第二十九單元 方向導數與梯度.

Presentation on theme: "第二十九單元 方向導數與梯度."— Presentation transcript:

1 第二十九單元 方向導數與梯度

2 Directional Derivatives and Gradient
Definition

3 Partial Derivatives and Directional Derivatives

4 How to Find Directional Derivatives
Theorem Proof As an exercise

5 Example Solution

6 Gradient Definition

7 Directional Derivatives and Gradient

8 Maximal Property of the Gradient

9 Proof of Maximal Property

10 Gradient and Level Curve

11 Geometric Interpretation for Gradient

12 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

13 Example

14 Normal Vector

15 Gradient of 3 Variable function

16 Example Hotter is Better

17 Solution

18 Example

19 Example(continued)

20 Example(continued)

21 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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