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Small Group Activity

30 min.

Calculating Coefficients for a Power Series

This activity starts with a brief lecture introduction to power series and a short derivation of the formula for calculating the power series coefficients.

\[c_n={1\over n!}\, f^{(n)}(z_0)\]

Students use this formula to compute the power series coefficients for a \(\sin\theta\) (around both the origin and (if time allows) \(\frac{\pi}{6}\)). The meaning of these coefficients and the convergence behavior for each approximation is discussed in the whole-class wrap-up and in the follow-up activity: Visualization of Power Series Approximations.

  • Taylor Series Coefficents Power Series
    Found in: Theoretical Mechanics, AIMS Maxwell, Static Fields, Problem-Solving, None course(s) Found in: Power Series Sequence (Mechanics), Power Series Sequence (E&M) sequence(s)