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Department of Mathematics
MATH331 - Waves
Unit Syllabus
One-Dimensional Waves:
- Partial differentiatial equations and
waves: advection, wave equation, Kline-Gordon, Korteweg-de Vries.
- Travelling waves and dispersive waves;
solitons (KdV).
- D'Alembert solution of the wave equation.
- Standing wave solutions of the wave
equation for homogeneous and nonhomogeneous string.
- Conservation Laws; examples.
- Transmission lines and one-dimensional
wave equation; current and voltage waves; reflection from terminating
impedance.
Two- and Three-Dimensional Waves:
- Acoustic waves: model for waves in fluids
and the scalar Helmholtz equation; plane waves, travelling and
standing; spherical waves and point sources; reflection and refraction
at an interface.
- Resonators: standing waves in rectangular
boxes and other cavities.
- Scattering from soft and hard obstacles:
boundary and radiation conditions for Helmholtz equation, integral
equation models.
- 2-dimensional scattering: the cylinder.
Electromagnetic Waves:
- Model for electric and magnetic fields:
Maxwell's equations, integral forms, existence of electromagnetic
waves.
- Plane waves, travelling and standing.
Waves in a conducting medium.
- Reflection and refraction at an interface.
- Wave guides, rectangular and circular
cross-section.
- Scattering from perfectly conducting
obstacles: boundary and radiation conditions for Maxwell's equations;
2-dimensional scattering: the cylinder.
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