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Mathematical analysis refers to a method of analyzing and solving practical problems by establishing mathematical models. It has been widely applied in modern science, engineering technology, and socio-economic fields. The steps of mathematical analysis include five steps: problem modeling, model assumptions, model establishment, model solving, and model analysis.

1、 Problem modeling. Firstly, it is necessary to clarify the goals, constraints, and constraints of the problem. Based on understanding the background of the problem, transform the actual problem into a mathematical problem, clarify the expression of the problem, and determine the quantitative indicators and evaluation criteria for the problem.

2、 Model assumptions. In the establishment of mathematical models, in order to simplify the problem and facilitate analysis, appropriate assumptions need to be made. Model assumption is a simplification of practical problems, which not only preserves the main characteristics of the problem but also reduces its complexity. The rationality of assumptions has a decisive impact on the establishment of the model and the accuracy of the results.

3、 Model establishment. In the process of model establishment, it is necessary to choose appropriate mathematical methods and tools, and select appropriate model types based on the characteristics of the problem. Common mathematical methods include linear programming, nonlinear programming, dynamic programming, probability theory, and statistics. Convert the problem into mathematical equations, optimization problems, dynamic equations, probability models, and other forms based on the selected mathematical methods and tools.

4、 Model solving. In model solving, it is necessary to select appropriate solving algorithms and tools, and use computers to solve the model. For complex mathematical models, software tools such as MATLAB, Python, etc. can be used for numerical solutions, or manual calculations can be used for analytical solutions.

5、 Model analysis. After the model is solved, it is necessary to conduct a reasonable analysis of the solution results. For optimization problems, sensitivity analysis of the optimal solution is necessary to understand its sensitivity to parameter changes and further determine the stability and reliability of the model. For other issues, rationality testing and practical interpretation of the model's results can be conducted.

In short, mathematical analysis is a scientific, systematic, and quantitative method. By establishing mathematical models to analyze practical problems, it can help us deeply understand the essence and internal relationships of problems, and provide scientific basis for decision-making. In practical applications, attention should be paid to the appropriate abstraction of the problem and the rationality of the assumptions, and the model should be continuously improved and optimized to reflect the actual problem more accurately and obtain solutions that meet the requirements.