Descriptif

In this course, we introduce vector and
Fourier analysis from a hands-on, application-
oriented perspective. Vector
analysis spans the differentiation and
integration of vectors in two and threedimensional
space, eventually culminating
with Green’s theorem in the plane
and its higher-dimensional generalization,
Stokes’ theorem. Changing gears,
we introduce the concept of Fourier
series, which give an approximation of
periodic functions as an infinite sum of
cosines and sines.
We conclude the course with a gentle
introduction to Fourier transforms,
viewed as a limit of Fourier series in the
limit of infinite periodicity. Besides their
intrinsic mathematical interest, these
tools are widely used in Physics (Electromagnetism,
Fluid mechanics, Quantum
mechanics…), signal processing and areas
of Economics (cycle analysis in financial
markets and business models).