Heaviside Function

The unit step function or Heaviside function is the function $u_{c}$ defined by

${\begin{aligned}u_{c}(t)&={\begin{cases}0&t<c\\1&t\geq c\end{cases}}&c\geq 0\end{aligned}}$

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Some systems (e.g. Wolfram|Alpha) use the following definition, in which case $u_{c}(t)=\theta (t-c)$:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta(t) = \begin{cases} 0 & t<0 \\ 1 & t \ge 0 \end{cases}}

This more closely parallels the dirac delta function.