第二十九單元 方向導數與梯度
Directional Derivatives and Gradient Definition
Partial Derivatives and Directional Derivatives
How to Find Directional Derivatives Theorem Proof As an exercise
Example Solution
Gradient Definition
Directional Derivatives and Gradient
Maximal Property of the Gradient
Proof of Maximal Property
Gradient and Level Curve
Geometric Interpretation for Gradient
Three Variable function A level surface for a function f of three variables is the graph of the set of points in three-dimensional space whose coordinates satisfy an equation ,where k is a constant
Example
Normal Vector
Gradient of 3 Variable function
Example Hotter is Better
Solution
Example
Example(continued)
Example(continued)
單元結語 要認識方向導數和梯度的觀念一定要看圖形並確實了解幾何意義。 梯度的方向與等高線呈垂直的關係，這觀念非常重要，後面單元求極大極小(拉格蘭吉乘子)時，要用到這觀念。
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