方向导数的几何可视化演示
2015-01-06 02:50
本 GeoGebra 范例演示多元函数方向导数的几何意义。通过三维曲面展示函数 f(x,y) 在某点沿指定方向向量 u 的方向导数，包含切平面、方向向量、偏导数 f_x 和 f_y 的计算，以及极限定义的可视化。用户可通过滑块调整点的位置和方向角 θ，观察方向导数如何由偏导数与方向余弦的线性组合得出，即 D_u f = f_x cosθ + f_y sinθ。适合微积分课程中多元函数微分学的教学与学习。
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