Notes in 01多元微分学基本概念

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Published	10/05/2024	二重极限的定义如何描述？
Published	10/05/2024	多元函数连续的定义，多元函数连续的有界性，最值性，介值性怎么描述（类比一元函数）
Published	10/05/2024	偏导数的定义\(f_{x}^{\prime}\left(x_{0}, y_{0}\right)=\text{______}\)\(f_{y}^{\prime}\left(x_{0}, y_{0}\right)=\text{______}\)
Published	10/05/2024	偏导数的几何意义(了解)
Published	10/05/2024	高阶偏导数定义\(\text { 设 } z=f(x, y) \text {, 则 }\)\(\frac{\partial^{2} z}{\partial x^{2}}=\text{______.}\)\(\frac{\partial^{2} z}{\partial x \partial y}=\t…
Published	10/05/2024	定理如果函数 \(z=f(x, y)\) 的两个二阶混合偏导数 \(f_{x y}^{\prime \prime}(x, y)\) 及 \(f_{y x}^{\prime \prime}(x, y)\) 在区域 \(D\) 内连续,则在区域 \(D\) 内恒有_____.
Published	10/05/2024	尝试描述可微，全微分的定义，全微分的等价命题
Published	10/05/2024	可微性判定的必要条件
Published	10/05/2024	可微性充分条件
Published	10/05/2024	可微性判定的充分条件-用定义判定
Published	10/05/2024	全微分的计算若 \(f(x, y)\) 可微, 则 \(\mathrm{d} z=\text{______}\)
Published	10/05/2024	一元函数，二元函数的连续，可导，可微的关系
Published	10/05/2024	隐函数存在定理设 \( F(x, y, z)=0 \) 在 \( \left(x_{0}, y_{0}, z_{0}\right) \) 的某个邻域内满足:(1) \( F\left(x_{0}, y_{0}, z_{0}\right)=0 \);(2) \( F_{x}^{\prime}, F_{…
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