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課程名稱 |
微積分一
Calculus(Ⅰ) |
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開課學期 |
107-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
余正道 |
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課號 |
MATH1211 |
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課程識別碼 |
201 49570 |
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班次 |
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學分 |
5.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期一7,8(14:20~16:20)星期四6,7,10(13:20~18:20) |
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上課地點 |
新505新204 |
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備註 |
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071MATH1211 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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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 |
專為以培養能夠深刻運用數學工具或計畫以數學研究為目標所開設之微積分. 數學系大一必修. 上學期著重於單變數, 下學期則進入多變數微積分. |
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課程目標 |
Real Numbers, Limits, Continuity, Differentiation, and Integration |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週五 09:00~10:00
每週三 14:00~15:00
每週二 08:00~09:00
每週一 16:30~17:30 備註： Monday: 441. Tuesday/Friday: 103. Wednesday: 461. All in Astro-
Math Building. |
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指定閱讀 |
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參考書目 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
9/10, 13 |
Limit of a sequence (§§1.1, 1.4 - 1.7) |
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Week 2 |
9/17, 20 |
Continuity and limit of a function (§§1.2, 1.8, Supplements of Chap 1) |
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Week 3 |
9/27 |
Derivative (§2.8); Quiz (Chap 1) |
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Week 4 |
10/1, 4 |
1. Integral (§§2.1 - 2.7)
2. Fundamental theorem, existence of integral (§2.9, Supplement) |
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Week 5 |
10/8, 11 |
1. Basic rules for derivative (§§3.1 - 3.3)
2. Exponentials (§§3.4, 3.5); Quiz (Chap 2) |
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Week 6 |
10/15, 18 |
1. Extremal points, some special functions (§3.6, some of §3.7, §Appendix)
2. Substitution, change of variable (§§3.8 - 3.10) |
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Week 7 |
10/22, 25 |
1. By parts (§3.11)
2. Integration of rational functions (§§3.12, 3.13); |
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Week 8 |
10/29, 11/1 |
1. Midterm (Chap 1 - §3.11)
2. Further integration (§§3.14, 3.15) |
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Week 9 |
11/5, 8 |
1. Arc length and area (§§4.1, 4.2)
2. Taylor's theorem (§§5.1 - 5.4) |
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Week 10 |
11/12 |
More Taylor, L'Hospital (§§5.5 - App.I) |
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Week 11 |
11/19, 22 |
1. Sequence/sum of numbers (§§7.1, 7.2)
2. Sequence/sum of functions (§§7.3, 7.4); Quiz (Chap 4,5) |
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Week 12 |
11/26, 29 |
1. Power series (§§7.5, 7.6)
2. Operating series and infinite product (§Appendix) |
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Week 13 |
12/3, 6 |
1. Periodic functions (§§8.1 - 8.3)
2. Fourier expansion (§§8.4, 8.5); Quiz (Chap 7) |
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Week 14 |
12/10, 13 |
1. Refinement (§8.6)
2. Newton's method, iteration, interpolation (§§6.3, 5.A.II) |
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Week 15 |
12/17, 20 |
Estimating integral, Stirling (§§6.1, 6.2, Appendix) |
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Week 16 |
12/24, 26 |
1. Final exam
2. (上課時間 12/26 (Wednesday), 1:30 - 3 pm，地點：新生403) Real numbers |
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