The Mathematical Modeling Process

Step 1. Identify the Problem
What is it you want to do or find out? This is often a difficult part of the modeling process since real-world situations are often described in vague and general terms.

Step 2. Make assumptions
Real-world situations are often too complicated to completely describe mathematically. Often you need reduce the complexity of the problem by making simplifying assumptions.

Classify the variables
What influences the behaviour identified in Step 1? What measurable quantities are involved? Determine which of the quantities are independent variables and which are dependent.

Relate the variables
Determine the relationship among the variables selected for study. Find equations that relate the variables.

Step 3. Solve and interpret the model
Perform whatever mathematical steps that are required to produce solutions out of the model. You may need to go back and modify Step 1 or 2 after you see how this step is going.

Step 4. Verify the model
Make sure the model addressses the problem identified in Step 1. Make sure the model is usable in a practical sense. And test the model with real-world data.

Step 5. Implement the model
Make the model user-friendly. Make it as easy as possible to input the data and interpret the output. Graphics often help in the output.

Step 6. Maintain the model
Things change. Re-evaluate the assumptions made earlier in the modeling process. Can you improve the model by taking more variables into account?