Note
Hint
\(\(\frac{\partial (x,y)}{\partial (u,v)}=\left|\begin{array}{cccc}\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} \end{array}\right|\)\)
傅里叶级数
\[
\frac{a_0}{2}+\sum_{n=1}^{+\infty}(a_n \cos \frac{n\pi x}{l}+b_n \sin \frac{n\pi x}{l})
\]
\[
\left\{
\begin{aligned}
a_n=\frac{1}{l}\int_{-l}^{l} f(x)\cos\frac{n\pi x}{l}dx, \quad n=0,1,2... \\
b_n=\frac{1}{l}\int_{-l}^{l} f(x)\sin\frac{n\pi x}{l}dx, \quad n=1,2,3...
\end{aligned}
\right.
\]
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