Pythagoras was a great Greek philosopher. His motto was “All is number,” which means that all things in the universe obey the rules of numbers. This shows how important numbers are in our life.
So analyzing the numbers are becoming necessary. Numerical analysis mainly focus on this.
Numerical analysis is the subject which uses computers to solve mathematical problems. It is one branch of Mathematics.
In fact, Numerical Analysis is a required course in some departments like Mathematics, Physics, and Chemistry. By smart Google, you can get tons of materials about Numerical analysis. In this post, I will mainly show you what I learned about it in university.
Firstly, the mainly research contents of Numerical analysis are Curvefitting, Interpolation, Approximation of Function, Solving equations and systems of equations, Solving Differential equations, and Solving singular value problems. I still remember my first class. When the instructor showed us its' strong ability by PPT(PowerPoint), I was shocked. I thought I finally got the magic wand to solve annoying differential equations.
Second, from the paragraph above, we can find Numerical analysis is like a generalist who can solve many complicated problems. However, maybe you will be disappointed when you know that it only gives people the approximate solution. In fact, I had the same feeling like you when I got it from my instructor. But with more and more knowledge, I find approximation is reality and exactness is dream in actual application. Approximated solution is enough for our actual problems.
Finally, in general, computers solve actual problems by 5 steps: presenting actual problems, creating mathematical model, numerical analysis, designing program, and implementing program. Every step is not easy. Especially, the step of analyzing the numerical is harder. Scientists need try their best to use all kinds of tools to give better approach of the "exact" solution.
reference:wiki
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