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課程名稱 |
微積分乙上
Calculus (general Mathematics) (b)(1) |
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開課學期 |
108-1 |
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授課對象 |
物理治療學系 |
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授課教師 |
張志中 |
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課號 |
MATH1203 |
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課程識別碼 |
201 101B1 |
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班次 |
06 |
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學分 |
3.0 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四10(17:30~18:20) |
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上課地點 |
新102新102 |
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備註 |
大二以上限20人.
限本系所學生(含輔系、雙修生)
總人數上限：130人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081MATH1203_06 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Differential and integral calculus of one variable functions with applications.
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課程目標 |
Study the process of approximation and its limitation/errors, learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. |
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課程要求 |
High School Mathematics |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
Textbook: Thomas' calculus, early transcendentals. 13th edition in SI units.
Revised by M. D. Weir and J. Hass. Pearson 2016. 東華書局/新月圖書 代理
注意: 多數 微積分教科書的內容 大同小異，已有一本微積分書的同學可考慮不必再買
上述課本，只需研讀既有書本其相應的章節內容即可。學習數學必須動手習做，因此我會勾選課本
每節較具代表性(講明白一點，較繁複)的計算題 請同學練習。沒有購買課本的同學請務必拿手中既
有的書本的習題切實演練。
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中考 |
35% |
暫定 |
2. |
期末考 |
35% |
暫定 |
3. |
max {quiz 1, quiz 2} |
15% |
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4. |
max {quiz 3, quiz 4} |
15% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/10, 9/12 |
2.3 The precise definition of a limit
2.2 Limit of a function and limit laws
(a proof on the limit of linear combination of functions was given)
2.4 One sided limit and its relation with two-sided limit |
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第2週 |
9/17, 9/19 |
9/17: 2.5 Continuity, examples of various types of discontinuity, and 2.6 limits involving infinity.
9/19: Asymptotes of graphs, properties of continuity, and intermediate value theorem |
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第3週 |
9/24, 9/26 |
9/24: 3.1, 3.2
9/26: 3.3 differentiation rules, derivatives of exponential functions, and higher order derivatives |
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第4週 |
10/1, 10/3 |
10/1: 3.5 derivatives of trig. functions, 3.6 the chain rule, and 3.7 implicit differentiation (3.4 is skipped)
10/3: 3.8 exponential and logarithmic functions |
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第5週 |
10/8, 10/10* |
10/08: 3.11 linear approximation and differentials |
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第6週 |
10/15, 10/17 |
10/15: 4.1 absolute/relative max. and min. values, extreme value theorem, and 4.2 mean value theorem
2019/10/17 (Thur.) Quiz 1 on chapters 2 and 3
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10/16: 3.9 a brief introduction of inverse trigonometric functions (including their derivatives), and 3.11 linearization and differentials
10/18: absolute/relative max. and min. values, and extreme value theorem。後半小時發小考1考卷
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第7週 |
10/22, 10/24 |
10/22: 4.3 and 4.4 concavity and curve sketching
10/24: 4.4 examples of curve sketching, 後半小時發小考1考卷
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10/23: theoretical parts of 4.1 - 4.3, and L'Hopital's rule in 4.5
10/25: 4.4 concavity and curve sketching |
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第8週 |
10/29, 10/31 |
10/29: 4.5 indeterminate forms
10/31: 4.6 applied optimization
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2018/10/30: more examples of curve sketching and indeterminate forms (4.4 and 4.5)
2018/11/01: quiz 2 |
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第9週 |
11/05, 11/07 |
11/05: 4.8 antiderivatives, 5.2 and 5.3 definition and properties of Riemann sums and definite integrals.
11/07: Quiz 2
------- 2018 ------------------------
11/6: 4.6 applied optimization
11/8: 4.8 antiderivatives and 5.2 partition of an interval, and so on.
4.7 and 5.1 are skipped
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第10週 |
11/12, 11/14 |
11/12: 5.4 The fundamental theorem of calculus, and 5.5 integration by substitution
11/14: 發 quiz 2 考卷與演習課
----------2018-------------------------
11/13: Definition and properties of Riemann integrals.
11/15: 校慶 |
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第11週 |
11/19, 11/21 |
11/19: Midterm exam.
11/21: 5.6 area between curves
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11/20: Midterm exam.
11/22: 5.4 The fundamental theorem of calculus |
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第12週 |
11/26, 11/28 |
11/26 and 11/28: 6.1 and 6.2 volumes by disk and shell methods
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11/27: 5.5 integration by substitution
11/29: 5.6 and 6.1 area between curves and volumes using cross-sections |
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第13週 |
12/03, 12/05 |
12/03: 6.3 arc length, inverse sine, and 7.1 formal definitions of logarithm and exponential functions (11:40-12:10 發，並檢討 期中考)
12/05: 7.2 separable differential equations, and 8.2 integration by parts
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12/4: 6.1 and 6.2 volumes by disk and shell methods
12/6: 6.3 arc length |
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第14週 |
12/10, 12/12 |
12/10: 8.1 and 8.2
12/12: Quiz 3 (up to 6.3)
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12/11: separable differential equations, integration by parts
12/13: Quiz 3 |
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第15週 |
12/17, 12/19 |
12/17: 8.5 integration of rational functions and partial fractions
12/19: 8.3 (sine and cosine)
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12/18: 8.2, 8.3 (sine and cosine), and 8.5
12/20: 8.5 |
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第16週 |
12/24, 12/26 |
12/24: Improper integrals, comparison and limit comparison theorems
12/26: 18:00 - 18:20 發 quiz 3 考卷
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12/25: Improper integrals
12/27: Improper integrals (direct and limit comparison theorems)
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第17週 |
12/31, 1/2 |
12/31: review. 11:20 - 12:10 recitation
1/2: quiz 4
1/7: final exam.
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(由這行說明開始，包含本週與以下之內容為系統複製去年課程之進度，其目的在提供同學了解往年課程進行之內容與快慢。日後，隨著日期與課程進行，將會逐週進行更新。同學請以最新逐週公布的『課程大綱』為準，進行複習並演練習題。）
1/3: quiz 4 on separable differential equations, integration by parts, and integrals of rational functions
1/8: Final exam. |
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