Mathematics, as a science that studies quantitative relationships and spatial forms in the real world, has always been closely related to the practical needs of people's lives throughout the history of its emergence and development. As the first step in applying mathematical methods to solve practical problems, mathematical modeling naturally has as long a history as mathematics. Newton's law of universal gravitation and Einstein's mass-energy formula are both successful examples of mathematical modeling in the history of scientific development. Marx once said that a science can only be considered perfect when it successfully uses mathematics. In the field of high-tech, mathematics is no longer just a science, but the basis of many applied technologies. In this sense, high-tech is essentially a mathematical technology. Since the second half of th century, due to the rapid development of computer software and hardware, mathematics is penetrating into all fields with unprecedented breadth and depth, and mathematical modeling is becoming more and more important as the key and foundation for applying mathematical methods to study quantitative relationships in various fields. receive people's attention.
In the process of applying mathematics to solve practical problems, we must first quantify the problem, then analyze which ones are constants and which ones are variables, and determine which one to select as the independent variable and which one as the dependent variable. Finally, we must determine the relationship between the variables in the actual problem. The functional relationship between them is correctly abstracted, and a mathematical model between them is established based on the meaning of the question.The establishment of mathematical models helps us use known mathematical tools to explore the underlying laws and help us grasp the current situation, predict and plan for the future. In this sense, we can think of mathematical modeling as aiming to study people A mathematical conception of a particular system or behavior of interest.
In the above process, the establishment of mathematical models is the core and most difficult part of mathematical modeling. In the study of this course, we will gradually explore different mathematical modeling problems in depth based on the content we have learned.
Note: In the process of establishing and solving the mathematical model-function relationship, it is important to understand the following points:
(1) A mathematical model established to describe a specific phenomenon is an idealized model of the actual phenomenon and is therefore far from a completely accurate representation.
(2) Most mathematical models that reflect practical problems are very complex. From the perspective of practical applications, it is usually impossible and unnecessary for people to pursue accurate solutions to mathematical models .
(3) Mastering excellent mathematical software tools and learning to apply them to solve practical problems in related fields has become an important ability that contemporary college students must possess.
