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The application of mathematical modeling in daily life.
- Apr 23, 2018 -

一、mathematical model and mathematical modeling basic meaning.

Mathematical model: in accurately grasp things within the system, on the basis of specific characteristics and relations, integration of abstract relations, using mathematical language, generalization and expression, the approximate to generate a mathematical structure system. The establishment of mathematical model is the way of similarity reflecting the objective existence form and various complex relations.

Mathematical modeling: a mathematical model to solve problems in real life.  

二、 Mathematical modeling procedure.

In theory, mathematical modeling is only a macroscopic specification for a specific mathematical model, and it is necessary to carry out the concrete analysis of the necessary specific problems in practical operation to achieve the flexible application of mathematical modeling form.

General procedures for mathematical modeling:

1.Prepare the model. The realization of this stage is based on the familiarity with the actual problems, the reason and background of the problem, and the purpose of mathematical modeling.  

2. Model building. On the basis of preparation, the data and data collected are analyzed and processed, and mathematical language is used to find the hypothesis conditions to ensure the relative accuracy of mathematical language. The related changes involved in the specific problems and the uncertainty of the relationship require the proper coordination of mathematical tools to establish the mathematical model. The mathematical model can include equations, inequalities, graph functions and tables. When modeling, we should strive for the simplification of mathematical tools in order to achieve the wide popularization and popularization of the model. Simplified modeling tools can be applied to the real life and can be widely adopted, accepted and applied.  

3.Solution model. The solution model requires the use of mathematical tools, which may be used in intuitive or indirect ways such as equations, logical reasoning and proofs, illustrations, etc. The results of the model need according to the practical problems correctly analysis to determine the relationship between various factors, the results analysis needs to be done according to the results of prediction mathematical formula, the choice of optimal decision and control the best implementation. The choice of the optimal decision is a common problem in solving practical problems, the comprehensive measure under the premise of a variety of options, the optimal choice is the key to decision, and the establishment of the mathematical model can be aided by mathematical tools, faster, more concise, more intuitive implementation choice optimization, solving practical problems.  

4. Test model. After the results of the comprehensive analysis of the model are completed, the analysis results need to be put into real life and tested. Check the correctness of the model and scientific to use the actual phenomena and data of the model the data and results were analyzed, corresponding analysis of the experimental data and access, accurately grasp the rationality of the mathematical model and practical value. The successful identification of mathematical modeling requires that the model should be able to predict the unknown phenomena and the ability and value to predict the unknown phenomena. In the process of modeling, the model hypothesis may have a problem, and the reason is usually derived from the inspection process, the result is not in line with the actual situation, but the solving process is not wrong. The model assumes that the error compensation measures are mainly modified and supplemented in time to make up for its error. In the modification and supplement model assumption, when the result, accuracy is required, can be regarded as the model hypothesis can be used, then the model can realize its application value and promotion function.  

三、Mathematical modeling and optimization problems in life.

Optimization problems include industrial and agricultural production, daily life and so on. The selection of scheme optimization and the formulation of test plan are all involved in the application of mathematical modeling. For the most value problem, the general method is to transform the actual problem and solution into a function form by establishing the function model, to solve the most value problem. The optimization of the scheme is similar to the establishment of corresponding functions of different schemes.