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).