1, problem understanding: to understand and define the actual problem, and to clarify the objectives and constraints of the problem. This includes determining the specific problem to be solved, understanding the background of the problem and knowledge in related fields, and collecting and sorting out relevant data and information.
2. Establish a mathematical model: according to the understanding of the problem, turn the actual problem into a mathematical model. Mathematical model is an abstract description of practical problems, and mathematical symbols and equations are usually used to express the key factors and relationships of problems. The model can be deterministic (based on accurate values and relationships) or probabilistic (considering uncertainty and randomness).
3. Analysis and solution: analyze the established mathematical model and use mathematical methods and skills to solve it. This may involve the application of mathematical tools, such as algebraic operation, calculus, statistics and optimization methods. The goal of analysis and solution is to obtain a quantitative understanding of the problem and a solution.
4. Model verification and evaluation: verify whether the established mathematical model can accurately describe practical problems and evaluate the effectiveness and reliability of the model. This includes comparing with actual data and observation results to check the accuracy and feasibility of model prediction.
5. Interpretation and application of results: Explain the results obtained from analysis and solution, and apply them to decision-making and optimization of practical problems. This requires the mathematical results to be transformed into meaningful and operational suggestions and recommendations for practical problems.
Mathematical modeling has applications in various fields, such as physics, engineering, economics, biology and so on. It plays an important role in solving practical problems, promoting scientific research, promoting innovation and optimizing decision-making. People can better understand and solve complex practical problems and provide quantitative prediction and optimization schemes. Mathematical modeling is a process of transforming practical problems into mathematical models and applying mathematical methods to analyze and solve them. It provides a theoretical and practical basis for solving problems through mathematical abstraction and calculation.
The origin of mathematical modeling
The origin of mathematical modeling can be traced back to the development of mathematics. As a discipline, mathematics mainly focuses on pure mathematical concepts and reasoning, such as geometry and algebra. However, with the increase of people's interest and demand for practical problems, mathematics began to be used to solve practical problems, and gradually developed the concept and method of mathematical modeling.