管院微積分(一) | NCUx雲端課程

課程形式

線上

課程名稱

管院微積分(一) (02040)

課程編號

432

課程期間

2023-02-13 ~

課程類別

自然科學

時數

18 (小時)

修課人數

簡介

單元名稱

lec1-1 Exponents and Radicals
lec1-2 Laws of Exponents & Example 1
lec1-3 Factoring & Example 2
lec2-1 Rational Expressions & Example 1
lec2-2 Example 2： Other Algebraic Fractions
lec2-3 Example 3：Rationalizing Algebraic Fractions
lec2-4 Inequality & Example 4
lec2-5 Absolute Value
lec2-6 Example 5
lec3-1 Cartesian Coordinate System
lec3-2 Distance Formula & Equation of a Circle
lec4-1 Slope of a Line, Parallel Lines and Perpendicular Lines
lec4-2 Equations of Lines
lec5-1 Functions
lec5-2 Example 1 & Example 2
lec5-3 Graphs of Functions
lec5-4 Translations of Functions
lec5-5 Piecewise defined Function
lec5-6 Curve
lec5-7 Vertical Line Test
lec6-1 The Sum, Difference, Product and Quotient of Functions & Example 1
lec6-2 Example 2
lec6-3 The Composition of Two Functions
lec6-4 Example 3
lec6-5 Example 4
lec7-1 Mathematical Models
lec7-2 Polynomial, Rational and Power Functions
lec7-3 Demand and Supply Functions & Example 5
lec7-4 Mathematical Modeling, Example 6 & Example 7
lec8-1 Introduction to Calculus
lec8-2 Intuitive Definition of a Limit
lec8-3 Limit of a Function & Example 1
lec8-4 Theorem 1：Properties of Limits
lec8-5 Example 2
lec8-6 Notes of Theorem 1
lec8-7 Indeterminate Forms, Example 3 & Example 4
lec8-8 Limit of a Function at Infinity & Example 5
lec8-9 Theorem 2 and Example 6
lec8-10 Example 7
lec9-1 One Sided Limits
lec9-2 Theorem 3 and Example 1
lec9-3 Continuous Functions
lec9-4 Example 2
lec9-5 Properties of Continuous Functions
lec9-6 Example 3
lec9-7 Intermediate Value Theorem
lec9-8 Existence of Zeros of a Continuous Function and Example 4
lec9-9 Example 5 and Example 6
lec10-1 Slope of the Tangent Line
lec10-2 Difference Quotient and Instantaneous Rates of Change
lec10-3 Derivative and Example 1
lec10-4 Example 2
lec10-5 Differentiability and Continuity
lec10-6 Example 3
lec10-7 Example 4
lec10-8 Example 5
lec10-9 Example 6
lec10-10 Example 7
lec10-11 Proof of Theorem
lec11-1 Derivative of a Constant
lec11-2 The Power Rule
lec11-3 Derivative of a Constant Multiple Function
lec11-4 The Sum Rule
lec11-5 Example 1
lec11-6 Example 2 & Example 3
lec12-1 The Product Rule
lec12-2 Example 1
lec12-3 The Quotient Rule
lec12-4 Example 2
lec12-5 Example 3 & Example 4
lec13-1 The Chain Rule
lec13-2 The Chain Rule for Power Functions
lec13-3 Example 1
lec13-4 Example 2
lec13-5 Example 3(Arteriosclerosis)
lec14-1 Marginal Cost Functions
lec14-2 Example 2
lec14-3 (Marginal) Average Cost Functions & Example 3
lec14-4 Example 4
lec14-5 (Marginal) Revenue Functions & Example 5
lec14-6 (Marginal) Profit Functions & Example 6
lec14-7 Elasticity of Demand
lec14-8 Example 7
lec14-9 Elastic, Unitary, and Inelastic Demand & Example 8
lec15-1 Higher-Order Derivatives & Example 1
lec15-2 Example 2 & Example 3
lec15-3 Example 4 & Example 5
lec15-4 Example 6(Inflation Rate)
lec16-1 Implicit Differentiation
lec16-2 Example 1 & Example 2
lec16-3 Example 3
lec16-4 Example 4
lec16-5 Example 5： Related-Rates Problem
lec16-6 Example 6： Related-Rates Problem
lec16-7 Example 7： Related-Rates Problem
lec16-8 Example 8： Related-Rates Problem
lec16-9 Example 9： Related-Rates Problem
lec17-1 Increments Example 1
lec17-2 Differentials
lec17-3 Example 2
lec17-4 Example 3
lec17-5 Example 4 and Example 5
lec17-6 Example6
lec17-7 Example 7 and Example 8
lec17-8 Example 9
lec18-1 Monotonicity
lec18-2 Example 1, Example 2 and Example 3
lec18-3 Relative Extrema
lec18-4 Critical Numbers
lec18-5 The First Derivative Test
lec18-6 Example 4 and Example 5
lec18-7 Example 6
lec18-8 Example 7 and Example 8
lec18-9 Example 9 and Example 10
lec19-1 Concavity
lec19-2 Theorem 1
lec19-3 Example 1, Example 2 and Example 3
lec19-4 Inflection Points
lec19-5 Example 4
lec19-6 Example 5
lec19-7 Example 6
lec19-8 Example 7
lec19-9 The Second Derivative Test
lec19-10 Notes
lec19-11 Example 8
lec19-12 Summary
lec20-1 Vertical Asymptotes
lec20-2 Example 1 and Note
lec20-3 Horizontal Asymptotes
lec20-4 Example 2, Example 3 and Asymptotes and Polynomials
lec20-5 Guide to Sketching a Curve
lec20-6 Example 4
lec20-7 Example 5
lec20-8 Example 6
lec20-9 Example 7
lec20-10 Example 8
lec20-11 Example 9
lec21-1 Absolute Extreme
lec21-2 Theorem
lec21-3 Finding Absolute Extreme
lec21-4 Example 1 ＆ Example 2
lec21-5 Example 3
lec21-6 Example 4
lec21-7 Example 5
lec21-8 Example 6
lec21-9 Example 7
lec21-10 Example 8
lec21-11 Example 9
lec21-12 Example 10
lec21-13 Example 11
lec22-1 Guidelines for Solving Optimization Problems
lec22-2 Example 1
lec22-3 Example 2
lec22-4 Example 3
lec22-5 Example 4
lec22-6 Example 5 (Inventory Problem)
lec22-7 Example 6
lec23-1 Exponential Function＆ Laws of Exponents
lec23-2 Example 1
lec23-3 Example 2
lec23-4 Properties of Exponential Functions
lec23-5 Natural Exponential Function
lec23-6 Example 3＆Example 4
lec24-1 Logarithms
lec24-2 Example 1
lec24-3 Logarithmic Notation＆Laws of Logarithms
lec24-4 Example 2＆Example 3
lec24-5 Logarithmic Functions
lec24-6 Properties of Logarithmic Functions
lec24-7 Example 4＆Example 5
lec25-1 Compound Interest Formula
lec25-2 Example 1
lec25-3 Effective Rate of Interest Formula
lec25-4 Example 2
lec25-5 Present Value, Example 3＆ Example 4
lec25-6 Continuous Compounding Interest Formula
lec25-7 Example 5＆ Example 6
lec25-8 Example 7＆ Example 8
lec25-9 Example 9
lec26-1 Derivative of the Natural Exponential Function
lec26-2 Example 1
lec26-3 Example 2
lec26-4 Example 3
lec26-5 Example 4
lec26-6 Derivative of the Exponential Function
lec26-7 Example 5
lec27-1 Derivative of the Natural Logarithm
lec27-2 Example 1
lec27-3 Example 2
lec27-4 Logarithmic Differentiation and Example 3
lec27-5 Derivative of the Logarithmic Function
lec27-6 Example 4

任課教授

于振華副教授

Email: yu@math.ncu.edu.tw

Tel: 03-4227151轉 65102

專長

應用機率

學經歷

美國俄亥俄州立大學博士

榮譽事蹟

國立中央大學99學年度「教學優良獎」
國立中央大學90學年度「優良導師」

相關連結

課程內容

第一章

單元01: 基本數學複習(一)

單元02: 基本數學複習(二)

單元03: 笛卡兒坐標

單元04 : 直線

第二章

單元05 : 函數及圖形

單元06 : 函數的運算

單元07 : 函數與數學模型

單元08 : 極限

單元09 : 單邊極限與連續性單元10 : 導函數

第三章

單元11 : 微分的基本規則

單元12 : 乘法規則與除法規則

單元13 : 連鎖規則

單元14 : 經濟上的邊際函數

單元15 : 高階導函數

單元16 : 隱微分與相關變化率

單元17 : 微分式

第四章

單元18 : 一階導函數的應用

單元19 : 二階導函數的應用

單元20 : 繪圖

單元21 : 最佳化 (第一部分)

單元22 : 最佳化 (第二部分)

第五章

單元23: 指數函數

單元24: 對數函數

單元25: 複利

單元26: 指數函數微分

單元27: 對數函數微分

報名資訊

報名期間

開始: 2023-02-10

總人數限制

無限制

報名費用

其他資訊

承辦人

蔡振瑋 / 教學發展中心 (電子郵件: dwtsai@ncu.edu.tw, 電話: 57137)

鄭雅軒 / 教學發展中心 (電子郵件: yahsuan@ncu.edu.tw, 電話: 57138)

開課單位

NCUx線上課程

課程 QR code

https://ocw.ncu.edu.tw/course/432

課程教材

1.
第一講
1. 1.1
  05:31
  
  lec1-1 Exponents and Radicals
2. 1.2
  06:56
  
  lec1-2 Laws of Exponents & Example 1
3. 1.3
  07:15
  
  lec1-3 Factoring & Example 2
2.
第二講
1. 2.1
  04:39
  
  lec2-1 Rational Expressions & Example 1
2. 2.2
  04:32
  
  lec2-2 Example 2： Other Algebraic Fractions
3. 2.3
  02:37
  
  lec2-3 Example 3：Rationalizing Algebraic Fractions
4. 2.4
  06:49
  
  lec2-4 Inequality & Example 4
5. 2.5
  05:13
  
  lec2-5 Absolute Value
6. 2.6
  03:14
  
  lec2-6 Example 5
3.
第三講
1. 3.1
  02:02
  
  lec3-1 Cartesian Coordinate System
2. 3.2
  02:56
  
  lec3-2 Distance Formula & Equation of a Circle
4.
第四講
1. 4.1
  05:02
  
  lec4-1 Slope of a Line, Parallel Lines and Perpendicular Lines
2. 4.2
  03:35
  
  lec4-2 Equations of Lines
5.
第五講
1. 5.1
  07:21
  
  lec5-1 Functions
2. 5.2
  06:59
  
  lec5-2 Example 1 & Example 2
3. 5.3
  03:06
  
  lec5-3 Graphs of Functions
4. 5.4
  07:34
  
  lec5-4 Translations of Functions
5. 5.5
  03:00
  
  lec5-5 Piecewise defined Function
6. 5.6
  03:08
  
  lec5-6 Curve
7. 5.7
  04:15
  
  lec5-7 Vertical Line Test
6.
第六講
1. 6.1
  06:26
  
  lec6-1 The Sum, Difference, Product and Quotient of Functions & Example 1
2. 6.2
  03:00
  
  lec6-2 Example 2
3. 6.3
  04:23
  
  lec6-3 The Composition of Two Functions
4. 6.4
  04:53
  
  lec6-4 Example 3
5. 6.5
  02:34
  
  lec6-5 Example 4
7.
第七講
1. 7.1
  06:39
  
  lec7-1 Mathematical Models
2. 7.2
  04:48
  
  lec7-2 Polynomial, Rational and Power Functions
3. 7.3
  06:20
  
  lec7-3 Demand and Supply Functions & Example 5
4. 7.4
  05:45
  
  lec7-4 Mathematical Modeling, Example 6 & Example 7
8.
第八講
1. 8.1
  09:03
  
  lec8-1 Introduction to Calculus
2. 8.2
  09:23
  
  lec8-2 Intuitive Definition of a Limit
3. 8.3
  10:31
  
  lec8-3 Limit of a Function & Example 1
4. 8.4
  04:14
  
  lec8-4 Theorem 1：Properties of Limits
5. 8.5
  06:39
  
  lec8-5 Example 2
6. 8.6
  08:58
  
  lec8-6 Notes of Theorem 1
7. 8.7
  07:04
  
  lec8-7 Indeterminate Forms, Example 3 & Example 4
8. 8.8
  04:45
  
  lec8-8 Limit of a Function at Infinity & Example 5
9. 8.9
  12:00
  
  lec8-9 Theorem 2 and Example 6
10. 8.10
  02:05
  
  lec8-10 Example 7
9.
第九講
1. 9.1
  06:37
  
  lec9-1 One Sided Limits
2. 9.2
  04:57
  
  lec9-2 Theorem 3 and Example 1
3. 9.3
  07:36
  
  lec9-3 Continuous Functions
4. 9.4
  08:18
  
  lec9-4 Example 2
5. 9.5
  05:17
  
  lec9-5 Properties of Continuous Functions
6. 9.6
  01:06
  
  lec9-6 Example 3
7. 9.7
  06:36
  
  lec9-7 Intermediate Value Theorem
8. 9.8
  03:04
  
  lec9-8 Existence of Zeros of a Continuous Function and Example 4
9. 9.9
  07:34
  
  lec9-9 Example 5 and Example 6
10.
第十講
1. 10.1
  05:17
  
  lec10-1 Slope of the Tangent Line
2. 10.2
  04:08
  
  lec10-2 Difference Quotient and Instantaneous Rates of Change
3. 10.3
  08:33
  
  lec10-3 Derivative and Example 1
4. 10.4
  07:42
  
  lec10-4 Example 2
5. 10.5
  05:46
  
  lec10-5 Differentiability and Continuity
6. 10.6
  06:25
  
  lec10-6 Example 3
7. 10.7
  03:15
  
  lec10-7 Example 4
8. 10.8
  03:23
  
  lec10-8 Example 5
9. 10.9
  07:31
  
  lec10-9 Example 6
10. 10.10
  05:43
  
  lec10-10 Example 7
11. 10.11
  06:10
  
  lec10-11 Proof of Theorem
11.
第十一講
1. 11.1
  03:10
  
  lec11-1 Derivative of a Constant
2. 11.2
  06:52
  
  lec11-2 The Power Rule
3. 11.3
  03:00
  
  lec11-3 Derivative of a Constant Multiple Function
4. 11.4
  05:07
  
  lec11-4 The Sum Rule
5. 11.5
  05:36
  
  lec11-5 Example 1
6. 11.6
  05:30
  
  lec11-6 Example 2 & Example 3
12.
第十二講
1. 12.1
  07:41
  
  lec12-1 The Product Rule
2. 12.2
  08:02
  
  lec12-2 Example 1
3. 12.3
  09:22
  
  lec12-3 The Quotient Rule
4. 12.4
  09:44
  
  lec12-4 Example 2
5. 12.5
  09:37
  
  lec12-5 Example 3 & Example 4
13.
第十三講
1. 13.1
  16:07
  
  lec13-1 The Chain Rule
2. 13.2
  04:20
  
  lec13-2 The Chain Rule for Power Functions
3. 13.3
  14:21
  
  lec13-3 Example 1
4. 13.4
  03:12
  
  lec13-4 Example 2
5. 13.5
  11:48
  
  lec13-5 Example 3(Arteriosclerosis)
14.
第十四講
1. 14.1
  08:18
  
  lec14-1 Marginal Cost Functions
2. 14.2
  04:18
  
  lec14-2 Example 2
3. 14.3
  04:54
  
  lec14-3 (Marginal) Average Cost Functions & Example 3
4. 14.4
  04:31
  
  lec14-4 Example 4
5. 14.5
  05:27
  
  lec14-5 (Marginal) Revenue Functions & Example 5
6. 14.6
  04:36
  
  lec14-6 (Marginal) Profit Functions & Example 6
7. 14.7
  08:29
  
  lec14-7 Elasticity of Demand
8. 14.8
  05:14
  
  lec14-8 Example 7
9. 14.9
  11:26
  
  lec14-9 Elastic, Unitary, and Inelastic Demand & Example 8
15.
第十五講
1. 15.1
  07:36
  
  lec15-1 Higher-Order Derivatives & Example 1
2. 15.2
  03:41
  
  lec15-2 Example 2 & Example 3
3. 15.3
  08:50
  
  lec15-3 Example 4 & Example 5
4. 15.4
  08:57
  
  lec15-4 Example 6(Inflation Rate)
16.
第十六講
1. 16.1
  08:58
  
  lec16-1 Implicit Differentiation
2. 16.2
  09:42
  
  lec16-2 Example 1 & Example 2
3. 16.3
  08:00
  
  lec16-3 Example 3
4. 16.4
  03:22
  
  lec16-4 Example 4
5. 16.5
  06:48
  
  lec16-5 Example 5： Related-Rates Problem
6. 16.6
  03:58
  
  lec16-6 Example 6： Related-Rates Problem
7. 16.7
  08:48
  
  lec16-7 Example 7： Related-Rates Problem
8. 16.8
  05:57
  
  lec16-8 Example 8： Related-Rates Problem
9. 16.9
  05:01
  
  lec16-9 Example 9： Related-Rates Problem
17.
第十七講
1. 17.1
  04:30
  
  lec17-1 Increments Example 1
2. 17.2
  07:18
  
  lec17-2 Differentials
3. 17.3
  02:18
  
  lec17-3 Example 2
4. 17.4
  10:39
  
  lec17-4 Example 3
5. 17.5
  04:25
  
  lec17-5 Example 4 and Example 5
6. 17.6
  07:36
  
  lec17-6 Example6
7. 17.7
  03:45
  
  lec17-7 Example 7 and Example 8
8. 17.8
  05:57
  
  lec17-8 Example 9
18.
第十八講
1. 18.1
  06:26
  
  lec18-1 Monotonicity
2. 18.2
  10:49
  
  lec18-2 Example 1, Example 2 and Example 3
3. 18.3
  06:09
  
  lec18-3 Relative Extrema
4. 18.4
  10:09
  
  lec18-4 Critical Numbers
5. 18.5
  03:16
  
  lec18-5 The First Derivative Test
6. 18.6
  05:17
  
  lec18-6 Example 4 and Example 5
7. 18.7
  06:31
  
  lec18-7 Example 6
8. 18.8
  04:22
  
  lec18-8 Example 7 and Example 8
9. 18.9
  10:45
  
  lec18-9 Example 9 and Example 10
19.
第十九講
1. 19.1
  10:21
  
  lec19-1 Concavity
2. 19.2
  05:14
  
  lec19-2 Theorem 1
3. 19.3
  06:25
  
  lec19-3 Example 1, Example 2 and Example 3
4. 19.4
  11:08
  
  lec19-4 Inflection Points
5. 19.5
  03:05
  
  lec19-5 Example 4
6. 19.6
  06:26
  
  lec19-6 Example 5
7. 19.7
  07:40
  
  lec19-7 Example 6
8. 19.8
  04:04
  
  lec19-8 Example 7
9. 19.9
  05:03
  
  lec19-9 The Second Derivative Test
10. 19.10
  10:17
  
  lec19-10 Notes
11. 19.11
  02:57
  
  lec19-11 Example 8
12. 19.12
  03:16
  
  lec19-12 Summary
20.
第二十講
1. 20.1
  05:05
  
  lec20-1 Vertical Asymptotes
2. 20.2
  05:36
  
  lec20-2 Example 1 and Note
3. 20.3
  03:21
  
  lec20-3 Horizontal Asymptotes
4. 20.4
  06:57
  
  lec20-4 Example 2, Example 3 and Asymptotes and Polynomials
5. 20.5
  02:10
  
  lec20-5 Guide to Sketching a Curve
6. 20.6
  10:29
  
  lec20-6 Example 4
7. 20.7
  14:50
  
  lec20-7 Example 5
8. 20.8
  13:59
  
  lec20-8 Example 6
9. 20.9
  13:54
  
  lec20-9 Example 7
10. 20.10
  14:55
  
  lec20-10 Example 8
11. 20.11
  15:58
  
  lec20-11 Example 9
21.
第二十一講
1. 21.1
  05:41
  
  lec21-1 Absolute Extreme
2. 21.2
  07:46
  
  lec21-2 Theorem
3. 21.3
  05:11
  
  lec21-3 Finding Absolute Extreme
4. 21.4
  04:50
  
  lec21-4 Example 1 ＆ Example 2
5. 21.5
  06:31
  
  lec21-5 Example 3
6. 21.6
  06:51
  
  lec21-6 Example 4
7. 21.7
  05:07
  
  lec21-7 Example 5
8. 21.8
  06:02
  
  lec21-8 Example 6
9. 21.9
  07:47
  
  lec21-9 Example 7
10. 21.10
  03:25
  
  lec21-10 Example 8
11. 21.11
  07:19
  
  lec21-11 Example 9
12. 21.12
  09:43
  
  lec21-12 Example 10
13. 21.13
  11:34
  
  lec21-13 Example 11
22.
第二十二講
1. 22.1
  02:03
  
  lec22-1 Guidelines for Solving Optimization Problems
2. 22.2
  05:17
  
  lec22-2 Example 1
3. 22.3
  07:38
  
  lec22-3 Example 2
4. 22.4
  11:32
  
  lec22-4 Example 3
5. 22.5
  05:54
  
  lec22-5 Example 4
6. 22.6
  09:38
  
  lec22-6 Example 5 (Inventory Problem)
7. 22.7
  14:57
  
  lec22-7 Example 6
23.
第二十三講
1. 23.1
  03:07
  
  lec23-1 Exponential Function＆ Laws of Exponents
2. 23.2
  06:36
  
  lec23-2 Example 1
3. 23.3
  05:20
  
  lec23-3 Example 2
4. 23.4
  05:09
  
  lec23-4 Properties of Exponential Functions
5. 23.5
  03:30
  
  lec23-5 Natural Exponential Function
6. 23.6
  09:15
  
  lec23-6 Example 3＆Example 4
24.
第二十四講
1. 24.1
  05:54
  
  lec24-1 Logarithms
2. 24.2
  03:59
  
  lec24-2 Example 1
3. 24.3
  06:54
  
  lec24-3 Logarithmic Notation＆Laws of Logarithms
4. 24.4
  07:56
  
  lec24-4 Example 2＆Example 3
5. 24.5
  09:40
  
  lec24-5 Logarithmic Functions
6. 24.6
  10:48
  
  lec24-6 Properties of Logarithmic Functions
7. 24.7
  08:32
  
  lec24-7 Example 4＆Example 5
25.
第二十五講
1. 25.1
  05:06
  
  lec25-1 Compound Interest Formula
2. 25.2
  03:32
  
  lec25-2 Example 1
3. 25.3
  03:41
  
  lec25-3 Effective Rate of Interest Formula
4. 25.4
  02:41
  
  lec25-4 Example 2
5. 25.5
  03:45
  
  lec25-5 Present Value, Example 3＆ Example 4
6. 25.6
  06:15
  
  lec25-6 Continuous Compounding Interest Formula
7. 25.7
  05:44
  
  lec25-7 Example 5＆ Example 6
8. 25.8
  03:56
  
  lec25-8 Example 7＆ Example 8
9. 25.9
  08:32
  
  lec25-9 Example 9
26.
第二十六講
1. 26.1
  04:59
  
  lec26-1 Derivative of the Natural Exponential Function
2. 26.2
  05:52
  
  lec26-2 Example 1
3. 26.3
  02:07
  
  lec26-3 Example 2
4. 26.4
  04:56
  
  lec26-4 Example 3
5. 26.5
  06:06
  
  lec26-5 Example 4
6. 26.6
  04:53
  
  lec26-6 Derivative of the Exponential Function
7. 26.7
  06:01
  
  lec26-7 Example 5
27.
第二十七講
1. 27.1
  05:42
  
  lec27-1 Derivative of the Natural Logarithm
2. 27.2
  03:52
  
  lec27-2 Example 1
3. 27.3
  07:27
  
  lec27-3 Example 2
4. 27.4
  10:22
  
  lec27-4 Logarithmic Differentiation and Example 3
5. 27.5
  07:38
  
  lec27-5 Derivative of the Logarithmic Function
6. 27.6
  02:53
  
  lec27-6 Example 4

課程資訊

課程資訊

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