ABSTRACT
In the middle of the eighteenth century much attention was given to the problem of determining the mathematical laws governing the motion of a vibrating string with fixed endpoints at 0 and π. In pure mathematics, the Poisson summation formula is a major tool in analytic number theory, and the Poisson integral pointed the way to many significant developments in Fourier analysis. Fourier analysis is a powerful tool in the study of partial differential equations (and ordinary differential equations as well). Fourier’s name has become universally known in modern analytical science. His ideas have been profound and influential. Harmonic analysis is the modern generalization of Fourier analysis, and wavelets are the latest implementation of these ideas. The method of separation of variables is used to find a solution of the boundary value problem.
