Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

NIntegrate[f, {x, x_min, x_max}] gives a numerical approximation to the integral \[Integral]_x_min^x_max\ f\ d \ x. NIntegrate[f, {x, x_min, x_max}, {y, y_min, y_max}, ...] ...

NSum[f, {i, i_min, i_max}] gives a numerical approximation to the sum \[Sum]i = i_min i_max f.NSum[f, {i, i_min, i_max, di}] uses a step di in the sum.

Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

DistanceTransform[image] gives the distance transform of image, in which the value of each pixel is replaced by its distance to the nearest background ...

EntropyFilter[image, r] filters image by replacing every value by the information entropy of the values in its range r neighborhood. EntropyFilter[data, r] applies entropy ...

Map[f, expr] or f /@ expr applies f to each element on the first level in expr. Map[f, expr, levelspec] applies f to parts of expr specified by levelspec.

This gives a result for the integral of x^n that is valid for almost all values of n. For the special case of x^-1, however, the correct result is different. The overall goal ...

You may have noticed that there are two different ways to make assignments in Mathematica: lhs=rhs and lhs:=rhs. The basic difference between these forms is when the ...