Plot3D[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a three-dimensional plot of f as a function of x and y. Plot3D[{f_1, f_2, ...}, {x, x_min, x_max}, {y, y_min, ...

The numerical method of lines is a technique for solving partial differential equations by discretizing in all but one dimension, and then integrating the semi-discrete ...

Graph[{e_1, e_2, ...}] yields a graph with edges e_j.Graph[{v 1, v 2, ...}, {e_1, e_2, ...}] yields the graph with vertices v_i and edges e_j. Graph[{..., w_i[v_i, ...], ...

Mathematica's approach to differential operators provides both an elegant and a convenient representation of mathematical structures, and an immediate framework for strong ...

Mathematica automatically uses sophisticated algorithms to track the precision of approximate numbers. Particularly for some verification applications, however, it is ...

Mathematica includes state-of-the-art algorithms for sequence alignment and comparison, capable of handling strings and lists containing very large numbers of elements.

$PerformanceGoal gives the default setting for the option PerformanceGoal for graphics and other algorithmic functions.

Structural Operations on Polynomials Finding the Structure of a Polynomial Polynomial Orderings

Differentiation Total Derivatives Derivatives of Unknown Functions

[1] Mehrotra, S. "On the Implementation of a Primal-Dual Interior Point Method." SIAM Journal on Optimization 2 (1992): 575–601. [2] Nelder, J.A. and R. Mead. "A Simplex ...