11.5.2.28 Метод Фурье

Методом Фурье решить уравнение Лапласа: \[ \left\{\begin{array}{l} \frac{\partial^{2} T}{\partial x^{2}}+\frac{\partial^{2} T}{\partial y^{2}}=0, \quad\left\{\begin{array}{l} 0 \leq x \leq 2 \\ 0 \leq y \leq 1 \end{array}\right. \\ T(0, y)=T(2, y)=0 \\ T(x, 0)=T(x, 1)=f(x)=\left\{\begin{array}{ll} 2, & 0 \leq x \leq 1 \\ 1, & 1 \leq x \leq 2 \end{array}\right. \end{array}\right. \]