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elementary applied partial differential equations quation involves an unknown function \( u(x_1, x_2, ..., x_n) \) of multiple independent variables, along with its partial derivatives. Formally, a PDE can be expressed as: \[ F\left(x_1, ..., x_n, u, \frac{\partial u}{\partial x_1}, ..., \frac{\partial u}{\partial x_n}, \frac{\partial^2 u}{\pa A Andreanne Hirthe Mar 16, 2026
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