1. 課程中心
  2. 理工微積分
  3. 課程資訊
課程形式
線上
課程名稱
理工微積分 (02031)
課程編號
423
課程期間
2023-02-13 ~
課程類別
自然科學
時數
18 (小時)
修課人數
62
簡介

任課教授

饒瑞彬 Re-Bin Rau 副教授

Email: rau@math.ncu.edu.tw

Tel: 03-4227151轉 65137

專長

  • 多重決策理論

  • 數理統計

學經歷

  • 美國普渡大學博士

  • 現任教於中央大學數學系

 

 
課程目標

學習微分與積分的基本知識, 培養列式, 求解及解釋問題的應用能力

 

 

 
課程內容

 

Ch10 參數方程式和極座標

    10-1 由參數方程式所定義的曲線

    10-2 參數曲線的微積分

    10-3 極座標

    10-4 極座標的面積跟長度

Ch11 無窮數列與級數

    11-1 數列

    11-2 級數

    11-3 Integral Test

    11-4 比較檢驗法

    11-5 交錯級數

    11-6 絕對收斂和條件收斂

    11-7 檢驗數列的策略

    11-8 冪級數

Ch12 空間的向量和幾何

    12-1 三維座標系統

    12-2 向量

    12-3 內積

Ch13 向量函數

    13-1 向量函數與空間曲線

    13-2 導數和單位切向量之定義

    13-3 平面空間曲線長、 弧長

    13-4 空間上的移動：速度和加速度

Ch14 數個變數的函數

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
0
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 / 課務組 (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://ncuxms.ncu.edu.tw/course/423
課程教材
  1. 1.
    Ch10 參數方程式和極座標
    1. 1.1
      02:19
      10-1-1 Introduction
    2. 1.2
      04:16
      10-1-2 Example 1
    3. 1.3
      03:29
      10-1-3 Parametric Curves
    4. 1.4
      07:41
      10-1-4 Example 2、3
    5. 1.5
      02:20
      10-1-5 Example 4
    6. 1.6
      09:11
      10-1-6 Example 7 Cycloid
    7. 1.7
      05:06
      10-1-7 Cycloids
    8. 1.8
      03:48
      10-2-1 Tangents
    9. 1.9
      10:36
      10-2-2 Example 1
    10. 1.10
      10:32
      10-2-3 Example 2
    11. 1.11
      03:59
      10-2-4 Areas
    12. 1.12
      04:37
      10-2-5 Example 3
    13. 1.13
      09:02
      10-2-6 Arc Length
    14. 1.14
      01:43
      10-2-7 Theorem 5
    15. 1.15
      04:27
      10-2-8 Example 4
    16. 1.16
      06:04
      10-2-9 Example 5
    17. 1.17
      08:03
      10-2-10 Surface Area
    18. 1.18
      02:52
      10-2-11 Example 6
    19. 1.19
      05:51
      10-3-1 Polar Coordinates
    20. 1.20
      04:21
      10-3-2 Example 1
    21. 1.21
      08:05
      10-3-3 Cartesian and Polar Coordinates
    22. 1.22
      03:10
      10-3-4 Example 2、3
    23. 1.23
      00:41
      10-3-5 Polar Curves
    24. 1.24
      04:17
      10-3-6 Example 4、5
    25. 1.25
      05:06
      10-3-7 Example 6
    26. 1.26
      07:19
      10-3-8 Example 7
    27. 1.27
      04:18
      10-3-9 Example 8
    28. 1.28
      07:35
      10-3-10 Symmetric Rules
    29. 1.29
      02:52
      10-3-11 Tangents to Polar Curves
    30. 1.30
      08:44
      10-3-12 Example 9
    31. 1.31
      10:04
      10-4-1 Areas in Polar Coordinates
    32. 1.32
      04:05
      10-4-2 Example 1
    33. 1.33
      06:26
      10-4-3 Example 2
    34. 1.34
      10:14
      10-4-4 Area of Bounded Region by Curves and Caution
    35. 1.35
      05:15
      10-4-5 Example 3
    36. 1.36
      05:42
      10-4-6 Arc Length
    37. 1.37
      03:04
      10-4-7 Example 4
  2. 2.
    Ch11 無窮數列與級數
    1. 2.1
      09:08
      11-1-1 Sequences and Example 1、2、3c
    2. 2.2
      13:22
      11-1-2 Graph and Limit of a Sequence and Theorem 3
    3. 2.3
      07:35
      11-1-3 Divergent Sequence, Limit Laws, Squeeze Theorem and Theorem 6
    4. 2.4
      05:52
      11-1-4 Example 4、6、7、8
    5. 2.5
      09:25
      11-1-5 Theorem 7 and Example 9、10、11
    6. 2.6
      04:29
      11-1-6 Monotonic Sequences and Example 12、13
    7. 2.7
      04:47
      11-1-7 Bounded Sequences
    8. 2.8
      04:30
      11-1-8 Monotonic Sequences Theorem 12
    9. 2.9
      10:20
      11-2-1 Series
    10. 2.10
      03:32
      11-2-2 Sum of Series v.s. Improper Integrals
    11. 2.11
      06:09
      11-2-3 Example 2 Geometric Series
    12. 2.12
      07:18
      11-2-4 Example 3、4、5
    13. 2.13
      07:10
      11-2-5 Example 7
    14. 2.14
      06:21
      11-2-6 Example 8 Harmonic Series
    15. 2.15
      08:22
      11-2-7 Theorem 6、Test for Divergence、Example 9 and Note 3
    16. 2.16
      08:04
      11-2-8 Theorem 8 and Example 10
    17. 2.17
      02:56
      11-2-9 Note 4
    18. 2.18
      11:30
      11-3-1 Foreword of Integral Test Example i
    19. 2.19
      05:40
      11-3-2 Foreword of Integral Test Example ii
    20. 2.20
      08:24
      11-3-3 Integral Test
    21. 2.21
      02:31
      11-3-4 Example 1
    22. 2.22
      07:04
      11-3-5 Example 2 p-series、Example 3a、3b and Note
    23. 2.23
      03:53
      11-3-6 Example 4
    24. 2.24
      13:53
      11-3-7 Estimating the Sum of a Series
    25. 2.25
      05:54
      11-3-8 Example 5
    26. 2.26
      02:59
      11-3-9 Estimate 3
    27. 2.27
      07:27
      11-3-10 Example 6 and Compare Example 5 with Example 6
    28. 2.28
      08:44
      11-4-1 Foreword of Comparison Tests
    29. 2.29
      03:01
      11-4-2 Comparison Test
    30. 2.30
      04:20
      11-4-3 Sequence vs Series、Known Series and Example 1
    31. 2.31
      03:35
      11-4-4 Note 1 and Example 2
    32. 2.32
      05:44
      11-4-5 Note 2 and Limit Comparison Test
    33. 2.33
      04:53
      11-4-6 Example 3、4
    34. 2.34
      10:46
      11-5-1 Alternating Series Test
    35. 2.35
      09:13
      11-5-2 Proof of Alternating Series Test
    36. 2.36
      08:10
      11-5-3 Example 1、2、 3
    37. 2.37
      06:06
      11-5-4 Alternating Series Estimation Theorem
    38. 2.38
      07:48
      11-5-5 Example 4
    39. 2.39
      04:02
      11-6-1 Absolute Convergence, Example 1、2 and Conditional Convergence
    40. 2.40
      04:12
      11-6-2 Theorem 3
    41. 2.41
      03:30
      11-6-3 Example 3
    42. 2.42
      01:44
      11-6-4 Ratio Test
    43. 2.43
      11:07
      11-6-5 Proof of Case i
    44. 2.44
      02:55
      11-6-6 Proof of Case ii
    45. 2.45
      03:25
      11-6-7 Proof of Case iii
    46. 2.46
      05:09
      11-6-8 Example 4、5
    47. 2.47
      03:24
      11-6-9 Root Test and Example 6
    48. 2.48
      11:10
      11-6-10 Rearrangements
    49. 2.49
      07:29
      11-7-1 Strategy for Testing Series
    50. 2.50
      05:52
      11-7-2 Example 1、2、3、4、5、6
    51. 2.51
      05:31
      11-8-1 Power Series
    52. 2.52
      03:06
      11-8-2 Example 1
    53. 2.53
      05:47
      11-8-3 Example 2
    54. 2.54
      09:19
      11-8-4 Example 3 Bessel Function
    55. 2.55
      09:23
      11-8-5 Theorem 3, Radius of Convergence and Interval of Convergence
    56. 2.56
      06:49
      11-8-6 Example 4
    57. 2.57
      06:27
      11-8-7 Example 5
  3. 3.
    Ch12 空間的向量和幾何
    1. 3.1
      10:40
      12-1-1 3-D Coordinate Systems
    2. 3.2
      04:12
      12-1-2 Example 1, Note and Example 3
    3. 3.3
      06:15
      12-1-3 Distance Formula
    4. 3.4
      07:53
      12-1-4 Example 4、5、6、7
    5. 3.5
      06:33
      12-2-1 Vector
    6. 3.6
      06:50
      12-2-2 Vector Addition and Example 1
    7. 3.7
      05:38
      12-2-3 Multiplying Vectors and Subtracting Vectors
    8. 3.8
      02:22
      12-2-4 Example 2
    9. 3.9
      05:50
      12-2-5 Components and Position Vector
    10. 3.10
      02:07
      12-2-6 Example 1、3
    11. 3.11
      02:11
      12-2-7 Length of Vector
    12. 3.12
      06:56
      12-2-8 Algebraic Vectors
    13. 3.13
      04:01
      12-2-9 Example 4
    14. 3.14
      07:35
      12-2-10 Components, Properties of Vectors, Standard Basis Vectors and Example 5
    15. 3.15
      03:03
      12-2-11 Unit Vectors and Example 6
    16. 3.16
      09:52
      12-2-12 Force, Example 7
    17. 3.17
      03:24
      12-3-1 The Dot Product and Example 1
    18. 3.18
      01:59
      12-3-2 Theorem 2 Properties of Dot Product
    19. 3.19
      03:06
      12-3-3 Proof of Theorem 2
    20. 3.20
      07:26
      12-3-4 Theorem 3 and Example 2
    21. 3.21
      02:42
      12-3-5 Corollary 6 and Example 3
    22. 3.22
      03:33
      12-3-6 Orthogonal Vectors, Theorem 7 and Example 4
    23. 3.23
      02:13
      12-3-7 Dot Product a‧b
    24. 3.24
      10:46
      12-3-8 Direction Angles and Cosines and Example 5
    25. 3.25
      05:35
      12-3-9 Projection
    26. 3.26
      03:23
      12-3-10 Example 6
    27. 3.27
      03:57
      12-3-11 Applications of Peojections Work
    28. 3.28
      03:55
      12-3-12 Example 7、8
  4. 4.
    Ch13 向量函數
    1. 4.1
      05:13
      13-1-1 Vector Functions and Example 1
    2. 4.2
      05:28
      13-1-2 Limit of a Vector and Example 2
    3. 4.3
      04:29
      13-1-3 Continuous Vector Function, Space Curve
    4. 4.4
      01:43
      13-1-4 Example 3
    5. 4.5
      13:17
      13-1-5 Plane Curves, Example 4, Example 5 and Example 6
    6. 4.6
      05:40
      13-2-1 Definition of Derivative, Unit Tangent Vector
    7. 4.7
      04:15
      13-2-2 Theorem 2
    8. 4.8
      03:35
      13-2-3 Example 1
    9. 4.9
      03:58
      13-2-4 Example 2
    10. 4.10
      03:21
      13-2-5 Example 3
    11. 4.11
      02:00
      13-2-6 Second Derivative
    12. 4.12
      06:35
      13-2-7 Theorem 3 Differentiation Rules
    13. 4.13
      03:42
      13-2-8 Example 4
    14. 4.14
      07:58
      13-3-1 Plane Space Curve Length, Arc Length
    15. 4.15
      03:32
      13-3-2 Example 1
    16. 4.16
      03:32
      13-3-3 Remark of Arc Length
    17. 4.17
      03:21
      13-3-4 Arc Length Function
    18. 4.18
      02:43
      13-3-5 Parametrization
    19. 4.19
      03:19
      13-3-6 Example 2
    20. 4.20
      04:33
      13-3-7 Smooth Parametrization and Smooth Curve
    21. 4.21
      05:03
      13-3-8 Curvature
    22. 4.22
      07:21
      13-3-9 Example 3 and Curvature of a Straight Line
    23. 4.23
      08:13
      13-3-10 Theorem 10 and Example 4
    24. 4.24
      09:24
      13-3-11 Curvature of a Plane Curve and Example 5
    25. 4.25
      06:04
      13-3-12 Normal Vectors and Binormal Vectors
    26. 4.26
      08:03
      13-3-13 Example 6
    27. 4.27
      06:07
      13-3-14 TNB Frame, Normal Plane, Osculating Plane and Osculating Circle
    28. 4.28
      06:57
      13-3-15 Example 7
    29. 4.29
      02:33
      13-3-16 Example 8
    30. 4.30
      01:13
      13-3-17 Summary
    31. 4.31
      08:09
      13-4-1 Velocity and Acceleration
    32. 4.32
      08:36
      13-4-2 Example 1 and Example 2
    33. 4.33
      08:11
      13-4-3 Example 3
    34. 4.34
      00:53
      13-4-4 Summary
  5. 5.
    Ch14 數個變數的函數
    1. 5.1
      10:17
      14-1-1 Functions of Two Variables and Example 1
    2. 5.2
      02:39
      14-1-2 Example 2
    3. 5.3
      03:01
      14-1-3 Example 4
    4. 5.4
      03:40
      14-1-4 Graph and Example 5
    5. 5.5
      04:20
      14-1-5 Example 6 and Example 8
    6. 5.6
      02:43
      14-1-6 Graphs by Computers
    7. 5.7
      09:19
      14-1-7 Level Curves
    8. 5.8
      05:10
      14-1-8 Example 9 and Example 10
    9. 5.9
      06:04
      14-1-9 Example 11 and Computer Generated Level Curves
    10. 5.10
      05:17
      14-1-10 Function of Three Variables, Example 14 and Example 15
    11. 5.11
      03:54
      14-1-11 Multiple Variable Functions
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