How many terms of the Fourier series must be used to approximate the function at the ends of the segment and in the region of the middle of the segment?

Question

Mathematics

How many terms of the Fourier series must be used to approximate the function at the ends of the segment and in the region of the middle of the segment?
segment from 0 to 1
How to determine this number of members of the series?

Answer 1

This is a tough question.
1. At the ends of the segment, everything will most likely be bad due to the Gibbs effect.
bourabai.ru/signals/ts0403.htm
2. The number of members depends on the function and on the requirements - what is considered a fairly accurate approximation.
Write a program in something like Maple - and have fun with different amounts. I did this - the program is written in 15 minutes, and then you can play.