Mathematical modeling comprehensively applies all kinds of knowledge to solve practical problems, which is one of the necessary means to cultivate and improve students' ability to apply what they have learned to analyze and solve problems.
General methods and steps of mathematical modeling
There is no certain pattern in the methods and steps of establishing mathematical model, but an ideal model should reflect all the important characteristics of the system: the reliability and availability of the model. General methods of modeling:
Mechanism analysis: according to the understanding of the physical characteristics, analyze the causal relationship and find out the laws reflecting the internal mechanism. The established model usually has clear physical or practical significance.
Test and analysis method: the research object is regarded as a "black box" system, and the internal mechanism cannot be directly sought. By measuring the input and output data of the system, and on this basis, using the statistical analysis method, the model with the best data fitting is selected from a certain type of model according to the predetermined standard. Test analysis method is also called system identification.
Combining these two methods is also a common modeling method, that is, the structure of the model is established through mechanism analysis, and the parameters of the model are determined through system testing.
In the actual process, which method to use for modeling mainly depends on our understanding of the research object and the purpose of modeling. The concrete steps of mechanism analysis and modeling are roughly as follows:
1, the variables and parameters are determined by abstraction, simplification and assumption in practical problems;
2. Establish a mathematical model, solve it mathematically and numerically, and determine the parameters;
3. Test the mathematical model with the measured data of practical problems.
4, in line with the reality, delivered to use, can produce economic and social benefits; Not realistic, re-model.
Classification of mathematical models:
1. According to the research methods and mathematical characteristics of the object, it can be divided into elementary model, geometric model, optimization model, differential equation model, graph theory model, logic model, stability model and statistical model.
2. According to the actual field (or discipline) of the research object, it is divided into population model, traffic model, environment model, ecological model, physiological model, urban planning model, water resource model, pollution model, economic model and social model.
Mathematical modeling needs rich mathematical knowledge, involving advanced mathematics, discrete mathematics, linear algebra, probability statistics, complex variable functions and other basic mathematical knowledge. At the same time, you need a wide range of interests, strong logical thinking ability and strong language expression ability.
What do you need to know to participate in the mathematical modeling competition?
I. National Mathematical Modeling Competition for College Students
Second, the methods and general steps of mathematical modeling
Third, important mathematical models and corresponding case studies.
1, case analysis of linear programming model and economic model
2. Case analysis of 2.AHP model and management model.
3. Statistical regression model and case analysis.
4. Graph theory model and case analysis.
5. Differential equation model and case analysis.
Fourth, related software.
1, Matlab software and programming; 2.Lingo software; 3.Lindo software.
Five, ten commonly used digital and analog algorithms
1. Monte Carlo algorithm 2. Data processing algorithms, such as data fitting, parameter estimation and interpolation. 3. Programming algorithms, such as linear programming, integer programming, multivariate programming and quadratic programming. 4. Graph theory algorithm. 5. Computer algorithms, such as dynamic programming, backtracking search, divide and conquer algorithm, branch and bound. 6. Three nonclassical algorithms of optimization theory. 7. Grid algorithm and exhaustive method. 8. Several discretization methods of continuous data. 9. Numerical analysis algorithm. 10. Image processing algorithm.
VI. How to obtain information
Seven, how to write a paper
Eight, how to organize the team: team spirit, good at cooperation, constantly ask questions and solve problems.
Nine, how to win the prize: relatively complete, there are several innovations.
X. how to deal with information: WORD, LaTeX, fly ball, QQ.
In fact, just look at the examples and understand some basic models. I also have many examples here. If there are important lectures in various schools, just ask me.