Generally speaking, a mathematical model can be described as a specific object in the real world, a mathematical structure obtained by simplifying some necessary assumptions and using appropriate mathematical tools for a specific purpose and according to unique internal laws. The whole process of establishing mathematical model is called mathematical modeling.

The simplest example is doing application problems in our middle school. Find out its law through the problem, list the mathematical formula and finally solve it.

General steps of mathematical modeling:

Model preparation-understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. Describe the problem in mathematical language.

Model Hypothesis-Simplify the problem according to the characteristics of the actual object and the purpose of modeling, and put forward some appropriate assumptions with accurate language.

Model building-on the basis of hypothesis, use appropriate mathematical tools to describe the mathematical relationship between variables and establish the corresponding mathematical structure (try to use simple mathematical tools).

Model solving-all parameters of the model are calculated (or approximately calculated) by using the obtained data.

Model analysis-mathematical analysis of the results obtained.

Model checking-comparing the results of model analysis with the actual situation to verify the accuracy, rationality and applicability of the model. If the model is in good agreement with the actual situation, the practical significance of the calculation results should be given and explained. If the model is not consistent with the actual situation, it is necessary to modify the assumptions and repeat the modeling process.

Model application-the application method varies with the nature of the problem and the purpose of modeling.