 相似文献
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拉格朗日中值定理是微分学中的重要的基本定理之一,也是三大微分中值定理中的核心定理,本文应用拉格朗日中值定理及推论证明等式、举例说明Lagrange中值定理在求解极限中的应用、就拉格朗日中值定理的一个推广进行了浅要说明,其中在拉格朗日中值定理推广上证明了拉格朗日中值定理在开区间有连续右导数的情况也能使用,这一推广大大拓宽了拉格朗日中值定理的使用范围。 相似文献
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介值定理是数学分析的一个重要定理,对研究函数方程根的存在性、不动点和积分中值定理等问题起到重要作用。在多元函数中推广介值定理,并且将只有第一类间断点的函数的介值定理推广运用到积分中值定理中,推广了文[4]的结论。 相似文献
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本文介绍高等数学中的三个创新案例,即多元函数极值的一阶导数判别准则、多变元情形下的罗尔中值定理,以及一元函数罗尔中值定理的推广定理。它们贴近高等数学课程中经典的教学内容,同时是在经典内容基础上的创新。本文研究这三个创新案例的推广过程,揭示其中蕴涵的数学创新思维方法,探讨其中体现的教学价值。 相似文献
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《Journal of The Franklin Institute》2022,359(18):10525-10557
This paper is concerned with an event-triggered adaptive fault-tolerant problem for an uncertain non-affine system. The implicit function theorem and mean value theorem are utilized to transform a non-affine system into an affine one, and an extended state observer and a tracking differentiator are used to estimate unknown dynamics and the derivative of virtual control laws, respectively. Adaptive laws are designed for unknown faults, and an event-triggered control scheme with a time-varying threshold, based on a tracking error and adaptive parameters, is developed. The tracking error is steered to converge to a bounded set with the help of a predefined performance function, and its transient performance is improved despite of faults. The stability of the closed-loop system is analyzed by the theorem of the input-to-state practically stability, and the Zeno behavior is excluded. Finally, two examples are given to illustrate the effectiveness of the proposed scheme. 相似文献
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This paper is concerned with finite-time stabilization of a class of pure-feedback systems with dead-zone input. A systematic design procedure is established to derive the finite-time controller. Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one. Then, based on the strengthened finite-time Lyapunov stability theorem as well as utilizing the bounds of dead-zone parameters, the finite-time stabilizer is explicitly constructed via backstepping design approach. It is proven that the designed controller can ensure all the states of the closed-loop system converge to zero in a finite time and maintain at zero afterwards. The proposed design framework is also extended to finite-time stabilization of uncertain pure-feedback systems and finite-time tracking control of pure-feedback systems. The effectiveness of the theoretical results are finally demonstrated by a numerical example and a realistic example. 相似文献
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高等数学的教材是以罗尔定理为基础,通过引进适当满足罗尔定理的辅助函数去证明拉格朗日中值定理和柯西中值定理。本文将讨论如何构造辅助函数去证明拉格朗日中值定理和柯西中值定理。此外,本文还给出了证明微分中值定理的另外一种方法：辅助定理法。 相似文献
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The design problem of collocated feedback controllers is addressed in this paper for a class of semi-linear distributed parameter systems described by parabolic partial differential equation (PDE), where a finite number of local actuators and sensors are intermittently distributed in space. A Lyapunov direct method for the exponential stability analysis of the resulting closed-loop system is first presented for the system, in which the first mean value theorem for integration and the Wirtinger's inequality are employed. The corresponding stabilization condition is then derived through the analysis result. Finally, the proposed design method is implemented on the feedback control of a fisher equation and its effectiveness is evaluated through simulation results. 相似文献
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The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms. 相似文献
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《Journal of The Franklin Institute》2022,359(10):4642-4660
In this paper, an adaptive fuzzy fixed time control scheme is developed for stochastic pure-feedback nonlinear systems with full state constraints. The mean value theorem is exploited to deal with the problem of nonaffine appearance in the systems and transform the structure of pure-feedback to the structure of strict-feedback. The barrier Lyapunov functions are constructed to guarantee that all states in the systems maintain within the prescribed constraints and the fuzzy logic systems are employed to approximate unknown nonlinear functions at each step. Then, an adaptive fuzzy fixed time controller is constructed by utilizing backstepping technique, which guarantees that all the signals in the considered systems are semiglobally uniform ultimately bounded in a fixed time. Finally, the validity of the proposed fixed time control scheme is verified via a simulation example. 相似文献