initial condition

简明释义

初始条件

英英释义

例句

1.In physics, the outcome of a system often depends on its initial condition (初始条件).

在物理学中，一个系统的结果通常取决于它的initial condition（初始条件）。

2.The simulation failed because the initial condition (初始条件) was set incorrectly.

模拟失败是因为initial condition（初始条件）设置不正确。

3.When modeling weather patterns, scientists must accurately define the initial condition (初始条件) to predict changes.

在建模天气模式时，科学家必须准确地定义initial condition（初始条件）以预测变化。

4.In mathematics, solving differential equations requires knowing the initial condition (初始条件).

在数学中，解决微分方程需要知道initial condition（初始条件）。

5.The robot's performance is influenced by its initial condition (初始条件) before it starts moving.

机器人的性能受到其在开始移动前的initial condition（初始条件）的影响。

作文

In the realm of science and mathematics, the term initial condition refers to the specific values or state of a system at the beginning of a process. Understanding initial condition is crucial because it often determines the trajectory of the system's evolution over time. For instance, in physics, when studying the motion of an object, the initial condition might include the object's initial position and velocity. These values are essential for predicting where the object will be at any given moment in the future.In the context of differential equations, initial condition plays a pivotal role in finding a unique solution. A differential equation describes how a quantity changes over time, but without specifying an initial condition, there could be infinitely many solutions. For example, consider a simple equation that models the growth of a population. If we know that the population was 100 at year zero, this information serves as our initial condition. Without it, we cannot accurately determine the population at any future time.Similarly, in the field of climate science, initial condition is vital for weather forecasting. Meteorologists use sophisticated models that rely on current atmospheric data to predict future weather patterns. The initial condition in this case includes temperature, humidity, wind speed, and other factors at the start of the forecasting period. Accurate initial condition data is essential; even small errors can lead to significantly different weather predictions down the line.In engineering, particularly in control systems, initial condition can influence the stability and performance of the system. Engineers must carefully analyze the initial condition to ensure that a machine or a structure behaves as intended. For example, when designing a bridge, knowing the initial load conditions—such as the weight it must support—is critical for ensuring safety and functionality.Moreover, the concept of initial condition is not limited to the hard sciences. In economics, understanding the initial condition of an economy can provide insights into its future growth and stability. Economists often analyze various indicators such as employment rates, inflation, and GDP at a specific point in time to assess the initial condition before making forecasts about future economic trends.In conclusion, the term initial condition encompasses a broad range of applications across various fields of study. Whether in physics, mathematics, meteorology, engineering, or economics, recognizing the importance of initial condition enables scientists, engineers, and analysts to make informed predictions and decisions. By understanding the state of a system at its inception, we can better navigate the complexities of change and development in the world around us. The significance of initial condition cannot be overstated; it is the foundation upon which future outcomes are built.

在科学和数学领域，术语初始条件指的是系统在过程开始时的特定值或状态。理解初始条件至关重要，因为它通常决定了系统随时间演变的轨迹。例如，在物理学中，当研究物体的运动时，初始条件可能包括物体的初始位置和速度。这些值对于预测物体在未来任何时刻的位置都是必不可少的。在微分方程的背景下，初始条件在找到唯一解方面发挥着关键作用。微分方程描述了一个量如何随时间变化，但如果不指定初始条件，则可能会有无数个解。例如，考虑一个简单的方程，它建模人口的增长。如果我们知道在零年时人口为100，这个信息就作为我们的初始条件。没有它，我们无法准确确定未来任何时刻的人口。同样，在气候科学领域，初始条件对于天气预报至关重要。气象学家使用依赖于当前大气数据的复杂模型来预测未来的天气模式。在这种情况下，初始条件包括预报期开始时的温度、湿度、风速和其他因素。准确的初始条件数据是至关重要的；即使是微小的错误也可能导致未来天气预测的显著不同。在工程学中，特别是在控制系统中，初始条件可以影响系统的稳定性和性能。工程师必须仔细分析初始条件以确保机器或结构按预期运行。例如，在设计桥梁时，了解初始载荷条件（例如它必须支持的重量）对于确保安全和功能至关重要。此外，初始条件的概念不限于硬科学。在经济学中，了解经济的初始条件可以提供对其未来增长和稳定性的洞察。经济学家通常会分析特定时间点的各种指标，如就业率、通货膨胀和GDP，以评估初始条件，然后对未来经济趋势作出预测。总之，术语初始条件涵盖了各个研究领域的广泛应用。无论是在物理学、数学、气象学、工程学还是经济学中，认识到初始条件的重要性使科学家、工程师和分析师能够做出明智的预测和决策。通过理解系统在其起始时的状态，我们可以更好地驾驭周围世界变化和发展的复杂性。初始条件的重要性不容小觑；它是未来结果构建的基础。