Mathematical modeling applies all kinds of knowledge to solve real problems, which is one of the necessary means to cultivate and improve students' ability to analyze and solve problems by applying what they have learned.
General methods and steps of mathematical modeling
There is no certain pattern for the methods and steps of building a mathematical model, but an ideal model should be able to reflect all the important characteristics of the system: the reliability of the model and the usability of the model. The general method of modeling:
Mechanism analysis: According to the understanding of the characteristics of the real object, analyze its cause and effect relationship, to find out the law reflecting the internal mechanism, the model often has a clear physical or practical significance.
Test analysis method: the research object as a "black box" system, the internal mechanism can not be sought directly, through the measurement of the system's input and output data, and based on the use of statistical analysis methods, according to pre-determined criteria in a certain type of model to select a model with the best data fit. The test analysis method is also called system identification.
The combination of these two approaches, i.e., mechanistic analysis to establish the structure of the model and systematic testing to determine the parameters of the model, is also a common modeling approach.
In the actual process of modeling with one of the methods is mainly based on our understanding of the object of study and the purpose of modeling to decide. Mechanical analysis of the modeling of the specific steps are as follows:
1, the actual problem through the abstraction, simplification, assumptions, to determine the variables, parameters;
2, the establishment of mathematical models and mathematical, numerical solution, to determine the parameters;
3, with the actual problem of the actual data to test the mathematical model;
4, in line with the actual, to be delivered to the use of the economic and social benefits; not in line with the economic and social benefits; not in line with the actual problem of the actual data to check the mathematical model;
4, to meet the practical, to deliver the use of the model, and thus can be used. economic and social benefits; not realistic, re-modeling.
The classification of mathematical models:
1, according to the research method and the mathematical characteristics of the object: primary models, geometric models, optimization models, differential equation models, graphical models, logical models, stability models, statistical models.
2. According to the actual field (or discipline) of the research object: population model, transportation model, environmental model, ecological model, physiological model, town planning model, water resources model, pollution model, economic model, social model, etc..
Mathematical modeling requires a wealth of mathematical knowledge, involving advanced mathematics, discrete mathematics, linear algebra, probability statistics, complex functions and other basic mathematical knowledge. At the same time, you need to have a wide range of interests, strong logical thinking ability, and the ability to express themselves verbally.
What you need to know to participate in the Mathematical Modeling Contest
One, the National Student Mathematical Modeling Contest
Two, the methodology of mathematical modeling and the general steps
Three, important mathematical models and the corresponding case study
1, linear programming model and economic model case study
2, hierarchical analysis model and management model. Case study
3, statistical regression model and case study
4, graph theory model and case study
5, differential equation model and case study
Four, related software
1, Matlab software and programming; 2, Lingo software; 3, Lindo software.
V. Ten commonly used algorithms in number modeling
1. Monte Carlo algorithm. 2. Data processing algorithms such as data fitting, parameter estimation, interpolation, etc. 3. Algorithms of planning class such as linear planning, integer planning, multivariate planning, quadratic planning, etc.
4. Algorithms of graph theory.
5. Computer algorithms such as dynamic planning, backtracking search, partition algorithms, and branching bounds, etc.
6. Three major non 7. lattice algorithms and exhaustive methods. 8. some continuous data discretization methods. 9. numerical analysis algorithms. 10. graphical processing algorithms.
VI. How to consult the data
VII. How to write a thesis
VIII. How to organize a team: teamwork, good cooperation, and continuous problem solving and problem solving.
nine, how to get an award: more complete, a few innovative points.
Ten, how to information processing: WORD, LaTeX, Feiqiu, QQ.
In fact, the main look at the example can be, know some basic models, I also have a lot of examples here, the lectures of the various schools have if you want to ask me directly