As of version 6.0, NearestNeighbor has been superseded by Nearest[{{x_1, y_1}, {x_2, y_2}, ...} -> Automatic, {a, b}].
As of Version 7.0, DTFourierTransform has been renamed to FourierSequenceTransform and is part of the built-in Mathematica kernel.
As of Version 7.0, FourierCoefficient is part of the built-in Mathematica kernel.
As of Version 7.0, FourierCosCoefficient is part of the built-in Mathematica kernel.
As of Version 7.0, FourierSeries is part of the built-in Mathematica kernel.
As of Version 7.0, FourierSinCoefficient is part of the built-in Mathematica kernel.
As of Version 7.0, FourierTrigSeries is part of the built-in Mathematica kernel.
As of Version 7.0, InverseDTFourierTransform has been renamed to InverseFourierSequenceTransform and is part of the built-in Mathematica kernel.
In Version 6, ListIntegrate has been superseded by Integrate[Interpolation[data, InterpolationOrder -> k][x], {x, Max[x_c], Min[x_c]}], for data = {{x_1, y_1}, ..., {x_n, ...