The wavelet transform is a tool for carving up functions, operators, or data into components of different frequency, allowing one to study each component separately. The term wavelet was itself coined in 1982, according to [Daubechies]. Wavelet analysis may be thought of as a generalization of analysis by the Hilbert space method, wherein one forms an orthogonal basis of the space of interest. Equations in that space may then be solved in terms of the basis. Hilbert space techniques are especially useful in the solution of linear ordinary differential equations (ODEs), and permit one to reduce certain partial differential equations (PDEs) to two or more ODEs related by variables of separation.