Introduction to Vibrations and Waves

This course aims to introduce students to the physical and mathematical properties shared by wave phenomena across scales and states of matter. It begins with the vibrations of a single particle, whether free or forced, with due consideration for resonances. It then moves on to collective vibrations of coupled systems of particles, with particular emphasis on normal modes of vibrations. Proper wave-like behavior will then appear in the continuous limit of the particle description and its properties (including reflection, transmission, refraction, polarisation, interference, and diffraction to list a few). In support of the analytic (as opposed to descriptive) approach to the subject, advanced mathematical techniques (to do with ordinary differential equations, linear algebra, and Fourier analysis) will be introduced as and when needed.