Heaviside Function

The unit step function or Heaviside function is the function 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 u_c} defined by

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 \begin{align} u_c(t) &= \begin{cases} 0 & t < c \\ 1 & t \ge c \end{cases} & c \ge 0 \end{align}}

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Some systems (e.g. Wolfram|Alpha) use the following definition, in which case 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 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.