MATH331 - Waves
Waves are ubiquitous. Our senses of sight and hearing depend very heavily on the interpretion of light and sound waves respectively. Also, water waves, elastic waves, seismic waves and other less obvious varieties of waves are important to us in natural and technological senses. The last century witnessed the advent of many new wave-based technologies, such as telecommunication, radars (including remote sensing and imaging radars) and lasers that utilise electromagnetic waves, whilst in the acoustic domain, ultrasonic imaging finds application in non-destructive testing and medicine. Further development and exploitation depends crucially on mathematical modelling and analysis. Such models allow us to interpret the intrinsic information contained in waves that are otherwise invisible (or inaudible), and infer the presence (or absence) of certain types of scattering features in the environment.
This unit introduces the theory of waves by a systematic study of the underlying partial differential equations. Waves involve the transfer, without bulk motion, of both energy and information. Fundamental properties of waves are first examined in the simplest 1-dimensional setting. The treatment is then broadened to 2- and 3-dimensional waves, particularly for acoustic and electromagnetic waves. Resonators and waveguides provide some examples of how waves behave in confined regions. In contrast, the scattering and diffraction of waves by obstacles in free space carries information about the scatterer itself; this is the basis of many imaging technologies.
Prerequisites: MATH235(P); MATH232(P) or MATH236(P).
Corequisites: None.
Not Counted for Credit With: None.