Changes

We observe <math>X\!</math> for a while, relative to a discrete time frame, and we write down the following sequence of values for <math>x.\!</math>

We observe <math>X\!</math> for a while, relative to a discrete time frame, and we write down the following sequence of values for <math>x.\!</math>

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" style="text-align:center"

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<math>\begin{array}{cc}

<math>\begin{array}{cc}

t & x \\

t & x \\

0 & 0 \\

0 & 0 \\

1 & 1 \\

1 & 1 \\

Another way to detect patterns is to write out a table of finite differences.  For this example, we would get:

Another way to detect patterns is to write out a table of finite differences.  For this example, we would get:

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" style="text-align:center"

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<math>\begin{array}{ccccc}

<math>\begin{array}{ccccc}

t &      x &    dx &  d^2 x & \ldots \\

t &      x &    dx &  d^2 x & \ldots \\

0 &      0 &      1 &      0 & \ldots \\

0 &      0 &      1 &      0 & \ldots \\

1 &      1 &      1 &      0 &        \\

1 &      1 &      1 &      0 &        \\