Step one, ask questions.

List the variables involved in the question, including the appropriate units. Be careful not to confuse variables with constants. List all assumptions about variables, including equality and inequality. Check the unit to ensure that the assumptions make sense. Give the goal of the problem with accurate mathematical expressions.

The second step is to choose the modeling method.

Choose a general solution to solve the problem. Generally speaking, this step requires some mathematical modeling experience and skills. At the same time, you need to be familiar with the relevant literature.

The third step is to derive the formula of the model.

Re-express the problem obtained in the first step into the form required by the modeling method selected in the second step. Make sure that the variable names in the first step are the same as those in the second step. Write down any supplementary assumptions made to adapt the problems described in the first step to the mathematical structure selected in the second step.

The fourth step is to solve the model.

Apply the method selected in the second step to the expression obtained in the third step. Pay attention to mathematical derivation to ensure that the derivation process is correct and the results are meaningful. Adopt appropriate methods to expand the scope of solving problems and reduce calculation errors.

Step five, answer the questions.

Restate the results of step 4 in non-technical language. Avoid mathematical symbols and terminology.

Mathematical technology:

With the rapid development of computer technology, the application of mathematics not only plays an increasingly important role in engineering technology, natural science and other fields, but also penetrates into new fields such as economy, management, finance, biology, medicine, environment, geology, population and transportation with unprecedented breadth and depth. The so-called mathematical technology has become an important part of modern high technology.

Mathematical model is a kind of simulation, which uses mathematical symbols, mathematical formulas, programs, graphics and so on to describe the essential attributes of practical topics abstractly and concisely. It may explain some objective phenomena, or predict the future development law, or provide an optimal strategy or a better strategy in a sense to control the development of a phenomenon.

Generally speaking, mathematical model is not a direct copy of real problems, and its establishment often requires people to observe and analyze real problems in depth and carefully, and also requires people to use all kinds of mathematical knowledge flexibly and skillfully. This process of abstracting mathematical models from practical problems with applied knowledge is called mathematical modeling.