Model hypothesis: according to the characteristics of the actual object and the purpose of modeling, simplify the problem and put forward some appropriate assumptions in accurate language.
Modeling: On the basis of hypothesis, use appropriate mathematical tools to describe the mathematical relationship between variables and establish the corresponding mathematical structure. (Try to use simple math tools)
Model solution: calculate (estimate) all parameters of the model by using the obtained data.
Model analysis: analyze the results by mathematical methods.
Model test: compare the results of model analysis with the actual situation to verify the accuracy, rationality and applicability of the model. If the model is in good agreement with the actual situation, the practical significance of the calculation results should be given and explained. If the model is inconsistent with the actual situation, the assumptions should be modified and recalculated.
Model application: the application method varies with the nature of the problem and the purpose of modeling.
First, the competition reference book
L, Mathematical Modeling Competition for Chinese College Students, edited by Li Daqian, Higher Education Press (1998).
2. Tutoring materials for college students' mathematical modeling contest, (1), (2) and (3), edited by Ye, Hunan Education Press (1993, 1997, 1998).
3. Mathematical Modeling Education and International Mathematical Modeling Competition "Engineering Mathematics" album, edited by Ye, "Engineering Mathematics" magazine, 1994).
Second, domestic teaching materials and series:
1, Mathematical Model, edited by Jiang Qiyuan, Higher Education Press (1st edition 1987, 2nd edition 1993, 3rd edition in 2003; The first edition won the "National Excellent Textbook Award" in the second national excellent textbook selection organized by the State Education Commission.
2. Mathematical Model and Computer Simulation, edited by Jiang and Xin Peiqing, University of Electronic Science and Technology of China Press, (1989).
3. Selection of Mathematical Models (from Books to Mathematics), Hua, Zhu, translated, Hunan Education Press; ( 199 1).
4. Mathematical Modeling-Methods and Examples, edited by Shou Jilin, Jiaotong University Press (1993).
5. Mathematical model, edited by Pu Dingguo and Tian Weiwen, Southeast University Press (1994).
6. Mathematical Model, edited by Zhu Siming and Li Shanglian, Sun Yat-sen University Press, (1995)
7. Mathematical model, edited by Chen Yihua, Chongqing University Press, (1995)
Modeling and Analysis of Mathematical Models, edited by Cai Changfeng, Science Press, (1995).
9. Course of Mathematical Modeling Competition, edited by Li Shangzhi, Jiangsu Education Press, (1996).
Introduction to Mathematical Modeling, edited by Xu and Yang Jinhao, Chengdu Dianzi University Press, (1996).
1 1, Mathematical Modeling, edited by Shen, Shi Jiuyu and Gao Zhenbin, Harbin Engineering University Press, (1996).
12, Fundamentals of Mathematical Models, edited by Wang Shuhe, University of Science and Technology of China Press, (1996).
13, Mathematical Model Method, edited by Qi Huan, Huazhong University of Science and Technology Press, (1996).
14, Mathematical Modeling and Experiment, Symposium on Mathematical Modeling and Industrial Mathematics in Nanjing Institute of Technology, Hohai University Press, (1996).
Mathematical Model and Mathematical Modeling, edited by Liu Zeng, Du Fu Publishing House, Beijing Normal University (1997).
16. Mathematical Modeling, edited by Yuan Zhendong, Lin Wuzhong and Jiang, edited by East China Normal University Press.
Mathematical Model, edited by Tan Yongji and Yu Wenpi, Fudan University Press, (1997).
Practical Course of Mathematical Models, edited by Fei Peizhi and Cheng Zhongyu, Sichuan University Press, (1998).
19, Selected Excellent Cases of Mathematical Modeling (Series of Construction of Engineering Mathematical Bases), edited by Wang Guoqiang, South China University of Technology Press, (1998).
20. Economic Mathematical Model (2nd Edition) (Engineering Mathematical Base Construction Series), edited by Hong Yi, He Dehua and Chang Zhihua, South China University of Technology Press, (1999).
2 1, Lecture Notes on Mathematical Models, edited by Lei, Peking University Publishing House (1999).
22. Excellent case of mathematical modeling, edited by Zhu Daoyuan, Southeast University Press, (1999),
23. Mathematical Model Method for Problem Solving, Liu Zeng, Beijing Normal University Press, (1999).
24. Theory and Practice of Mathematical Modeling, edited by Wu Xiang, Ng Man Tat and Cheng Lizhi, National University of Defense Technology Press, (1999).
25. Case analysis of mathematical modeling, edited by Bai Qiling, Ocean Press, (Beijing, 2000).
26. Mathematical Experiment (series of textbooks for colleges and universities), edited by Xie and Zhang Zhirang, Science Press, 2000.
27. Mathematical Experiment, edited by Fu Peng, Gong Li and Liu Qiongsun, and edited by Zhongshi He, Science Press, 2000.
28. Mathematical Modeling and Mathematical Experiments, edited by Zhao Jing and Qi Dan, Higher Education Press, 2000.
Three, foreign reference books (Chinese translation):
1, Introduction to Mathematical Models, E.A. Bender, translated by Zhu, Science Popularization Press (1982).
2. Mathematical Model, author, translation, etc. , machinery industry press, (1985).
3. Differential equation model, (Applied Mathematical Model SeriesNo. 1 Volume), edited by ]W.F.Lucas, Zhu Yumin, etc. , National University of Defense Technology Press, (1988).
4. Politics and Related Models, (Volume 2 of Applied Mathematical Models Series), [edited by W.F. Lucas, translated by Wang Guoqiu, etc. , National University of Defense Technology Press, (1996).
5. Discrete and System Model (Volume 3 of Applied Mathematical Model Series), [edited by W.F. Lucas, translated by Cheng Lizhi, etc. , National University of Defense Technology Press, (1996).
6. life science model, (volume 4 of applied mathematical model series), [edited by US 65438+W.F. Lucas, translated by Zhai Xiaoyan, etc. , National University of Defense Technology Press, (1996).
7. Model Mathematics-Continuous Dynamical System and Discrete Dynamical System, [compiled by UK 1 H.B. Grif6ths and A.0 1 D Know, compiled by Xiao Li and Zhang Zhijun, Science Press, (1996).
8. Mathematical Modeling —— Case Studies from Four Industries in the UK (Series 4 of Applied Mathematics Translation), translated by D. Burglas and others, translated by Ye and Wu, World Book Publishing Company, (1997).
Fourth, professional reference books (there are many books in this field, but not many for reference only):
Mathematical model of water environment, [Germany] W. Kinze 1bach, Yang Rujun, edited by Liu, China Building Industry Press, (1987).
2. Mathematical model in science and technology engineering, edited by Kan, Railway Press (1988).
3. Biomedical Mathematical Model, edited by Qingyi Research, Hunan Science and Technology Press (1990).
4. Mathematical model and application of crop pest management, edited by Pu Zhelong, Guangdong Science and Technology Press (1990).
5. Mathematical Models in System Science, edited by Ouyang Liang, Shandong University Press, (1995).
6. Mathematical Modeling and Research of Population Ecology, Ma Zhien, Anhui Education Press, (1996)
7. Modeling, Transformation and Optimization-New Progress of Structural Synthesis Method, Sui, Dalian University of Technology Press, (1986)
8. Genetic model analysis, by Zhu Jun, China Agricultural Press (1997). (Edited by Wang Shousong, Department of Mathematics, Sun Yat-sen University, April 5438+0, 2006)