MATHEMATICAL MODELLING

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What is mathematical modelling ?
Mathematical modelling is an attempt to study some part ( or form ) of the real-life problems in mathematical terms.

Conversion of physical situation into mathematics with some suitable conditions is known as mathematical modelling. 

Mathematical modelling is nothing but a technique and the pedagogy taken from fine arts and not from the basic sciences.

  • The use of mathematics in solving real-world problems has become widespread especially due to the increasing computational power of digital computers and computing methods, both of which have facilitated the handling of lengthy and complicated problems. 
  • The process of translation of real-life problem into mathematical form can give a better representation and solution of certain problems.


Example
  • Suppose a surveyor wants to measure the height of a tower. It is physically very difficult to measure the height using measuring tape. So, the other option is to find out the factors that are useful to find the height.
  • From the knowledge of trigonometry, he knows that if he has an angle of elevation and the distance of the foot of the tower to the point where he is standing, then he can calculate the height of the tower.
  • So, his job is simplified to find the angle of elevation to the top of the tower and the distance from the foot of the tower to the point where he is standing. Both of which are easily measurable.


Steps involved in mathematical modelling
  1. Understanding the problem ( making assumptions/axioms )
  2. Mathematical description and formulation
  3. Finding the set of solutions
  4. Interpreting the solutions
  5. Validating the model


MATHEMATICAL MODELLING

















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