anonymous
  • anonymous
Express the peice-wise function: \[ f(x) = \begin{cases} g(x)& x>a\\ h(x) &x
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
The heaviside function is \[ H(t) = \begin{cases} 1&t>0\\ 0&t<0 \end{cases} \]
anonymous
  • anonymous
If we put in \(t-a\) we get: \[ H(t-a) = \begin{cases} 1&t>a\\ 0&t

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anonymous
  • anonymous
Another thing we could do is: \[ f(t)+[g(t)-f(t)]H(t-a) \]
anonymous
  • anonymous
So one simple thing we could do is: \[ h(t)H(a-t) + g(t)H(t-a) \]
anonymous
  • anonymous
Another thing we could do is: \[ f(t) =h(t)+[g(t)-h(t)]H(t-a) \]
anonymous
  • anonymous
I'm producing a method of expressing peice-wise functions without using \(\large\{\) notation but instead by using \(H(t)\).

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