The mathematical model is a mathematical description of some real-life situation. The mathematical modelling is the method of creating a mathematical model of a problem, and using it to analyze and solve the problem.
So in mathematical modelling, we take a real-word problem and convert it to an equivalent mathematical problem. We then solve the mathematical problem, and interpret its solution in the situation of the real – word problem.
Mathematical modelling is an interdisciplinary subject. Mathematics and specialists in other fields share their knowledge and expertise to improve existing products, develop better ones, or predict the behavior of certain products.
There are, of course, many specific reasons for the importance of modelling, but most are related in some ways to the following:
If we have a mathematical model which reflects the essential behavior of a real-world system of interest, we can understand that system better through an analysis of the model. Furthermore, in the process of building the model we find out which factors are most important in the system, and how the different aspect of the system is related.
Very often, we wish to know what a real- world system will do in the future, but it is expensive, impractical or impossible to experiment directly with the system.
Often, we need to estimate large values.
why is mathematical modelling important?-Example
1.) In weather prediction, to study drug efficiency in humans, finding an optimum design of a nuclear reactor, and so on.
2.) For forecasting in marketing departments, reliable forecasts of demand help in planning of the sale strategies.
Before elections, the contesting parties want to predict the probability of their party winning the elections. In particular, they want to estimate how many people in their constituency would for their party. Based on their predictions, they may want to select the campaign strategy. Exit polls have been used widely to predict the number of seats; a party is expected to get in elections.