integrable

简明释义

英[ˈɪntɪɡrəbl]美[ˈɪntəɡrəbl]

adj. 可积（分）的

英英释义

单词用法

同义词

反义词

例句

1.It is studied that the CMC surfaces in the sphere space of dimension 3 by means of integrable system and its spectral transformation is given.

利用可积系统的方法研究3维球空间中的常中曲率(CMC)曲面，并给出了曲面的谱变换。

2.In addition, to be integrable, the classical dynamic institution for high-strain-rate materials is decoupled and natural strain is introduced.

同时为便于积分，在经典的高应变率材料动态本构关系中，使应变强化项与应变率项相互解耦，并引入自然应变形式。

3.A direct method for finding the integrable couplings is proposed.

给出了直接求可积耦合的一种方法。

4.The physical phenomena concerning with the gauge field are most completely and exactly described by non-integrable phase factor.

因此不可积相位因子最完整地描述了与规范场有关的物理现象。

5.Thus, how to realize the integration of multimedia technology based on Integrable ware notion and classroom teaching remains a problem to be further explored.

怎样实现基于积件思想的多媒体技术与课堂教学整合，就成了目前亟待深入探讨和研究的课题。

6.The derivative nonlinear Schrodinger equation (DNLSE) is an integrable equation of many physical applications.

微商非线性薛定谔方程(DNLSE)是有众多物理应用的可积方程。

7.To solve this differential equation, we need to determine if the solution is integrable.

要解决这个微分方程，我们需要确定解是否可积的。

8.The function is considered integrable if its integral can be calculated over a given interval.

如果在给定区间内可以计算其积分，则该函数被认为是可积的。

9.The area under the curve can be found if the function is integrable.

如果函数是可积的，则可以找到曲线下方的面积。

10.In calculus, we often look for integrable functions to apply the Fundamental Theorem of Calculus.

在微积分中，我们经常寻找可积的函数以应用微积分基本定理。

11.A continuous function on a closed interval is always integrable.

在闭区间上的连续函数总是可积的。

作文

In the realm of mathematics, particularly in calculus and analysis, the term integrable refers to a function that can be integrated over a certain interval. This concept is fundamental for understanding various applications in physics, engineering, and economics. When we say a function is integrable, we imply that its integral exists, which means that we can find the area under the curve represented by this function over a specified range. To illustrate this, consider the simple function f(x) = x. This function is integrable over the interval [0, 1]. The integral of f from 0 to 1 gives us the area of the triangle formed under the line y = x, which equals 0.5. Thus, not only does this function meet the criteria of being integrable, but it also provides us with a tangible geometric interpretation of integration.However, not all functions are integrable. For example, the function f(x) = 1/x over the interval [0, 1] is not integrable because it approaches infinity as x approaches 0. This highlights an essential aspect of the concept: for a function to be integrable, it must be well-behaved over the interval in question. If a function has discontinuities or infinite values within the interval, it may fail to be integrable.The importance of integrable functions extends beyond pure mathematics. In physics, for instance, the concept of work done by a force can be computed using the integral of the force function over a distance. If the force function is integrable, we can calculate the total work done efficiently. Similarly, in economics, the area under a demand curve can be found through integration, provided the demand function is integrable.Moreover, the study of integrable functions leads to deeper mathematical theories. For example, Lebesgue integration extends the idea of integrability to a broader class of functions compared to the traditional Riemann integration. This advancement allows for the integration of functions that are not integrable in the Riemann sense, thus expanding the toolkit available for mathematicians and scientists alike.In conclusion, the term integrable is not just a mathematical jargon; it represents a crucial concept that allows us to compute areas, understand physical phenomena, and solve real-world problems. Grasping the notion of integrable functions opens doors to various applications across different fields, making it an essential part of both theoretical and applied mathematics. As we delve deeper into the world of calculus and analysis, recognizing which functions are integrable will enhance our ability to tackle complex problems and contribute to advancements in science and technology.

在数学的领域，特别是微积分和分析中，术语integrable指的是一个可以在某个区间上进行积分的函数。这个概念对于理解物理、工程和经济学中的各种应用至关重要。当我们说一个函数是integrable时，我们暗示它的积分存在，这意味着我们可以找到该函数在指定范围内所代表的曲线下的面积。为了说明这一点，考虑简单的函数f(x) = x。这个函数在区间[0, 1]上是integrable的。从0到1对f的积分给我们带来了在y = x的直线下形成的三角形的面积，等于0.5。因此，这个函数不仅符合成为integrable的标准，而且还为我们提供了积分的具体几何解释。然而，并非所有函数都是integrable的。例如，函数f(x) = 1/x在区间[0, 1]上并不是integrable的，因为当x接近0时，它趋向于无穷大。这突显了这个概念的一个重要方面：为了使一个函数成为integrable，它必须在所讨论的区间内表现良好。如果一个函数在区间内存在不连续性或无穷大值，它可能无法成为integrable。integrable函数的重要性超越了纯数学。在物理学中，例如，力做功的概念可以通过对力函数在一定距离上的积分来计算。如果力函数是integrable的，我们就能有效地计算出总的功。同样，在经济学中，通过积分可以找到需求曲线下的面积，前提是需求函数是integrable的。此外，对integrable函数的研究引出了更深层次的数学理论。例如，Lebesgue积分将积分的概念扩展到比传统Riemann积分更广泛的函数类。这一进展使得能够对在Riemann意义上不可integrable的函数进行积分，从而扩展了数学家和科学家可用的工具包。总之，术语integrable不仅仅是数学术语；它代表了一个关键的概念，使我们能够计算面积、理解物理现象以及解决现实问题。掌握integrable函数的概念为我们在不同领域的各种应用打开了大门，使其成为理论与应用数学的一个重要部分。当我们深入微积分和分析的世界时，认识哪些函数是integrable的将增强我们解决复杂问题的能力，并为科学和技术的进步作出贡献。