MATHEMATICAL MODELLING

-
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

















Comments

Post a Comment

Popular posts from this blog

DOT PUZZLE ( CONNECT ALL THE DOTS WITHOUT LIFTING THE PEN AND WITH ONLY FOUR STRAIGHT LINES WITHOUT ANY OVERLAP )

-
Image
Here we would solve a dot puzzle Consider the figure below Connect all the dots without lifting the pen with only 4 straight lines and the lines do not overlap. Here are some examples already done for you but not been solved because some dots left to be crossed. You could see that some dots have been left to be crossed by the line. So do you think you could solve it. Let us try one more time. Now, what do you see, the puzzle has been solved with the required conditions. Find out some more solutions to this question.
Read more

EULER TRAIL PUZZLE

-
Image
What is an Euler trail ? An Euler trail ( Euler path ) is a trail in a finite graph which visits every edge exactly once. An Euler trail is a walk on the edges of a graph which uses each edge exactly once. Euler trail is also called an Euler chain , Euler walk , Euler path . Here is the puzzle as you could see in the picture. Your job is to cross each line exactly once without lifting your pen.  In the following figure consider every marked line as a single line and each must be crossed once without lifting you pen. Here are some examples already done, but in each case, one line is left ( marked red ) to be crossed . See the figures. Have you got the solution ? well, this is impossible to do however hard you try.  Explanation Consider the figure below and find the numbers of line reaching the centre of each box. In the figure you could see that there are three centre points with odd number of lines
Read more