Skip to main content Contents Index Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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Section 17.10 Fourier Series: Small Group Activity
Make sure to complete the activity in
Section 17.2 before attempting this one.
Activity 17.8 . Calculating Fourier Coefficients.
Refer to
Section 17.5 to find the formulas for the coefficients in a Fourier series. Use the Sage code below to calculate the coefficients
\(a_m\) and
\(b_m\) for
\(m=0,1,2,3\) for the function
\(-\frac12+\sin(2\pi x)\sin(4\pi x)\text{.}\)
The applet in
Figure 17.7 shows the function
\(-\frac12+\sin(2\pi x)\sin(4\pi x)\) (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 17.7. An applet for manipulating the individual Fourier coefficients.
