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微積分統一教學網

模17-19班課程大綱

微積分1

Week

授課內容 Course Content

1

1.1 函數與圖形 Functions and Their Graphs

1.2 方程式與平面曲線;隱函數 Equations of Planes ; Implicit Functions

1.3 反函數 Inverse Functions

2

1.4 連續函數與極限 Limits and Continuous Functions

1.5 e與自然對數 The Number e and Natural Logarithms (ln)

3

2.1 導函數 Derivative as a Function

4

2.1 導函數 Derivative as a Function

2.2 平均值定理 Mean Value Theorem

10/19() 8:30-9:00 Quiz 1 (範圍:1.1 1.5)

5

2.3 切線與線性逼近  Tangent Lines and Linear Appoximations

2.4 應用:描述函數圖形 Applications of Differentiation: Graph of a Function

10/26() 8:30-9:00 Quiz 2 (範圍:2.1 2.2)

6

2.4 應用:描述函數圖形 Applications of Differentiation: Graph of a Function

2.5 微分的應用-最佳化 Applications of Differentiation: Optimizations

7

緩衝時間 Buffer time

11/9() 8:30-9:00 Quiz 3 (範圍:2.3 2.5)

8

11/11() 期考 範圍:1.1 2.5

 

 

微積分2

Week

授課內容 Course Content

9

3.1 積分的觀念:黎曼和與定積分 Riemann sums and Definite Integrals

3.2 微積分基本定理 The Fundamental Theorem of Calculus

3.3 基本積分技巧 Techniques of Integration

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3.3 基本積分技巧 Techniques of Integration

發期考考卷

11

3.3 基本積分技巧Techniques of Integration

12/7() 8:30-9:00 Quiz 1 (範圍:3.1 3.3.1)

12

3.4 積分的應用 (3.4.1~3.4.2) Applications of Integration

13

3.4 積分的應用 (3.4.1~3.4.2) Applications of Integration

4.1 典型的例子:從等比級數談起 Classical Example : Geometric Series

4.2 泰勒定理 Taylor’s Theorem

12/21() 8:30-9:00 Quiz 2 (範圍:3.3.2 3.3.4)

14

4.3 常用函數的泰勒展式 Taylor’s Series of Standard Functions

15

4.4 泰勒定理的應用(4.4.1-4.4.2) Applications of Taylor Series

1/4() 8:30-9:00 Quiz 3 (範圍:3.4 4.2)

16

1/6() 期考 範圍:3.1 4.4

 

微積分3

Week

授課內容 Course Content

1

5.1多變數函數 Functions of Several Variables

5.2多變數函數的微分 Partial Derivatives

2

5.3多變數函數之連鎖法則 Chain Rule for Multivariable Functions

5.4方向導數與梯度 Directional Derivatives and Gradient Vectors

3

5.5.1高階偏導數 Partial Derivatives of Higher Orders

5.6極值測試與應用 Tests for Extrema and Applications

3/1()  Quiz 1 (範圍:5.1 5.3)

4

5.7 Lagrange乘子法 Lagrange Multipliers

6.1二重積分 Double Integrals

5

6.2 Fubini定理 Fubini's Theorem

6.3二重積分的極坐標形式Double Integrals in Polar Coordinates

3/15()  Quiz 2 (範圍:5.4 5.7)

6

6.4二重積分之變數變換 Change of Variables for Double Integrals

7.1使用指數函數的模型 Modeling with Exponential Functions

7

7.2一階微分方程 First Order Differential Equations

3/29()  Quiz 3 (範圍:6.1 6.4)

8

4/7() 期考 範圍:5.1 7.2