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The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle.
The convention is that a sawtooth wave ramps upward and then sharply drops. However, in a reverse (or inverse) sawtooth wave, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave.The piecewise linear function
x
(
t
)
=
t
−
⌊...
In the theory of Lie groups, the exponential map is a map from the Lie algebra
g
{\displaystyle {\mathfrak {g}}}
of a Lie group
G
{\displaystyle G}
to the group, which allows one to recapture the local group structure from the Lie algebra. The existence of the exponential map is one of the primary reasons that Lie algebras are a useful tool for studying Lie groups.
The ordinary exponential function of mathematical analysis is a special case of the exponential map when...
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse
f
−
1
{\displaystyle f^{-1}}
of a continuous and invertible function
f
{\displaystyle f}
, in terms of
f
−
1
{\displaystyle f^{-1}}
and an antiderivative of
f
{\d...
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