sign change

简明释义

正负变换

英英释义

例句

1.During the experiment, we noted a sign change 符号变化 in the voltage across the resistor.

在实验中，我们注意到电阻器两端的电压发生了sign change 符号变化。

2.In calculus, we often look for sign changes 符号变化 to find critical points.

在微积分中，我们常常寻找sign changes 符号变化来找到临界点。

3.The sign change 符号变化 in the temperature readings suggests a shift in weather patterns.

温度读数中的sign change 符号变化暗示天气模式的变化。

4.The function exhibits a sign change 符号变化 at x = 0, indicating a root.

这个函数在x = 0处表现出一个sign change 符号变化，表明有一个根。

5.A sign change 符号变化 in the graph indicates a transition from positive to negative values.

图中的sign change 符号变化表示从正值转变为负值。

作文

In mathematics, particularly in calculus and algebra, the concept of sign change is crucial for understanding the behavior of functions. A sign change occurs when the value of a function shifts from positive to negative or vice versa. This phenomenon can provide valuable insights into the roots of equations and the intervals where functions are increasing or decreasing. For instance, if we have a polynomial function that changes from positive to negative at a certain point, we can conclude that there is a root in that interval. This is often visualized using graphs, where the x-axis represents the input values and the y-axis represents the output values of the function. When the graph crosses the x-axis, it indicates a sign change, confirming that the function has a root at that point.Understanding sign change is not only important in theoretical mathematics but also in practical applications such as engineering and physics. Engineers often need to analyze systems where forces may change direction, which can be modeled using functions that exhibit sign change. For example, in mechanical systems, the tension in a cable might switch from being under tension to slack, indicating a sign change in force. Recognizing these changes can help engineers design safer and more efficient structures.Furthermore, in numerical methods, sign change plays a vital role in root-finding algorithms such as the bisection method. This method relies on the principle that if a continuous function changes sign over an interval, there must be at least one root within that interval. By repeatedly halving the interval and checking for sign change, we can home in on the root with increasing accuracy. This approach highlights the practical importance of understanding sign change in computational mathematics.In addition to its mathematical significance, sign change can also be observed in various real-world phenomena. For example, consider temperature changes throughout the day. As the sun rises, temperatures typically increase, representing a positive trend. However, as the sun sets, temperatures drop, leading to a sign change in temperature trends. This concept is not limited to temperature; it can apply to various other contexts, such as financial markets, where the price of a stock may experience sign change due to market fluctuations.In conclusion, the concept of sign change is a fundamental aspect of mathematics that extends beyond theoretical frameworks into practical applications across various fields. Whether analyzing functions, designing engineering solutions, or observing real-world phenomena, recognizing and understanding sign change allows us to make informed decisions and predictions. As we continue to explore the complexities of mathematics and its applications, the significance of sign change will undoubtedly remain a key topic of discussion and study.

在数学中，特别是在微积分和代数中，符号变化的概念对于理解函数的行为至关重要。符号变化发生在函数值从正变为负或反之亦然时。这种现象可以提供有关方程根和函数递增或递减区间的宝贵见解。例如，如果我们有一个多项式函数在某个点上从正变为负，我们可以得出结论，在该区间内存在一个根。这通常通过图形来可视化，其中x轴代表输入值，y轴代表函数的输出值。当图形穿过x轴时，它表示发生了符号变化，确认函数在该点有一个根。理解符号变化不仅在理论数学中重要，在工程和物理等实际应用中也同样重要。工程师通常需要分析可能改变方向的力的系统，这可以通过表现出符号变化的函数来建模。例如，在机械系统中，电缆中的张力可能会从受张力转变为松弛，这表明力的符号变化。识别这些变化可以帮助工程师设计更安全、更高效的结构。此外，在数值方法中，符号变化在根查找算法（如二分法）中也起着至关重要的作用。该方法依赖于这样一个原理：如果一个连续函数在一个区间内发生符号变化，那么该区间内至少存在一个根。通过反复对区间进行二分并检查符号变化，我们可以逐渐提高对根的准确性。这种方法凸显了理解符号变化在计算数学中的实际重要性。除了其数学意义外，符号变化还可以在各种现实世界现象中观察到。例如，考虑一天中温度的变化。随着太阳升起，温度通常会升高，代表一种正趋势。然而，随着太阳落下，温度下降，导致温度趋势发生符号变化。这一概念并不限于温度；它可以适用于其他各种上下文，例如金融市场，股票价格可能由于市场波动而经历符号变化。总之，符号变化的概念是数学的一个基本方面，超越了理论框架，延伸到各个领域的实际应用。无论是分析函数、设计工程解决方案，还是观察现实世界现象，识别和理解符号变化使我们能够做出明智的决策和预测。随着我们继续探索数学及其应用的复杂性，符号变化的重要性无疑将仍然是讨论和研究的关键主题。