We claim that if m and n are positive integers cos nt

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Unformatted text preview: es. It is a crucial tool for understanding waves, including water waves, sound waves and light waves. Suppose, for example, that the function f (t) represents the amplitude of a light wave arriving from a distant galaxy. The light is a superposition of many frequencies which encode information regarding the material which makes up the stars of the galaxy, the speed with which the galaxy is receding from the earth, its speed of rotation, and so forth. Much of our knowledge of the universe is derived from analyzing the spectra of stars and galaxies. Just as a prism or a spectrograph is an experimental apparatus for dividing light into its components of various frequencies, so Fourier analysis is a mathematical technique which enables us to decompose an arbitrary function into a superposition of oscillations. In the following chapter, we will describe how the theory of Fourier series can be used to analyze the flow of heat in a bar and the motion of a vibrating string. Indeed, Joseph Fourier’s original investigatio...
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This document was uploaded on 01/12/2014.

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