NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

Function[body] or body & is a pure function. The formal parameters are # (or #1), #2, etc. Function[x, body] is a pure function with a single formal parameter x. ...

Total[list] gives the total of the elements in list. Total[list, n] totals all elements down to level n. Total[list, {n}] totals elements at level n. Total[list, {n_1, n_2}] ...

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

Characters that are not letters, letter-like forms, or structural elements are treated by Mathematica as operators. Mathematica has built-in rules for interpreting all ...

NDSolve[eqns, y, {x, x_min, x_max}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range ...

For minimization problems for which the objective function is a sum of squares, it is often advantageous to use the special structure of the problem. Time and effort can be ...

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

The utility functions FindMinimumPlot and FindRootPlot show search data for FindMinimum and FindRoot for one- and two-dimensional functions. They work with essentially the ...

NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot ...