As a student, a question popped in my mind as soon as I heard about Numerical Analysis. What is so special about this field of mathematics and how is it different?
In the search for my answer to this question, I explored Numerical Analysis. To put it simply numerical analysis is used to help us find solutions to lengthy problems in general or statistically indeterminant problems (i.e. where the number of variables is more than the number of equations available).
If this is such a powerful tool, then why do we need to remember lengthy equations to find the roots of equations, to begin with?
Numerical analysis even though a powerful tool has its downsides, as you always get an approximation and not the exact answer. The error in results can be reduced to a significant amount depending upon our needs.
Thus, if you’re designing a system for nuclear power plant you need a very high level of accuracy and if you’re designing a system for a college project you may need significantly lesser accuracy.
As for importance take the example of weather predictions.
Have you ever wondered how do they calculate how the weather is going to be like in the future? The advanced numerical analysis provides you the solution with approximate but accurate results.
You know that it takes time to solve an order 3 equation and there are limited ways in which you can solve it. What if I say that you’ve to solve a 100-order equation? Which is not possible to solve using the analytical method?
You’re working in a manufacturing plant and you want to predict the sales based upon the trend that has been followed in the past and if there is a lot of variation then it gets tedious to do it manually.
There is software such as MATLAB or Octave where you can code that calculates the solution to these and many other complicated problems.