The Application Of Ordinary Differential Equations In Mathematical Modeling

The formation and development of ordinary differential equations are closely related to mechanics, astronomy, physics, as well as other scientific and technological development. Other branches of mathematics and the new development, such as the complex variable function, Lie group, combination of topology and so on, had a profound impact on the development of ordinary differential equations; the current development of the computer also served as a very powerful tool for the application of ordinary differential equations and its theoretical research.When Newton was studying on celestial mechanics and mechanical study of mechanics, he used differential equations as the tools, and got the theoretical principle of the movement of planets. Later, the French astronomer Le Verrier and British astronomer Adams using the differential equations to calculate their time has not yet found the location of Neptune. These are more convinced to make a mathematician in the understanding of differential nature, the great transformation of natural forces.With the gradual improvement of the theory of differential equations, it can accurately describe the change of things according to the basic laws followed; as long as the corresponding differential equations are listed, there are ways to solve the equation. Differential equation has become the most vibrant branch of mathematics. Mathematical model is a mathematical simplification of actual objects. It is often closer to the real thing is a sense of abstract form, but it has a clear distinction with real things. There are many ways by which we can describe a real phenomenon, such as sound recordings, films, analogy, hearsay and so on. In order to describe things more scientifically, more logically, more objectively and make it more repeatable, it is generally agreed that we can use a more stringent language to describe the phenomena, this language is mathematics. Using mathematical language to describe things is called the mathematical model. Sometimes we need to do some experiments, but these experiments often come out with an abstract mathematical model as a substitute for actual objects and the corresponding experiments of the actual operation itself is a theoretical alternative.When we use applied mathematics to solve practical problems, the establishment of mathematical model is not only a very crucial step, but also a very difficult step. The process of establishing teaching model is to simplify the complex practical problems, and make it the abstract mathematical structure for a reasonable process. Through surveys, data collection, observation and study of the inherent characteristics of the actual object and the inherent law, we can seize the issue of the principal contradiction, and establish the relationship between the number of practical problems, and then use mathematical theories and methods to analyze and solve problems. This requires a solid mathematical foundation for a deep, keen insight and imagination, the practical problems of interest and broad knowledge. Mathematical modeling is linked with the practical problems of mathematics, is the mathematics in the wider use of firearms from the media, and is becoming more and more appreciated by the people in mathematical science and technology field, as well as in engineering field. It has become one of the important ability which is essential for modern science and technology workers.Mathematics to be applied in practice must be based on the model, and mathematical modeling is the mathematical language which is used to describe the process of the actual phenomena; when we apply mathematics to solve practical problems, the establishment of mathematical model is not only a very crucial step, but also very difficult step. The process of establishing teaching model is to simplify the complex practical problems, and make them the abstract mathematical structure for a reasonable process. Through surveys, data collection, observation and study of the inherent characteristics of the actual object and the inherent law, seize the issue of the principal contradiction, establish the relationship which can reflect the relationship between the number of practical problems, and then we can use mathematical theories and methods to analyze and solve problems.This paper first introduces the development of the ordinary differential equations, and then introduces the mathematical modeling, and then introduces the combination of the characteristics of the two, and then introduced in different fields related to specific examples. Last but not least, there comes the final summary of ordinary differential equations in mathematical modeling, as well as how to delelop in the teaching process.