This course covers the mathematical description of wave motion and fluid mechanics. It begins by reviewing some key equations in particle mechanics and then considers the equations for waves and fluids. The emphasis throughout is on understanding the equations and obtaining actual solutions where possible. Wave examples will include kinematic waves, electromagnetic waves, pressure and shear waves in solids, surface and internal waves in fluids and gravitational waves. Fluid topics include surface tension, viscosity, pressure, streamlines and stream functions, circulation and vorticity, viscous flow and aerodynamics with lift and drag.