(1) Clarify the problem. The problems of mathematical modeling are usually practical problems in various fields, and these problems are often vague, so it is difficult to directly find the key points and clearly put forward what methods to use. Therefore, the primary task of establishing the model is to identify the problem, analyze the related conditions and problems, make the problem as simple as possible at first, and then improve it step by step according to the purpose and requirements.

(2) Reasonable assumptions. Making reasonable assumptions is the key step of modeling. A practical problem can hardly be directly transformed into a mathematical problem without simplification and assumption, even though it may be too complicated to be solved. Therefore, the problem should be simplified reasonably according to the characteristics of the object and the purpose of modeling.

The function of reasonable assumption is not only to simplify the problem, but also to limit the application scope of the model. The basis of making assumptions is usually the understanding of the inherent laws of the problem, or the analysis of data or phenomena, or the combination of the two.

When putting forward a hypothesis, we should not only use the professional knowledge related to the problem, such as physics, chemistry, biology, economy, machinery, etc., but also give full play to our imagination, insight and judgment, identify the priorities of the problem and simplify the problem as much as possible. In order to ensure the rationality of the hypothesis, in the case of data, we should test the hypothesis and the inference of the hypothesis, and pay attention to the implied hypothesis.

(3) Establish a model. Modeling is to establish the relationship between variables according to the basic principles or laws of practical problems. To describe the change of one variable with another, the easiest way is to draw a picture, or draw a table, or use a mathematical expression.

In modeling, one form is usually transformed into another. It is easy to convert mathematical expressions into graphs and tables, and vice versa. Through the combination of some simple typical functions, various function forms can be formed. Using functions to solve specific practical problems can better grasp some essential characteristics of problems than giving the values of various parameters and seeking the realistic explanations of these parameters.