Mathematica 6.0 fundamentally redefined Mathematica and introduced a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, ...

Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient search methods use ...

ParametricPlot[{f_x, f_y}, {u, u_min, u_max}] generates a parametric plot of a curve with x and y coordinates f_x and f_y as a function of u. ParametricPlot[{{f_x, f_y}, ...

ParameterMixtureDistribution[dist[\[Theta]], \[Theta] \[Distributed] wdist] represents a parameter mixture distribution where the parameter \[Theta] is distributed according ...

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

Mathematica 8 adds major new areas, including probability and statistics, graphs and networks, computational finance, control systems, wavelet analysis, and group theory. ...

QHypergeometricPFQ[{a_1, ..., a_r}, {b_1, ..., b_s}, q, z] gives the basic hypergeometric series \[Null]_r \[Phi]_s (a; b; q; z).

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

ComplexExpand[expr] expands expr assuming that all variables are real. ComplexExpand[expr, {x_1, x_2, ...}] expands expr assuming that variables matching any of the x_i are ...

GCD[n_1, n_2, ...] gives the greatest common divisor of the n_i.