工程數學 Chapter 09 Vector Differential Calculus Grad, Div, Curl 楊學成 老師.

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1 工程數學 Chapter 09 Vector Differential Calculus Grad, Div, Curl 楊學成 老師

2 單元架構 9-1 Vector Algebra in 2-space and 3-space 9-2 inner product
9-3 Vector Product(cross product) 9-4 Vector and scalar Functions and Fielels Derivatives. 9-5 curves ,tangent ,are length 9-6 Gradient of a scalar Field. 9-7 Divergence of a vector Field 9-8 curl of a vector Field

3 9.1 Vector Algebra in 2-space and 3-space
學習目標 學習完本小節後，您將能： 1. 能理解什麼是Vector Algebra in 2-space and 3-space 2. 能說明什麼是Vector Algebra in 2-space and 3-space 3. 能計算Vector Algebra in 2-space and 3-space 的方程式

4 Basic concepts

5 Basic concepts

6 Basic concepts

7 Basic concepts

8 Basic concepts

9 9.2 inner product 學習完本小節後，您將能： 1. 能理解什麼是inner product
學習目標 學習完本小節後，您將能： 1. 能理解什麼是inner product 2. 能說明什麼是inner product 3. 能繪出inner product的相關圖形 4. 能計算inner product的方程式

10 Basic concepts

11 Basic concepts

12 Basic concepts

13 Basic concepts

14 9.3 Vector Product(cross product)
學習目標 學習完本小節後，您將能： 1. 能說明什麼是Vector Product 2. 能繪出Vector Product的相關圖形 3. 能計算Vector Product的方程式

15 Basic concepts

16 Basic concepts

17 Basic concepts

18 Basic concepts

19 Basic concepts

20 Basic concepts

21 9.4 Vector and scalar Functions and Fielels Derivatives.
學習目標 學習完本小節後，您將能： 1. 能說出何謂 Vector and scalar Functions and FielelsDerivatives. 2. 能具體描述Vector and scalar Functions and Fielels Derivatives. 3. 能寫出Vector and scalar Functions and Fielels Derivatives. 4. 能進行具有Vector and scalar Functions and Fielels Derivatives.計算

22 Basic concepts

23 Basic concepts

24 Basic concepts

25 Basic concepts

26

27 9.5 curves ,tangent ,are length .
學習目標 學習完本小節後，您將能： 1. 能說出何謂 curves ,tangent ,are length. 2. 能具體描述 curves ,tangent ,are length. 3. 能寫出 curves ,tangent ,are length. 4. 能進行具有curves ,tangent ,are length.計算

28 Basic concepts

29 Basic concepts

30 Basic concepts

31 Basic concepts

32 Basic concepts

33 Basic concepts

34 Basic concepts

35 Basic concepts

36 9.6 Gradient of a scalar Field
學習目標 學習完本小節後，您將能： 1. 能說出什麼是Gradient of a scalar Field 2. 能具體描述Gradient of a scalar Field.的特性 3. 能寫出Gradient of a scalar Field的解題順序 4. 能進行Gradient of a scalar Field的方程式求解

37 Basic concepts

38 Basic concepts

39 Basic concepts

40 Basic concepts

41 Basic concepts

42 9.7 Divergence of a vector Field
學習目標 學習完本小節後，您將能： 1. 能說出什麼是Divergence of a vector Field 2. 能具體描述Divergence of a vector Field的特性 3. 能寫出Divergence of a vector Field的解題順序 4. 能進行Divergence of a vector Field的方程式求解

43 Basic concepts

44 Basic concepts

45 Basic concepts

46 Basic concepts

47 Basic concepts

48 9.8 curl of a vector Field 學習完本小節後，您將能：
學習目標 學習完本小節後，您將能： 1. 能說出什麼是curl of a vector Field 2. 能具體描述curl of a vector Field的特性 3. 能寫出curl of a vector Field的解題順序 4. 能進行curl of a vector Field的方程式求解

49 Basic concepts

50 Basic concepts