The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

Mathematica 6.0 represented a major new level in Mathematica's distinguished twenty-year history of broad cutting-edge algorithm development. Mathematica's unified ...

Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of ...

LiftingWaveletTransform[data] gives the lifting wavelet transform (LWT) of an array of data.LiftingWaveletTransform[data, wave] gives the lifting wavelet transform using the ...

CentsToHertz[{i_1, i_2, ...}] converts a list of intervals i_1, i_2, ..., measured in cents to a list of frequencies measured in Hertz, beginning at 440 ...

Permutations are among the most basic elements of discrete mathematics. They can be used to represent discrete groups of transformations and in particular play a key role in ...

ConjugateTranspose[m] or m^\[ConjugateTranspose] gives the conjugate transpose of m.

WaveletImagePlot[dwd] plots the basis tree of wavelet image coefficients in the DiscreteWaveletData dwd.WaveletImagePlot[dwd, r] plots coefficients up to refinement level ...

FindRoot[f, {x, x_0}] searches for a numerical root of f, starting from the point x = x_0.FindRoot[lhs == rhs, {x, x_0}] searches for a numerical solution to the equation lhs ...