Definition of Differentiability --- Multivariable Calculus (Where does it come from?)

最新推荐文章于 2024-10-17 13:41:16 发布

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本文探讨了多元函数的可微性定义及其等价性，通过多个教育机构的视频资源，如斯沃斯莫尔学院、MIT、Technion的课程，深入解析了方向导数的概念，并证明了梯度向量指向最大斜率方向的原理。同时，提供了苏德矿和蔡高厅教授的视频链接，用于理解多元函数的全微分和直观感受。

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Videos in sequence:

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MIT - Herbert Gross

(Also proved the gradient has the maximum slope)

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Technion - Aviv Censor

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We have two commonly used definitions of differentiablity. They are equivalent and can be derived from each other.