The precise details of the naming of files differ from one computer system to another. Nevertheless, Mathematica provides some fairly general mechanisms that work on all ...

There are many variants of quasi-Newton methods. In all of them, the idea is to base the matrix B_k in the quadratic model on an approximation of the Hessian matrix built up ...

Mathematica includes comprehensive support for XML, the meta-markup language developed by the World Wide Web Consortium (W3C) for describing structured documents and data. ...

"Introduction to Manipulate" and "Introduction to Dynamic" provide most of the information you need to use Mathematica's interactive features accessible through the functions ...

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...

PathGraph[{v_1, v_2, ...}] yields a path with vertices v_i and edges between v_i and v i +\[ThinSpace]1 .PathGraph[{e_1, e_2, ...}] yields a path with edges ...

VectorPlot[{v_x, v_y}, {x, x_min, x_max}, {y, y_min, y_max}] generates a vector plot of the vector field {v_x, v_y} as a function of x and y. VectorPlot[{{v_x, v_y}, {w_x, ...

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

ND[expr, x, x_0] gives a numerical approximation to the derivative of expr with respect to x at the point x_0.ND[expr, {x, n}, x_0] gives a numerical approximation to the ...

CirculantGraph[n, j] gives the circulant graph with n vertices and jump j C_n (j).CirculantGraph[n, {j_1, j_2, ...}] gives the circulant graph with n vertices and jumps j_1, ...