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 ...

When you set up mathematical formulas, you often have to introduce various kinds of local objects or "dummy variables". You can treat such dummy variables using modules and ...

In just one Mathematica command, you can easily specify a calculation that is far too complicated for any computer to do. For example, you could ask for ...

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}] gives the generalized eigenvalues and ...

Manipulate[expr, {u, u_min, u_max}] generates a version of expr with controls added to allow interactive manipulation of the value of u. Manipulate[expr, {u, u_min, u_max, ...

In almost every area where probability and statistics are used there have been found a few parametric distribution families that are known to be good models. The origins vary ...

NormFunction is an option for functions such as FindFit and NDSolve which gives a function to be minimized in generating results.

It is often useful to carry out a numerical integration using fixed step sizes. For example, certain methods such as "DoubleStep" and "Extrapolation" carry out a sequence of ...

An important subset of optimization problems is constrained nonlinear optimization, where the function is not linear and the parameter values are constrained to certain ...

KernelMixtureDistribution[{x_1, x_2, ...}] represents a kernel mixture distribution based on the data values x_i.KernelMixtureDistribution[{{x_1, y_1, ...}, {x_2, y_2, ...}, ...