2015-48.md

course	course_year	question_number	tags	title	year
Methods	IB	48	IB 2015 Methods	Paper 2, Section I, C	2015

(i) Write down the trigonometric form for the Fourier series and its coefficients for a function $f:[-L, L) \rightarrow \mathbb{R}$ extended to a $2 L$-periodic function on $\mathbb{R}$.

(ii) Calculate the Fourier series on $[-\pi, \pi)$ of the function $f(x)=\sin (\lambda x)$ where $\lambda$ is a real constant. Take the limit $\lambda \rightarrow k$ with $k \in \mathbb{Z}$ in the coefficients of this series and briefly interpret the resulting expression.