共查询到19条相似文献，搜索用时 125 毫秒
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定积分的求解方法很多,掌握定积分的求解方法与技巧对学习定积分的应用,微分方程的求解,重积分的求解以及解决曲线积分,曲面积分问题都是十分必要的。本文介绍了定积分的求解方法,以及在求解过程中的一些技巧。 相似文献
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本文分别叙述了无穷积分与定积分、无穷积分与瑕积分的一些区别。对于无穷积分与定积分有定积分可积一定绝对可积,而无穷积分收敛不一定绝对收敛等差别。瑕积分与无穷积分的差别是瑕积分平方收敛可得绝对收敛,而对无穷积分不成立。 相似文献
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含定积分的不等式的证明是高中数学学习中的一个重点也是难点,证明方法多种多样,本文归纳并列举了几种定积分不等式的证明方法。通过运用定积分的知识对不等式进行证明,来探析定积分在数学证明中的作用。 相似文献
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正定积分是微积分的主要内容之一,它概念抽象,解题方法灵活多变,学生难于掌握。本文通过具体例子讨论了利用定积分几何意义求定积分的特殊解法。定积分的计算方法有很多:凑微分法、换元积分法、分部积分法、循环推证求解法等。这些方法当然是计算定积分的重要方法,对被积函数比较复杂的定积分,用这些方法,确实能起到良好的计算效果。但是这些计算一般都比较复杂,很多题 相似文献
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近年来,对于积分区间上不连续的函数应用牛顿-莱布尼兹公式求定积分的探讨很多。实际上,对于条件更加严苛的定积分的分部积分法也可以进行更深入分析和研究。本文通过对几种不满足定积分分部积分法条件的情况进行探讨和分析,并得出相应的结论,从而扩大了该公式的应用范围,并且这些结论在像傅里叶级数和变换的运算等方面能发挥实际的作用。 相似文献
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主要探讨了一些特殊类型的定积分计算所采用的方法和技巧,由于特殊类型的定积分计算的形式很多,不拘一格,因此本文以举例的形式来讨论,介以开拓解题思路,提高计算能力。 相似文献
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分部积分法因其对积分具有转化作用，在定积分的估值计算，及积分等式、不等式证明，和二重积分计算等方面具有一些特殊计算作用。此外，分部积分的计算方法可推广至渐次积分。 相似文献
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教材在定积分的定义中。通常特别强调分法和选取的两个任意性。利用此定义讨论问题比较繁琐．因此在此定义基础上做出进一步讨论．即将定义中分法的任意性用特殊分割来代替．这样不仅给解决问题带来了方便．而且可以帮助大家更深刻地理解和掌握定积分定义的实质。同时还给出了一个可积的充分必要条件．即关于函数收敛的Cauchy收敛准则．但应用此定理证明关于函数的可积性问题相当麻烦．由此我们对该定理做出改进．得出一个简单易行的判定定理。 相似文献
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T.S. Gray 《Journal of The Franklin Institute》1931,212(1):77-102
A machine for the purpose of facilitating mathematical solution of problems requiring the evaluation of an integral in which the integrand involves a variable parameter is described in this article. It involves the use of an optical system in which the transmission of light is limited in a definite manner by apertures having the shape of the area under curves representing mathematical functions. The accuracy of the machine itself is from 2 to 5 per cent. Examples of the use of the device in the solution of the superposition theorem integral and a form of integral equation are given. Its application to other problems including the Fourier transform, correlation analysis, and periodogram analysis is discussed, and its limitations are considered. 相似文献
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《Journal of The Franklin Institute》2023,360(12):7898-7911
This paper proposes new inequality-based functions to be Lyapunov functionals for the stability analysis of time-varying delay systems. The novel Lyapunov functionals are developed using a slack-matrices-based integral inequality for the first time. This is unlike most inequality-based functions that have been used as Lyapunov functionals which consist of single-matrices in their integral terms. Based on the new Lyapunov functionals, a new stability criterion is derived in the form of a matrix-valued quadratic function, which is proven to be negative definite using a geometry-based negativeness lemma. Two numerical examples showcase the effectiveness of our presented method. 相似文献
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《Journal of The Franklin Institute》2023,360(3):1690-1705
This paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated. 相似文献
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本文针对以往高职生数学应用能力差的现状,在教学过程中进行了改革,强化极限、导数和定积分的应用,通过几个具体实例说明了具体的做法。 相似文献