Oscillations and waves : an introduction Preface Oscillations and waves are ubiquitous phenomena in the world around us. An oscillation is defined as a disturbance in a physical system that is repetitive in time. A wave is defined as a disturbance in a continuous spatially extended physical system that is both repetitive in time and periodic in space. In general an oscillation involves a continual back and forth flow between two different energy types. For example in the case of a pendulum the two energy types are kinetic and gravitational potential energy. A wave involves similar repetitive energy flows to an oscillation but in addition is capable of transmitting energy (and information) from one place to another. Although sound waves and electromagnetic waves for example rely on quite distinct physical mechanisms they nevertheless share many common properties. This is also true of different types of oscillation. It turns out that the common factor linking the various types of wave and oscillation is that they are all described by the same mathematical equations. The aim of this textbook is to develop a unified mathematical theory of oscillations and waves. Examples are drawn from the physics of discrete mechanical systems; continuous gases fluids and elastic solids; electronic circuits; electromagnetic waves; optical systems; and finally quantum mechanical systems. It is assumed that readers of this book possess a basic familiarity with the laws of physics such as might be obtained from a standard two semester introductory college level survey course. Readers are also assumed to be conversant with collegelevel mathematics up to and including algebra trigonometry linear algebra ordinary differential equations and partial differential equations