## ABSTRACT

The introductory chapter has basic deﬁnitions of a wave, basic equations of motion, diﬀerent conservation laws, the concept of phase and group velocities, and the resulting notion of dispersion relation. Chapters 2 and 3 deal with waves in electromagnetic ﬁelds and the diﬀerent modes in an uniform media. In this chapter, for the ﬁrst time, we shall discuss waves and oscillations in ﬂuids (both liquids and gases). We shall discuss diﬀerent types of waves in ﬂuids, depending on the geometry and the external forces acting on them. To begin we shall concentrate mostly on waves in liquids. In particular, we shall deal with incompressible ﬂuids. The diﬀerent sections in the chapter will include discussion on small amplitude waves, the study of waves in

water under the inﬂuence of gravity, linear capillary and gravity waves, and surface waves. The derivation of Klein−Gordon and Boussinesq equations is mentioned brieﬂy. The concept of shallow water waves (the depth of the layer being smaller than the wavelength of the wave) is discussed in detail. We will also discuss nonlinear eﬀects of the otherwise small amplitude waves.The special case of plane waves in a layer of constant depth is dealt with brieﬂy. We shall present some examples as applicable to geophysical ﬂuid dynamics (Poincare´, Kelvin, inertial waves). Application of Rayleigh and Lamb waves to hydrodynamics and soil mechanics is mentioned in passing. Waves which have large wavelengths have to be discussed in a rotating frame. Thus, we shall discuss waves, both in nonrotating as well as rotating systems.