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

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

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

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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

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Basic concepts

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Basic concepts

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

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Basic concepts

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

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Basic concepts

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Basic concepts

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

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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

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Basic concepts

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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

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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

Basic concepts

Basic concepts