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
- 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?