Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 14 / a

Table of contents
- Solution a

Solution

In the real Fourier series convention for period

2 π

,

y (x) \sim \frac{a _{0}}{2} + n = 1 \sum \infty [a_{n} cos (n x) + b_{n} sin (n x)],

where the Fourier coefficients are

a_{n} = \frac{1}{π} \int_{0}^{2 π} y (x) cos (n x) d x (n \geq 0), b_{n} = \frac{1}{π} \int_{0}^{2 π} y (x) sin (n x) d x (n \geq 1) .

These formulas apply to integrable periodic functions. Writing equality at each point requires appropriate convergence hypotheses; the periodic solution sought below is smooth, so its series causes no such difficulty.

 Ancestors (12)

 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