With the rapid development of computer technology, the application of mathematics not only plays an increasingly important role in engineering technology, natural science and other fields, but also penetrates into new fields such as economy, finance, biology, medicine, environment, geology, population and transportation with unprecedented breadth and depth. Whether solving practical problems in the fields of science and technology and production by mathematical methods or combining 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.
When people observe, analyze and study an object, they often use models, such as airplane models and dam models in exhibition halls. In fact, photos, toys, maps and circuit diagrams are all models, which can reflect some characteristics of real objects in a general and concentrated way, thus helping people to understand and master that object quickly and effectively. The mathematical model is just a more abstract model.
When it is necessary to analyze and study a practical problem from a quantitative point of view, people should, on the basis of in-depth investigation and study, understanding the object information, making simplified assumptions and analyzing the internal laws, express it as a mathematical formula, that is, a mathematical model, with mathematical symbols and language, and then use the calculated model results to explain the actual problem and accept the actual test. This whole process of establishing mathematical model is called mathematical modeling. Mathematical modeling is an important means to solve practical problems by using mathematical tools. Mathematics education should not only teach students mathematical knowledge, but also teach students to use what they have learned to solve practical problems. In view of the clear learning characteristics of the comprehensive department of junior college, teachers should be good at modeling the conceptual laws and problem-solving methods of mathematics in teaching, so that students can master the basic knowledge of mathematics and apply it to solve problems in life and production.
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.