Introduction to mathematical modeling
Mathematical modeling is to establish a mathematical model according to actual problems, solve the mathematical model, and then solve the actual problems according to the results. When it is necessary to analyze and study a practical problem from a quantitative perspective, people should conduct in-depth investigation and study.
On the basis of understanding the object information, making simplified assumptions and analyzing the internal laws, a mathematical model is established by using mathematical symbols and languages.
Second, the mathematical technology of mathematical modeling
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 contemporary technology.
Thinking method and applied mathematical model of mathematical modeling
1, thinking method
Mathematical modeling is a mathematical thinking method, and it is a powerful mathematical means to describe and "solve" practical problems by using mathematical language and methods through abstraction and simplification. Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include specific natural phenomena such as free fall.
It also contains abstract phenomena, such as customers' value tendency to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.
2. Apply mathematical model
When applying mathematics to solve various practical problems, it is a very crucial and difficult step to establish a mathematical model. The process of establishing mathematical model is the process of simplifying and abstracting complex practical problems into reasonable mathematical structure. Through investigation and data collection, observe and study the internal characteristics and laws of actual objects.
Grasp the main contradiction of the problem, establish the quantitative relationship reflecting the actual problem, and then use mathematical theory and methods to analyze and solve the problem. This requires a deep and solid mathematical foundation, keen insight and imagination, strong interest in practical problems and extensive knowledge. Mathematical modeling is a bridge between mathematics and practical problems, and it is a medium in which mathematics is widely used in various fields.