Mathematica contains a very powerful system of integration. It can do almost any integral that can be done in terms of standard mathematical functions.

In calculus, infinite sums and products can pose a challenge to manipulate by hand. Mathematica can evaluate a huge number of different types of sums and products with ease.

Lists are central constructs in Mathematica that are used to represent collections, arrays, sets, and sequences of all kinds. Well over a thousand built-in functions ...

When summarizing data, it is often useful to analyze it by subgroup. For example, crop yields could be categorized by seed variety, or average patient recovery time by ...

ArrayPad[array, m] gives an array with m 0s of padding on every side. ArrayPad[array, m, padding] uses the specified padding.ArrayPad[array, {m, n}, ...] pads with m elements ...

Binarize[image] creates a binary image from image by replacing all values above a globally determined threshold with 1 and others with 0.Binarize[image, t] creates a binary ...

BinaryWrite[channel, b] writes a byte of data, specified as an integer from 0 to 255. BinaryWrite[channel, {b_1, b_2, ...}] writes a sequence of bytes. BinaryWrite[channel, " ...

BooleanCountingFunction[k_max, n] represents a Boolean function of n variables that gives True if at most k_max variables are True.BooleanCountingFunction[{k}, n] represents ...

EdgeDetect[image] finds edges in image and returns the result as a binary image.EdgeDetect[image, r] finds edges at the scale of the specified pixel range r.EdgeDetect[image, ...

EllipticExp[u, {a, b}] is the inverse for EllipticLog. It produces a list {x, y} such that u == EllipticLog[{x, y}, {a, b}].