Mathematical modeling is the whole process of explaining practical problems, accepting practical tests and establishing mathematical models through calculation results. When it is necessary to analyze and study a practical problem from a quantitative point of view, people should use mathematical symbols and language to establish a mathematical model on the basis of in-depth investigation, understanding of object information, making simplified assumptions and analyzing internal laws.

Model preparation

Understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. The essence of the problem is contained in mathematical thought and runs through the whole process of the problem, and then the problem is described in mathematical language. Requirements in line with mathematical theory, in line with mathematical habits, clear and accurate.

Model hypothesis

According to the characteristics of the actual object and the purpose of modeling, the problem is simplified with accurate language and some appropriate assumptions are put forward.

Model structure

On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and constants, and establish the corresponding mathematical structure (try to use simple mathematical tools).

Model solving

Using the obtained data, all parameters of the model are calculated (or approximately calculated).

model analysis

The idea of establishing the model is expounded, and the results are analyzed mathematically.

model testing

The model analysis results are compared 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.