mathematical modelling

简明释义

数学模拟

英英释义

例句

1.Scientists rely on mathematical modelling 数学建模 to understand climate change and its effects.

科学家依赖于数学建模 mathematical modelling来理解气候变化及其影响。

2.The team used mathematical modelling 数学建模 to predict the spread of the virus in the community.

团队使用数学建模 mathematical modelling来预测病毒在社区的传播。

3.Using mathematical modelling 数学建模, researchers were able to simulate the effects of different drug dosages.

研究人员利用数学建模 mathematical modelling模拟不同药物剂量的效果。

4.In engineering, mathematical modelling 数学建模 helps in designing structures that can withstand earthquakes.

在工程中，数学建模 mathematical modelling有助于设计能够抵御地震的结构。

5.The financial analysts employed mathematical modelling 数学建模 to forecast market trends.

金融分析师使用数学建模 mathematical modelling来预测市场趋势。

作文

Mathematical modelling is a powerful tool that allows us to represent real-world phenomena using mathematical concepts and structures. By translating complex systems into mathematical terms, we can analyze, predict, and optimize behaviors in various fields, including engineering, biology, economics, and environmental science. The process of creating a mathematical modelling involves several key steps: defining the problem, formulating the model, solving the model, and validating the results against real-world data.The first step in mathematical modelling is to clearly define the problem at hand. This requires a deep understanding of the system we are trying to analyze. For instance, if we want to model the spread of a disease, we need to identify the key factors that influence transmission, such as population density, contact rates, and recovery times. Once we have a clear understanding of the problem, we can begin to formulate our model.Formulating a model typically involves selecting appropriate mathematical tools. This could include differential equations, statistical methods, or computational algorithms. For example, in epidemiology, the SIR model (Susceptible, Infected, Recovered) is often used to represent the dynamics of disease spread. By using this model, researchers can simulate different scenarios and understand how changes in parameters affect outcomes.After formulating the model, the next step is to solve it. This may involve analytical techniques, where we derive explicit solutions, or numerical methods, where we use computational tools to approximate solutions. The choice of method depends on the complexity of the model and the specific questions we are trying to answer. For instance, a simple linear model might be solvable with basic algebra, while a complex nonlinear model may require sophisticated numerical simulations.Once we obtain solutions from our mathematical modelling, it is crucial to validate them against real-world data. Validation ensures that our model accurately represents the system we are studying. This step often involves comparing model predictions to observed data and assessing the model's performance. If the model does not fit the data well, we may need to revisit our assumptions and refine the model accordingly.The applications of mathematical modelling are vast and varied. In the field of engineering, models can help design more efficient structures or systems. In environmental science, they can predict the impact of climate change on ecosystems. In economics, they can analyze market trends and inform policy decisions. The versatility of mathematical modelling makes it an invaluable tool across disciplines.Moreover, mathematical modelling encourages critical thinking and problem-solving skills. It challenges individuals to break down complex issues into manageable parts and think systematically about solutions. As technology continues to advance, the importance of mathematical modelling will only grow, enabling us to tackle increasingly complex challenges in our world.In conclusion, mathematical modelling serves as a bridge between abstract mathematics and practical applications. It allows us to make sense of the complexities of the world around us, providing insights that can lead to informed decisions and innovative solutions. By mastering the art of mathematical modelling, we equip ourselves with the tools necessary to navigate and address the multifaceted problems of our time.

数学建模是一种强大的工具，它使我们能够使用数学概念和结构来表示现实世界的现象。通过将复杂的系统转化为数学术语，我们可以在工程、生物学、经济学和环境科学等各个领域分析、预测和优化行为。创建数学建模的过程包括几个关键步骤：定义问题、制定模型、求解模型和根据现实数据验证结果。数学建模的第一步是清楚地定义手头的问题。这需要对我们试图分析的系统有深入的理解。例如，如果我们想要建模疾病的传播，我们需要识别影响传播的关键因素，如人口密度、接触率和恢复时间。一旦我们对问题有了清晰的理解，就可以开始制定我们的模型。制定模型通常涉及选择合适的数学工具。这可能包括微分方程、统计方法或计算算法。例如，在流行病学中，SIR模型（易感者、感染者、恢复者）通常用于表示疾病传播的动态。通过使用该模型，研究人员可以模拟不同的情景，了解参数变化如何影响结果。在制定模型之后，下一步是求解它。这可能涉及分析技术，即推导显式解，或数值方法，即使用计算工具近似解。选择方法取决于模型的复杂性和我们试图回答的具体问题。例如，一个简单的线性模型可能可以用基本代数求解，而一个复杂的非线性模型可能需要复杂的数值模拟。一旦我们从数学建模中获得了解决方案，验证它们与现实数据的一致性是至关重要的。验证确保我们的模型准确地表示我们研究的系统。这一步骤通常涉及将模型预测与观察数据进行比较，并评估模型的性能。如果模型与数据不匹配，我们可能需要重新审视我们的假设并相应地完善模型。数学建模的应用广泛而多样。在工程领域，模型可以帮助设计更高效的结构或系统。在环境科学中，它们可以预测气候变化对生态系统的影响。在经济学中，它们可以分析市场趋势并为政策决策提供信息。数学建模的多功能性使其成为跨学科的宝贵工具。此外，数学建模鼓励批判性思维和问题解决能力。它挑战个人将复杂问题分解为可管理的部分，并系统地思考解决方案。随着技术的不断进步，数学建模的重要性只会增加，使我们能够应对日益复杂的全球挑战。总之，数学建模作为抽象数学与实际应用之间的桥梁。它使我们能够理解周围世界的复杂性，提供可以导致明智决策和创新解决方案的洞察。通过掌握数学建模的艺术，我们为自己装备了应对和解决我们时代多面问题所需的工具。