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Contents Index Dark Mode Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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Section 4.8 Fourier Series: Exploration
Make sure to complete the activity in
Section 4.3 before attempting this one.
Activity 19 . Guessing the Fourier Coefficients.
In
Figure 47 below, use the sliders to match the given function (shown in blue) exactly. Use only graphical reasoning.
Hint: Only three of the sliders need to be set to nonzero values.
When you are done, make a note of any relationship you see between the values of the coefficients and the shape of the graph.
Figure 47. Use the applet to set the individual Fourier coefficients to try to match the given function.Hint . Use the Sage code below to calculate the coefficients, if you are having trouble guessing.
Activity 20 . Comparing an exact calculation to your guess.
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 for the function
\(f(x)=-\frac12+\sin(x)\sin(2x)\) used in the previous activity. Check that your calculated coefficients agree with your earlier guess.
Hint . The Sage code calculates \(a_0\text{.}\) You will need to make minor changes in order to calculate the remaining coefficients.
