Control variable method: change the parameter value and observe its change through line chart.

1. Change the value of an important parameter in the model while keeping other parameters unchanged.

2. Observe the change of the result caused by the change of the parameter value, and judge how much the changed parameter affects the output, that is, the sensitivity.

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Mathematical modeling background

Mathematical technology

Over the past half century, with the rapid development of computer technology, the application of mathematics has not only played an increasingly important role in engineering technology, natural science and other fields, but also penetrated into new fields such as economy, management, finance, biology, medicine, environment, geology, population and transportation with unprecedented breadth and depth. The so-called mathematical technology has become an important part of modern high technology.

Mathematical model is a kind of simulation, which is an abstract and concise description of the essential attributes of practical topics with mathematical symbols, mathematical formulas, programs and graphics. It can not only explain some objective phenomena, but also predict the future development law, and also provide an optimal strategy or a better strategy in a sense for controlling the development of a phenomenon. Generally speaking, mathematical model is not a direct copy of real problems, and its establishment often requires people to observe and analyze real problems in depth and carefully, and also requires people to use all kinds of mathematical knowledge flexibly and skillfully. This process of abstracting mathematical models from practical problems with applied knowledge is called mathematical modeling.

No matter what practical problems in the fields of science, technology and production are solved by mathematical methods, or combined with other disciplines to form an interdisciplinary subject, the first and key step is to establish a mathematical model of the research object and calculate and solve it (usually with the help of a computer); Mathematical modeling and computer technology play a more powerful role in the era of knowledge economy.