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Learn More微積分二 (廣東話)
What you'll learn
- 更多積分技巧
- 體積、弧長、表面積
- 參數曲線與極坐標曲線
- 無窮級數
Explore related topics
Course content
6 sections • 172 lectures • 11h 46m total length
- 事前準備0:01
- Lecture 1.1: Introduction to Integration by Parts2:46
- Lecture 1.2: LIATE1:29
- Lecture 1.3: Integration by Parts Examples 1-412:39
- Quiz 1 (Integration By Parts)0:03
- Lecture 2.1: Introduction to Reduction Formula + Examples 1-27:06
- Lecture 2.2: Reduction Formula Examples 3-44:24
在 04:13，最後答案中的 6x 應為 6e^x。
- Quiz 2 (Reduction Formula)0:03
- Lecture 3.1: Integrating Power of Trigonometric Functions5:23
- Lecture 3.2: Integrating Products of Trigonometric Functions Examples 1-26:27
- Lecture 3.3: Integrating Products of Trigonometric Functions Examples 3-45:28
- Quiz 3 (Integrating Products of Trigonometric Functions)0:03
- Lecture 3.4: Integration using Trigonometric Identities + Examples 5-64:20
- Quiz 4 (Integration using Trigonometric Identities)0:03
- Lecture 4.1: Introduction to Trigonometric Substitution9:08
- Lecture 4.2: Trigonometric Substitution Example 14:49
- Lecture 4.3: Trigonometric Substitution Example 26:03
- Lecture 4.4: Trigonometric Substitution Example 35:33
- Lecture 4.5: Trigonometric Substitution Example 44:42
- Quiz 5 (Trigonometric Substitution)0:03
- Lecture 5.1: Warm Up4:51
- Lecture 5.2: Partial Fraction Decomposition8:38
- Lecture 5.3: Partial Fractions Example 15:48
- Lecture 5.4: Partial Fractions Example 23:04
- Lecture 5.5: Partial Fractions Example 34:56
- Quiz 6 (Partical Fraction Decomposition)0:03
- Lecture 6.1: Riemann Sum Approximations (Idea)7:28
- Lecture 6.2: Riemann Sum Approximations Example 13:46
- Quiz 7 (Riemann Sum Approximation)0:03
- Lecture 6.3: Trapezoidal Rule (Idea)3:42
- Lecture 6.4: Trapezoidal Rule Example 23:28
- Quiz 8 (Trapezoidal Rule)0:03
- Lecture 6.5: Simpson's Rule (Idea)5:05
- Lecture 6.6: Simpson's Rule Example 34:32
- Quiz 9 (Simpson's Rule)0:03
- Lecture 6.7: Error Bounds (Idea)5:20
- Lecture 6.8: Error Bounds Example 48:34
- Quiz 10 (Error Bounds)0:03
- Lecture 7.1: Improper Integral (Infinite Intervals)5:43
- Lecture 7.2: Infinite Interval Example 18:06
- Lecture 7.3: Infinite Interval Example 23:16
- Quiz 11 (Improper Integral - Infinite Interval)0:03
- Lecture 7.4: Improper Integral (Infinite Discontinuities)4:53
- Lecture 7.5: Infinite Discontinuities Example 33:45
- Lecture 7.6: Infinite Discontinuities Example 44:06
- Quiz 12 (Improper Integral - Infinite Discontinuities)0:03
- Lecture 7.7: Both Infinite Intervals + Infinite Discontinuities Example 58:01
- Quiz 13 (Improper Integral - Both)0:03
- Lecture 7.8: Comparison Theorem + Example 66:05
- Quiz 14 (Comparison Theorem)0:03
- Lecture 8.1: Volume (Slicing Method)12:37
- Lecture 8.2: Slicing Method Example 16:41
- Lecture 8.3: Slicing Method Example 27:07
- Quiz 15 (Volume - Slicing Method)0:03
- Lecture 8.4: Volume (Disk Method)3:32
- Lecture 8.5: Disk Method Example 34:24
- Lecture 8.6: Disk Method Example 43:23
- Quiz 16 (Volume - Disk Method)0:03
- Lecture 8.7: Region Bounded by Curves (Idea)3:39
- Lecture 8.8: Region Bounded by Curves Example 55:25
- Lecture 8.9: Region Bounded by Curves Example 66:12
- Lecture 8.10: Volume (Shell Method) Part 17:00
- Lecture 8.11: Volume (Shell Method) Part 27:37
- Lecture 8.12: Shell Method Example 78:50
- Lecture 8.13: Shell Method Example 88:55
- Quiz 17 (Volume - Shell Method)0:03
- Lecture 8.14: Summary1:19
- Lecture 9.1: Arc Length (Idea)7:42
- Lecture 9.2: Arc Length Example 13:39
- Quiz 18 (Arc Length)0:03
- Lecture 10.1: Surface Area (Idea)9:24
At 7:25, I forgot the Summation Sign from k = 1 to n in the second last line.
- Lecture 10.2: Surface Area Example 13:37
- Lecture 10.3: Surface Area Example 25:31
- Quiz 19 (Surface Area)0:03
- Lecture 11.1: Parametric Equations (Idea)2:53
- Lecture 11.2: Parametric Equations Example 12:23
- Lecture 11.3: Parametric Equations Examples 2-34:36
- Lecture 11.4: Parametric Equations Example 42:07
- Lecture 11.5: Parametric Equations Example 54:22
- Quiz 20 (Parametric Equations - Basics)0:03
- Lecture 11.6: Slope of Tangent (Idea)2:29
- Lecture 11.7: Slope of Tangent Example 63:59
- Quiz 21 (Parametric Equations - Slope of Tangent)0:03
- Lecture 11.8: Arc Length (Idea)4:09
- Lecture 11.9: Arc Length Example 72:32
- Quiz 22 (Parametric Equations - Arc Length)0:03
- Lecture 12.1: Introduction to Polar Coordinates2:42
- Lecture 12.2: Polar Coordinates Example 15:01
- Lecture 12.3: Relationship between Polar and Rectangular Coordinates (Idea)2:17
- Lecture 12.4: Relationship between Polar and Rectangular Coordinates Examples 2-3:39
- Lecture 12.5: Polar Equations and Graphs5:29
- Quiz 23 (Polar Coordinates - Basics)0:03
- Lecture 12.6: Slope of Tangent and Example 45:47
- Quiz 24 (Polar Equations - Slope of Tangent)0:03
- Lecture 12.7: Arc Length (Idea)3:57
- Lecture 12.8: Arc Length Examples 5-64:43
- Quiz 25 (Polar Equations - Arc Length)0:03
- Lecture 12.9: Area (Idea)6:44
- Lecture 12.10: Area Example 78:06
- Lecture 12.11: Area Example 86:53
- Lecture 12.12: Area Example 95:15
- Quiz 26 (Polar Equations - Area)0:03
- Lecture 13.1: Introduction to Infinite Sequences + Example 18:11
- Lecture 13.2: Limits of Sequences + Examples 2-35:57
- Lecture 13.3: Squeeze Theorem + Example 44:11
- Quiz 27 (Sequences - Basics)0:03
- Lecture 13.4: Monotone Sequences + Example 57:15
- Lecture 13.5: Monotone Convergence Theorem + Example 611:37
在 05:50，f''(x) should be 3/x^3 instead of 6/x^3. However, the flow afterwards is still correct.
- Quiz 28 (Monotone Sequences)0:03
- Lecture 14.1: Introduction to Infinite Series and Partial Sums + Example 19:37
- Lecture 14.2: Geometric Series + Example 27:59
- Lecture 14.3: Telescoping Series + Example 33:13
- Lecture 14.4: Harmonic Series4:52
- Quiz 29 (Infinite Series - Basics)0:03
- Lecture 14.5: Divergence Test + Example 46:06
- Quiz 30 (Divergence Test)0:03
- Lecture 14.6: Integral Test (Idea)9:13
- Lecture 14.7: Integral Test Example 5 (p-Series)7:17
- Quiz 31 (Integral Test)0:03
- Lecture 14.8: Comparison Test (Idea)3:38
- Lecture 14.9: Comparison Test Example 66:16
- Quiz 32 (Comparison Test)0:03
- Lecture 14.10: Limit Comparison Test (Idea)3:31
- Lecture 14.11: Limit Comparison Test Example 75:18
- Quiz 33 (Limit Comparison Test)0:03
- Lecture 14.12: Alternating Series Test (Idea)6:29
- Lecture 14.13: Alternating Series Test Example 85:01
- Quiz 34 (Alternating Series Test)0:03
- Lecture 14.14: Approximating Sums of Alternating Series (Idea)4:28
- Lecture 14.15: Approximating Sums of Alternating Series Example 93:13
- Quiz 35 (Approximating Sums of Alternating Series)0:03
- Lecture 14.16: Absolute and Conditional Convergence (Idea)5:56
- Lecture 14.17: Absolute and Conditional Convergence Example 103:56
- Quiz 36 (Absolute and Conditional Convergence)0:03
- Lecture 14.18: Ratio Test (Idea)10:16
- Lecture 14.19: Ratio Test Example 115:19
- Quiz 37 (Ratio Test)0:03
- Lecture 14.20: Root Test (Idea)1:55
- Lecture 14.21: Root Test Example 124:44
- Quiz 38 (Root Test)0:03
- Lecture 14.22: Summary8:29
- Lecture 15.1: Local Linear Approximation Review5:37
- Lecture 15.2: Local Quadratic Approximation5:15
- Lecture 15.3: Maclaurin Polynomials (Idea)4:53
- Lecture 15.4: Maclaurin Polynomials Example 15:23
- Lecture 15.5: Maclaurin Polynomials Example 28:24
- Lecture 15.6: Maclaurin Polynomials Example 35:43
- Lecture 15.7: Taylor Polynomials (Idea)5:36
- Lecture 15.8: Taylor Polynomials Example 44:15
- Quiz 39 (Maclaurin Polynomials and Taylor Polynomials)0:03
- Lecture 15.9: Remainder Estimation Theorem (Idea)8:39
- Lecture 15.10: Proof of Remainder Estimation Theorem Part 16:55
- Lecture 15.11: Proof of Remainder Estimation Theorem Part 26:17
- Lecture 15.12: Remainder Estimation Theorem Example 57:58
- Lecture 15.13: Remainder Estimation Theorem Example 65:59
- Quiz 40 (Remainder Estimation Theorem)0:03
- Lecture 16.1: Introduction to Power Series3:18
- Lecture 16.2: Interval of Convergence and Radius of Convergence (Idea)4:55
- Lecture 16.3: Interval of Convergence and Radius of Convergence Example 18:24
- Quiz 41 (Interval of Convergence and Radius of Convergence)0:03
- Lecture 16.4: Taylor Series and its Convergence (Idea)6:30
- Lecture 16.5: Taylor Series and its Convergence Example 25:41
- Lecture 16.6: Taylor Series and its Convergence Example 35:56
- Quiz 42 (Maclaurin Series and Taylor Series)0:03
- Lecture 16.7: Important Maclaurin Series2:11
- Lecture 16.8: Finding Power Series by Substitution + Example 44:25
- Quiz 43 (Finding Power Series by Substitution)0:03
- Lecture 16.9: Power Series and Taylor Series2:45
- Lecture 16.10: Differentiating and Integrating a Power Series (Idea)4:08
- Lecture 16.11: Differentiating and Integrating a Power Series Examples 5-75:28
- Lecture 16.12: Finding Power Series by Differentiation and Integration + Example5:33
- Quiz 44 (Differentiation and Integration of Power Series)
Requirements
- 微積分一
Description
內容參考科大大一微積分課程的內容，這個課程主要圍繞三大主題，分別為積分技巧、參數曲線與極坐標曲線、無窮級數。當中例子會較多，相對地亦較微積分一困難。
詳細內容如下:
積分
分部積分
遞迴公式
三角代換
部分分式
梯形法則與辛普森法則
瑕積分
體積、弧長、表面積
參數曲線與極坐標曲線
參數方程
極坐標方程
弧長與面積
無窮級數
幾何級數、重疊級數、調和級數
積分檢驗法、比較檢驗法、極限比較檢驗法、交錯級數檢驗法、比值檢驗法、根檢驗法
麥克勞林與泰勒多項式
冪級數與泰勒級數
每節短片後會有少量練習作鞏固。
部份短片可能有誤，一人團隊，請原諒我暫時未有時間重拍。
Who this course is for:
- 所有人