試聽影片
2021-自學課程-微積分一
本課程可奠定一般理工學院所需的基本數學能力,針對單元主要定義或定理作講解,同時推導定理或公式,並配合例題運用之,將可奠定工程數學、複變函數與高等微積分的學習基礎,同時經由演算之過程培養學生邏輯分析之能力。
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本課程可奠定一般理工學院所需的基本數學能力,針對單元主要定義或定理作講解,同時推導定理或公式,並配合例題運用之,將可奠定工程數學、複變函數與高等微積分的學習基礎,同時經由演算之過程培養學生邏輯分析之能力。
購買講義方式請洽:http://www.math.nthu.edu.tw/~dyyan/MOOCsCalculus.html
講義相關疑問請洽:梁宏志助教 gary684268426842@gmail.com本課程為線上自主學習課程(搭配影片、練習題、測驗等),修讀者可申請人工智慧 (AI) 學習履歷,作為多元選修、自主學習課程之佐證。
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* 以下章節為預覽,請點報名後點選開始上課,進入課程 -
第1週:Limit
- Limit:01極限概念簡介
- 練習01
- Limit:02-01極限的定義
- 練習02-01
- Limit:02-02極限的定義(續)
- 練習02-02
- Limit:03-01例題講解
- Limit:03-02例題講解(續)
- Limit:04例題講解(續)
- Limit:05例題講解(續)
- 練習04~05
- Limit:06左極限與右極限
- 練習06
- Limit:07極限唯一性
- Limit:08極限四則運算(加法、常數倍)
- Limit:09極限四則運算(加法、常數倍)(續)
- Limit:10極限四則運算(乘法)
- Limit:11極限四則運算(乘法)(續)
- Limit:12極限四則運算(多項式、倒數)
- Limit:13極限四則運算(倒數、除法)
- 練習07~13
- Limit:14連續和不連續的定義
- 練習14
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第2週:Continuity
- Continuity:15連續-例題講解
- Continuity:16連續-四則運算、例題
- Continuity:17連續-合成函數
- 練習15~17
- Continuity:18夾擠定理
- 練習18
- Continuity:19三角函數極限
- Continuity:20三角函數極限(續)
- Continuity:21三角函數極限(續)
- Continuity:22三角函數極限-例題講解
- 練習19~22
- Continuity:23中間值定理與極值定理
- Continuity:24導函數定義、例題講解
- Continuity:25例題講解(續)
- 練習23~25
- Continuity:26微分與連續;微分運算(例題)
- Continuity:27微分四則運算-加法、常數倍
- Continuity:28微分四則運算-乘法
- 練習26~28
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第3週:Differentiations
- Differentiations:29 冪法則1、例題講解
- Differentiations:30 微分四則運算-倒數
- Differentiations:31 冪法則2;微分四則運算-商法則
- 練習29~31
- Differentiations:32 例題講解、二次微分
- 練習32
- Differentiations:33 鏈鎖律-例題講解
- Differentiations:34 例題講解(續)
- 練習33~34
- Differentiations:35 三角函數微分
- Differentiations:36 三角函數微分(續)
- 練習35~36
- Differentiations:37三角函數鏈鎖律、例題講解
- Differentiations:38例題講解(續)
- 練習37~38
- Differentiations:39隱函數微分-例題講解
- Differentiations:40 例題講解(續)
- 練習39~40
- Differentiations:41 冪法則有理數版、例題
- Differentiations:42 均值定理:前置
- 練習41
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第4週:Mean-value theorem
- Mean-value theorem:43 洛爾(Rolle′s)定理
- Mean-value theorem:44 均值定理
- Mean-value theorem:45 均值定理-例題
- 練習43~45
- Mean-value theorem:46 遞增遞減函數-定義及例題
- Mean-value theorem:47 遞增遞減函數性質3.2.4
- Mean-value theorem:48 遞增遞減函數性質3.2.5
- Mean-value theorem:49 遞增遞減函數-例題1
- Mean-value theorem:50 遞增遞減函數-例題2
- 練習46~50
- Mean-value theorem:51 局部極值-定義
- Mean-value theorem:52 局部極值-定理
- 練習51~52
- Mean-value theorem:53 臨界點-例題
- 練習53
- Mean-value theorem:54 一階導函數檢驗法
- Mean-value theorem:55 例題講解
- 練習54~55
- Mean-value theorem:56 二階導數測試
- 練習56
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第5週:Applications of the first and second derivatives
- Applications of the first and second derivatives:57 絕對極值
- 練習57
- Applications of the first and second derivatives:58 凹凸性
- 練習58
- Applications of the first and second derivatives:59 反曲點
- 練習59
- Applications of the first and second derivatives:60 例題講解
- 練習60
- Applications of the first and second derivatives:61 數列極限的定義
- 練習61
- Applications of the first and second derivatives:62 數列極限的四則運算
- 練習62
- Applications of the first and second derivatives:63 定積分的定義
- Applications of the first and second derivatives:64 定積分的定義(續)
- 練習63~64
- Applications of the first and second derivatives:65 定積分的例題
- 練習65
- Applications of the first and second derivatives:66 定積分的例題(續)
- 練習66
- Applications of the first and second derivatives:67 定積分的性質
- 練習67
- Applications of the first and second derivatives:68 定積分的性質(續)
- 練習68
- Applications of the first and second derivatives:69 微積分第一基本定理 Part1
- 練習69
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第6週:Integrations
- Integrations:70 微積分第一基本定理 Part2
- 練習70
- Integrations:71 微積分第一基本定理 Part3
- 練習71
- Integrations:72 微積分第一基本定理 Part4
- 練習72
- Integrations:73 微積分第一基本定理 Part5
- 練習73
- Integrations:74 微積分第一基本定理 Part6
- 練習74
- Integrations:75 微積分第一基本定理例題
- 練習75
- Integrations:76 微積分第二基本定理
- 練習76
- Integrations:77 微積分第二基本定理例題
- 練習77
- Integrations:78 面積計算
- Integrations:79 面積計算(續)
- Integrations:80 面積計算(續)
- 練習78~80
- Integrations:81 不定積分與變數變換法
- Integrations:82 不定積分與變數變換法(續)
- 練習81~82
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第7週:Areas and volumes from the definite integrals
- Areas and volumes from definite integrals:83 更多面積計算
- 練習83
- Areas and volumes from definite integrals:84 旋轉體體積(1)
- Areas and volumes from definite integrals:85 旋轉體體積(2)
- 練習84~85
- Areas and volumes from definite integrals:86 旋轉體體積(3)
- Areas and volumes from definite integrals:87 旋轉體體積(4)
- 練習86~87
- The transcendental functions:88 反函數(1)
- The transcendental functions:89 反函數(2)
- 練習88~89
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第8週:The natural logarithm function
- The transcendental functions:90 自然對數函數(1)
- The transcendental functions:91 自然對數函數(2)
- The transcendental functions:92 自然對數函數(3)
- The transcendental functions:93 自然對數函數(4)
- 練習90~93
- The transcendental functions:94 自然對數函數之計算(1)
- The transcendental functions:95 自然對數函數之計算(2)
- 練習94~95
- The transcendental functions:96 自然指數函數(1)
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第9週:The natural exponential function and the inverse trigonometric functions
- The transcendental functions:97 自然指數函數(2)
- The transcendental functions:98 自然指數函數(3)
- The transcendental functions:99 自然指數函數之計算
- 練習96~99
- The transcendental functions:100 任意次方(1)
- The transcendental functions:101 任意次方(2)
- 練習100~101
- The transcendental functions:102 反三角函數 sin cos
- The transcendental functions:103 反三角函數 tan cot
- The transcendental functions:104 反三角函數 sec csc
- 練習102~104
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第10週:Integration by parts and the trigonometric identities
- The techniques of integration:105 分部積分(1)
- The techniques of integration:106 分部積分(2)
- The techniques of integration:107 分部積分(3)
- 練習105~107
- The techniques of integration:108 三角函數恆等式之積分技巧
- The techniques of integration:109 三角代換法(1)
- The techniques of integration:110 三角代換法(2)
- The techniques of integration:111 三角代換法(3)
- 練習108~111
- The techniques of integration:112 部分分式(1)
- The techniques of integration:113 部分分式(2)
- The techniques of integration:114 部分分式(3)
- 練習112~114
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第11週:The trigonometric substitution and the partial fractions
- Sequences:115 完全公設(1)
- Sequences:116 完全公設(2)
- 練習115~116
- Sequences:117 遞增遞減數列
- 練習117
- Sequences:118 數列極限(1)
- 練習118
- Sequences:119 數列極限(2)
- 練習119
- Sequences:120 數列極限(3)
- Sequences:121 數列極限(4)
- 練習120~121
- Sequences:122 數列極限(5)
- 練習122
- Sequences:123 羅必達(1)
- 練習123
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第12週:L' Hopital's rule and improper integrals
- Sequences:124 羅必達(2)
- 練習124
- Sequences:125 羅必達(3)
- 練習125
- Sequences:126 羅必達(4)
- 練習126
- Sequences:127 瑕積分(1)
- Sequences:128 瑕積分(2)
- Sequences:129 瑕積分(3)
- Sequences:130 瑕積分(4)
- Sequences:131 瑕積分(5)
- Sequences:132 瑕積分(6)
- Sequences:133 瑕積分(7)
- 練習127~133
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第1週:Limit
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