数学专业英语翻译3.4.5.pdfVIP

3.4 数学的应用与应用数学 3.4.5 Construction of mathematical model （建立数学模型） In the preceding discussion we viewed modeling as a process and considered briefly the form of the model.Now lets focus attention on the construction of mathematical models. （在前面的讨论中，我们将建模视为一个过程，并简要地仔 细思考了模型的形式。现在让我们把注意力集中在数学模型的构建上。）We begin by presenting an outline of a peocedure that is helpful in constructing models.In the next section,we illustrate the various steps in the procedure by discussing several real-world examples. （我们首先介绍一种有助于构建模型的概述。在下一节中， 我们通过讨论几个实际示例来说明过程中的各个步骤。） STEP 1 Identify the problem （确定问题） What is the problem you would like to explore?Typically this is a difficult step because in real-life situations no one simply hands you a mathematical problem to solve. （你想探索的问题是什么？通常这是一个困难的步骤，因为在现实生活中， 没有人只是给你一个数学问题来解决。）Usually you have to sort through large amounts of data and identify some particular aspect of the situation to study.Moreover,it is imperative to be sufficiently precise(ultimately) in the formulation of the problem to allow for translation of the verbal statements describing the problem into mathematical symbology. （通常你必须对大量数据进行 排序，并确定要研究的某些特定情况。另外，必须确定 （根本）问题的准确性， 以便将口头描述的问题转化为数学的符号问题。）This translation is accomplished through the next steps.It is important to realize that the answer to the question posed might not lead directly to a usable problem identification.（这个转化过程是通 过下一个步骤完成的，重要的是要认识到所提出问题的答案可能不会立刻引出一 个可用的问题。） STEP 2 Make assumptions （做出假设） Generally,we cannot hope to capture in a usable mathematical model all the factors influencing the identified problem.The task is simplified by reducing the number of factors under consideration. （一般来说，我们不希望在可用的数学模型 中捕获所有影响已识别问题的因素。通过减少所考虑因素的数量来简化任务。） Then,relationships among the remaining variables must be determined.Again,by assuming relatively simple relationships,we can reduce the complexity of the problem.Thus the assumptions fa