What kind of functions can be decomposed into Fourier aerUs

What kind of functions can be decomposed into Fourier aerUs and what into Fourier integral? (b) When analyzing stability of equilibrium states in various physical problems, why do we suppose variations about equilibrium values to be small? (c) In which physical problems do we come across Bessel\'s equations (mention one or two problems commenting on symmetry properties of solutions)? (d) When solving the wave or heat equation by separation of variables, we first seek particular solutions in the form F(x)G(t) and then sum them up. Why are we sure that the sum satisfies the equation? (Comment on a property of the governing equation).

Solution

1.a)odd and even function