Interpolating Polynomials

• we have a table of $x$ and $y$-values. Two entries in this table might be
  $y=2.36$ at $x=0.41$ and
  $y=3.11$ at $x=0.52$.
  If we desire an estimate for $y$ at $x=0.43$, we would use the two table values for that estimate.
• Why not interpolate as if $y(x)$ was linear between the two $x$-values?
• We will be most interested in techniques adapted to situations where the data are far from linear. The basic principle is to fit a polynomial curve to the data.
• We assume that the tabulated data are exact. Later, we will consider the case where the data may have errors of measurement, which is true for most experimental results.