15. Mathematical formula list

The number of combinations to obtain r elements out of
n elements is given by following formula.

For example, there are three (ab, bc, ca) types on how
to take 2 items from 3 items data a, b, c.

The number of permutations to obtain r elements out of
n elements is given by following formula.

For example, there are six ab, ba, bc, cb,ca, ac)
types of permutation to take 2 elements from 3
elements data a, b, c.

The number in which a is nth times multiplied is
expressed by
, and is called nth exponent. Following formulas are
basic calculation of exponent.

Trigonometric table is defined as follows by using the
right-angled triangle.

The mutual relationship of the trigonometric table is
expressed by the following formula.

That is, at the time of
, it is said that a is c root of b, and expressed by
. The following relation is established in the root.

Among the root,

is called as imaginary number, and expressed by i.

When
,

is called logarithm of c that considers b as base.

Also, the following relation is established when the
base is same.

Among the logarithm, the logarithm that considers 10
as base is called common logarithm.

or expressed as

Moreover, the logarithm that considers e=2.718281828 …
as base is called the natural logarithm.

Or expressed by

The derivation formula of a typical function is shown
as follows.

The integration formula of a typical function is shown
as follows.