approximate solution

简明释义

近似解

英英释义

例句

1.The researchers presented an approximate solution 近似解 to the mathematical model they were studying.

研究人员提出了他们研究的数学模型的 近似解 approximate solution 。

2.When dealing with complex equations, finding an approximate solution 近似解 can save a lot of time.

在处理复杂方程时，找到一个 近似解 approximate solution 可以节省很多时间。

3.In optimization problems, sometimes an approximate solution 近似解 is more practical than an exact one.

在优化问题中，有时 近似解 approximate solution 比精确解更实用。

4.In many engineering problems, an approximate solution 近似解 is often sufficient to make informed decisions.

在许多工程问题中，近似解 approximate solution 通常足以做出明智的决定。

5.The software provides an approximate solution 近似解 for users who need quick results.

该软件为需要快速结果的用户提供了一个 近似解 approximate solution 。

作文

In the realm of mathematics and science, the concept of an approximate solution plays a crucial role in problem-solving. An approximate solution refers to a value or a set of values that are close to the actual answer but not exact. This is particularly important in fields where exact solutions are difficult or impossible to obtain due to complex variables and intricate equations. For instance, in calculus, when dealing with integrals that cannot be solved analytically, mathematicians often resort to numerical methods to derive an approximate solution. These methods may include techniques such as the trapezoidal rule or Simpson's rule, which allow us to estimate the area under a curve by breaking it into smaller, manageable segments.The significance of an approximate solution extends beyond mathematics into various scientific disciplines. In physics, for example, researchers frequently encounter problems that require simplifications. When studying the motion of planets, the gravitational interactions can be modeled using Newton's laws; however, the calculations can become exceedingly complicated. Thus, physicists often seek an approximate solution that provides insight into the behavior of celestial bodies without needing to account for every minute detail. This approach allows them to make predictions about planetary positions and movements with reasonable accuracy.Moreover, in engineering, the quest for an approximate solution is vital when designing structures or systems. Engineers must consider numerous factors such as material properties, load conditions, and environmental influences. Often, they use simulations and models to arrive at an approximate solution that guides their design process. For instance, when designing a bridge, engineers may use computational fluid dynamics to simulate how wind will affect the structure. The results yield an approximate solution that helps ensure safety and functionality while also considering economic constraints.In everyday life, we also rely on approximate solutions more than we realize. Consider the realm of budgeting. When planning personal finances, individuals often do not have exact figures for future expenses or income. Instead, they create budgets based on estimates, which serve as approximate solutions to guide their spending and saving decisions. These estimations help people manage their finances effectively, even if they are not perfectly accurate.However, it is essential to recognize the limitations of approximate solutions. While they provide valuable insights and guidance, relying solely on them can lead to errors or misconceptions. Therefore, it is crucial to understand the context in which an approximate solution is applied and to continually refine our methods for obtaining better approximations. This iterative process of improving our estimates is what drives innovation and advancement in various fields.In conclusion, the idea of an approximate solution is fundamental in mathematics, science, engineering, and daily decision-making. It allows us to tackle complex problems and make informed choices, despite the inherent uncertainties we face. By embracing the concept of approximation, we can navigate challenges more effectively, paving the way for progress and understanding in a world that is often too intricate for exact answers.

在数学和科学领域，近似解的概念在解决问题中起着关键作用。近似解是指一个接近实际答案但不完全准确的值或一组值。这在那些由于复杂变量和复杂方程而难以或不可能获得精确解决方案的领域中尤为重要。例如，在微积分中，当处理无法解析解的积分时，数学家们经常采用数值方法来推导出近似解。这些方法可能包括梯形法则或辛普森法则等技术，这些方法通过将曲线下的面积分割成较小、可管理的部分来估算面积。近似解的重要性超越了数学，延伸到各种科学学科。例如，在物理学中，研究人员经常遇到需要简化的问题。当研究行星的运动时，重力相互作用可以使用牛顿定律进行建模；然而，计算可能变得极其复杂。因此，物理学家们通常寻求近似解，这为他们提供了对天体行为的洞察，而无需考虑每一个细微的细节。这种方法使他们能够合理准确地预测行星的位置和运动。此外，在工程学中，寻找近似解在设计结构或系统时至关重要。工程师必须考虑许多因素，例如材料特性、载荷条件和环境影响。通常，他们使用模拟和模型来得出指导设计过程的近似解。例如，在设计桥梁时，工程师可能会使用计算流体动力学来模拟风对结构的影响。结果产生了一个近似解，有助于确保安全性和功能性，同时也考虑了经济限制。在日常生活中，我们也比我们意识到的更依赖于近似解。考虑预算的领域。当规划个人财务时，个人通常没有未来支出或收入的确切数字。相反，他们根据估计制定预算，这些预算作为近似解来指导他们的支出和储蓄决策。这些估算帮助人们有效管理财务，即使它们并不完全准确。然而，必须认识到近似解的局限性。虽然它们提供了有价值的见解和指导，但仅仅依赖它们可能导致错误或误解。因此，理解近似解应用的上下文并不断改进我们获得更好近似的方法至关重要。这种不断改进估算的迭代过程正是推动各个领域创新和进步的动力。总之，近似解的概念在数学、科学、工程和日常决策中是根本性的。它使我们能够应对复杂问题并做出明智的选择，尽管我们面临固有的不确定性。通过接受近似的概念，我们可以更有效地应对挑战，为在一个往往难以给出确切答案的世界中取得进步和理解铺平道路。