With the progress of mankind, the development of science and technology, and the increasing digitalization of society, the application of mathematical modeling is more and more extensive, and the mathematical content around people is becoming more and more abundant. It is of great significance to emphasize the application of mathematics and cultivate the consciousness of applied mathematics to promote the implementation of quality education. The position of mathematical modeling in mathematical education has been promoted to a new height. Solving mathematical application problems through mathematical modeling can improve students' comprehensive quality. Based on the characteristics of mathematical application problems, this paper analyzes how to use mathematical modeling to solve mathematical application problems, hoping to get help and correction from colleagues.
First, the characteristics of mathematical application problems
We often call it a kind of mathematical problem, which comes from the reality of the objective world, has practical significance or background, and needs to be transformed into mathematical form through mathematical modeling, so as to be solved. Mathematical application problems have the following characteristics:
First, the mathematical application problem itself has practical significance or background. Reality here refers to all aspects of the real world, such as production reality, social reality, life reality and so on. For example, practical problems closely related to textbook knowledge and originated from real life; Application problems related to the intersection of modular subject knowledge networks; Application problems related to the development of modern science and technology, social market economy, environmental protection and realistic politics.
Secondly, the solution of mathematical application problems needs the method of mathematical modeling, which makes the problem mathematical, that is, the problem is transformed into mathematical form to express and then solved.
Third, there are many knowledge points involved in mathematical application problems. It is a test of the ability to comprehensively apply mathematical knowledge and methods to solve practical problems. It examines students' comprehensive ability and generally involves more than three knowledge points. If you don't master a certain knowledge point, it is difficult to answer the question correctly.
Fourthly, there is no fixed pattern or category for the proposition of mathematical application problems. It is often a novel practical background, which makes it difficult to train the problem model and solve the changeable practical problems with "sea tactics" Solving problems must rely on real ability, and the examination of comprehensive ability is more real and effective. Therefore, it has broad development space and potential.
Second, how to model mathematical application problems
Establishing mathematical model is the key to solving mathematical application problems. How to build a mathematical model can be divided into the following levels:
The first level: direct modeling.
According to the subject conditions, the ready-made mathematical formulas, theorems and other mathematical models are applied, and the explanatory diagram is as follows:
Conditional translation of themes
In mathematical expression,
Substitute the problem setting conditions of the application test into the mathematical model to solve.
Select the one that can be used directly.
mathematical model
The second level: direct modeling. You can use the existing mathematical model, but you must summarize this mathematical model, analyze the application problems, and then determine the specific mathematical model needed to solve the problems or the mathematical quantities needed in the mathematical model before you can use the existing mathematical model.
The third level: multiple modeling. Only by refining and dealing with complex relations, ignoring secondary factors and establishing several mathematical models can we solve the problem.
The fourth level: hypothesis modeling. Before the mathematical model is established, it needs to be analyzed, processed and assumed. For example, when we study the traffic flow at intersections, we can only model them when the traffic flow is stable and there are no emergencies.