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Contents Index Dark Mode Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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Section 4.9 Fourier Series: Small Group Activity
Make sure to complete the activity in
Section 4.3 before attempting this one.
Activity 21 . Calculating Fourier Coefficients.
Refer to
Section 4.2 to find the formulas for the coefficients in a Fourier series. Use the Sage code below to calculate the coefficients
\(a_n\) and
\(b_n\) for
\(n=0,1,2,3\) for the function
\(-\frac12+\sin(x)\sin(2x)\text{.}\)
The applet in
Figure 48 shows the function
\(-\frac12+\sin(x)\sin(2x)\) (in blue). As you move the sliders, the corresponding Fourier series is also shown (in green). Set the sliders to the values that you calculated. Write as many statements as you can about the relationships between the values of the coefficients and the shape of the graph.
Figure 48. An applet for manipulating the individual Fourier coefficients.
