linearise

简明释义

英[/ˈlɪn.i.ə.raɪz/]美[/ˈlɪn.i.ə.raɪz/]

v. 使直线化；用直线方式表达（等于 linearize）

第 三 人 称 单 数 l i n e a r i s e s

现 在 分 词 l i n e a r i s i n g

过 去 式 l i n e a r i s e d

过 去 分 词 l i n e a r i s e d

英英释义

单词用法

同义词

反义词

例句

1.The figure of regression equation of linearise turned from the functional equation of exponential curve is the best line to express the correlation of exponential curve in colorimetric analysis.

在比色分析中，由指数曲线函数方程转换的直线化回归方程的图形，是表达指数曲线相关的最佳直线。

2.The figure of regression equation of linearise turned from the functional equation of exponential curve is the best line to express the correlation of exponential curve in colorimetric analysis.

在比色分析中，由指数曲线函数方程转换的直线化回归方程的图形，是表达指数曲线相关的最佳直线。

3.To improve the accuracy of predictions, we should linearise 线性化 the input data.

为了提高预测的准确性，我们应该对输入数据进行线性化。

4.The software can automatically linearise 线性化 non-linear functions for better performance.

该软件可以自动对非线性函数进行线性化以提高性能。

5.The engineers decided to linearise 线性化 the equations to make calculations more manageable.

工程师们决定对方程进行线性化以使计算更加可控。

6.To simplify the complex data, we will linearise 线性化 the model for easier analysis.

为了简化复杂的数据，我们将对模型进行线性化以便于分析。

7.In order to apply statistical methods, we need to linearise 线性化 the relationship between the variables.

为了应用统计方法，我们需要对变量之间的关系进行线性化。

作文

In the realm of mathematics and engineering, the concept of linearization plays a critical role in simplifying complex systems. To linearise (线性化) a nonlinear function means to approximate it by a linear function in a small neighborhood around a specific point. This technique is particularly useful because many real-world phenomena can be described by nonlinear equations that are difficult to solve directly. By linearising (线性化) these equations, we can gain insights into the behavior of the system without having to deal with the intricacies of the original nonlinear models.For instance, consider the motion of a pendulum. The equation governing its motion is inherently nonlinear due to the sine function involved. However, if we are only interested in small angles, we can linearise (线性化) the equation by using the approximation sin(θ) ≈ θ. This simplification allows us to analyze the pendulum's motion using basic linear dynamics, making it easier to calculate its period and other relevant parameters.The process of linearising (线性化) functions is not limited to physics; it extends to various fields such as economics, biology, and even social sciences. For example, in economics, the relationship between supply and demand can often be nonlinear. By linearising (线性化) this relationship around a point of equilibrium, economists can develop linear models that help predict market behavior under certain conditions.Moreover, the technique of linearisation (线性化) is vital in control theory, where engineers design systems to maintain desired outputs despite disturbances. When designing controllers for complex systems like aircraft or robots, engineers often linearise (线性化) the system dynamics to apply linear control strategies. These strategies are much easier to implement and analyze compared to their nonlinear counterparts, allowing for more efficient designs and better performance.However, it is essential to recognize the limitations of linearisation (线性化). While it simplifies analysis, the accuracy of the linear model depends on how well the linear approximation represents the original nonlinear function within the specified range. If the operating conditions change significantly, the linear model may no longer be valid, leading to erroneous predictions and potentially catastrophic failures in engineering applications.In conclusion, the ability to linearise (线性化) complex nonlinear functions is an invaluable tool across various disciplines. It enables us to simplify our understanding of complicated systems and make informed decisions based on linear approximations. Nevertheless, one must always be cautious and aware of the limitations that come with such simplifications. As we continue to explore and innovate in our respective fields, the practice of linearising (线性化) will remain a fundamental skill that enhances our analytical capabilities and fosters deeper insights into the complexities of the world around us.

在数学和工程领域，线性化的概念在简化复杂系统中发挥着关键作用。将一个非线性函数linearise（线性化）意味着在特定点附近的小范围内用线性函数来近似它。这一技术尤其有用，因为许多现实世界现象可以用难以直接求解的非线性方程来描述。通过linearising（线性化）这些方程，我们可以在不必处理原始非线性模型复杂性的情况下，深入了解系统的行为。例如，考虑一个摆的运动。其运动方程由于涉及正弦函数而本质上是非线性的。然而，如果我们只对小角度感兴趣，我们可以通过使用近似sin(θ) ≈ θ来linearise（线性化）该方程。这一简化使我们能够利用基本的线性动力学来分析摆的运动，从而更容易计算其周期和其他相关参数。Linearising（线性化）函数的过程不仅限于物理学，它还扩展到经济学、生物学甚至社会科学等多个领域。例如，在经济学中，供需之间的关系往往是非线性的。通过在平衡点附近linearising（线性化）这一关系，经济学家可以建立线性模型，帮助预测在某些条件下市场行为。此外，linearisation（线性化）技术在控制理论中至关重要，工程师设计系统以在干扰下保持期望输出。当为复杂系统如飞机或机器人设计控制器时，工程师通常会linearise（线性化）系统动态，以应用线性控制策略。这些策略比非线性对应物更易于实施和分析，从而使设计更高效，性能更好。然而，必须认识到linearisation（线性化）的局限性。尽管它简化了分析，但线性模型的准确性取决于线性近似在指定范围内对原始非线性函数的代表程度。如果操作条件发生显著变化，线性模型可能不再有效，导致错误的预测，甚至在工程应用中可能导致灾难性的故障。总之，能够linearise（线性化）复杂的非线性函数是各个学科中一种无价的工具。它使我们能够简化对复杂系统的理解，并基于线性近似做出明智的决策。然而，人们必须始终谨慎并意识到这种简化所带来的局限性。随着我们在各自领域的探索和创新，linearising（线性化）的实践将继续成为一种基本技能，增强我们的分析能力，并促进我们对周围世界复杂性的更深入理解。