Physics would be one of a few examples of fourier transform. One would also use it when they are using engineering so, yeah that is basically it as far as the fourier transform is concerned.
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we use fourier transform to convert our signal form time domain to frequency domain. This tells us how much a certain frequency is involve in our signal. It also gives us many information that we cannot get from time domain. And we can easily compare signals in frequency domain.
when we have need to know the temperature in a bar about any distance we can use fourier series to know that and then we can apply sufficient temperature.
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
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yes it can, if you know how to use or have mathematica have a look at this demo http://demonstrations.wolfram.com/ApproximationOfDiscontinuousFunctionsByFourierSeries/