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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.
- Winter '14