Past exam of the mathematics course of the University of Cambridge / 2014 / ib / Paper 2 / 5D / iii

Table of contents
- Solution iii

Solution

Every sine term vanishes at zero, so $G (0) = 0$ . The one-sided values of the periodic extension of

f^{'}

are

f_{per}^{'} (0 -) = - 1

and

f_{per}^{'} (0 +) = 1

. The Fourier series converges at this jump to their midpoint,

G (0) = \frac{f _{per}^{'} ( 0 - ) + f _{per}^{'} ( 0 + )}{2} = 0.

This midpoint need not equal the arbitrarily assigned value of the periodic derivative at the endpoint.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version