NIntegrate[f, {x, x_min, x_max}] gives a numerical approximation to the integral \[Integral]_x_min^x_max\ f\ d \ x. NIntegrate[f, {x, x_min, x_max}, {y, y_min, y_max}, ...] ...

FindFit[data, expr, pars, vars] finds numerical values of the parameters pars that make expr give a best fit to data as a function of vars. The data can have the form {{x_1, ...

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Automatically selecting between hundreds of powerful and in many cases original algorithms, Mathematica provides both numerical and symbolic solving of differential equations ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

When building an initial statistical model, you may not have a good idea of what parametric distribution family it should come from. Nonparametric distributions make very few ...

BSplineBasis[d, x] gives the zeroth uniform B-spline basis function of degree d at x.BSplineBasis[d, n, x] gives the n\[Null]^th uniform B-spline basis function of degree ...

WaveletPsi[wave, x] gives the wavelet function \[Psi](x) for the symbolic wavelet wave evaluated at x.WaveletPsi[wave] gives the wavelet function as a pure function.

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica ...

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...