Answer the following questions in detail: a) What are Fourier series and what do they mean physically? b) What is the Fo

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Answer the following questions in detail: a) What are Fourier
series and what do they mean physically? b) What is the Fourier
transform and what is the inverse, what do they mean physically? c)
When applying the derivative to a Fourier series, what happens to
the expression? d) What is the solution of a differential equation
like and what is the Fourier transform used for? e) What is a
particular solution to the differential equations? f) what is the
principle of superposition and how is the general solution to the
wave equation determined? g) What is the spectrum and what are the
infinite sums? g) What is convolution and what does it mean
physically? h) what is the convolution theorem and what is it
physically useful for?