Descriptif

In this course, we introduce vector and Fourier analysis from a hands-on, application-oriented perspective, in coordination with PHY104: Electromagnetism and Light. Vector analysis spans the differentiation and integration of vectors in two and three-dimensional 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 then use this tool to solve the wave equation on a finite domain. 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…).