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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
103-1 |
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授課對象 |
數學系 |
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授課教師 |
余正道 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
06 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必帶 |
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上課時間 |
星期二5,6(12:20~14:10)星期四5,6,9(12:20~17:20) |
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上課地點 |
新103新103 |
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備註 |
四9為實習課。
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031mathcal |
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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 |
另約時間 備註： Thursdays 3:30 - 5 pm |
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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 |
9/16,9/18 |
§§1.1, 1.2 |
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Week 2 |
9/23,9/25 |
1. Limit of sequence (§1.3 - §1.6)
2. Limit of sequence and function (§§1.7, 1.8) |
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Week 3 |
9/30,10/02 |
1. Real numbers, etc. (Supplements of Chapter 1)
2. Integral (§2.1 - §2.7); Quiz (Chap 1) |
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Week 4 |
10/07,10/09 |
1. Derivative (§2.8)
2. Fundamental theorem, existence of integral (§2.9, Supplement) |
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Week 5 |
10/14,10/16 |
1. Basic rules for derivative (§§3.1 - 3.3) 2. Exponentials (§§3.4, 3.5); Quiz (Chap 2) |
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Week 6 |
10/21,10/23 |
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 |
10/28,10/30 |
1. By parts (§3.11) 2. Integration of rational functions (§§3.12, 3.13); Quiz (Differentiation) |
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Week 8 |
11/04,11/06 |
1. Further integration (§§3.14 - 3.15)
2. Arc length and area (§§4.1, 4.2) |
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Week 9 |
11/11,11/13 |
1. Midterm (Chap 1 - 3) 2. Motion, Newton's law |
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Week 10 |
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1. Restoration
2. Revisit Chap. 1-3 and prepare Chap. 4 |
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Week 11 |
11/25,11/27 |
1. Taylor's theorem (§§5.1 - 5.4) 2. More Taylor, L'Hospital (§§5.5 - App.I); Extra quiz |
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Week 12 |
12/02,12/04 |
1. Sequence/sum of numbers (§§7.1, 7.2) 2. Sequence/sum of functions (§§7.3, 7.3); Quiz (Chap 4,5) |
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Week 13 |
12/09,12/11 |
1. Power series (§§7.5, 7.6)
2. Operating series and infinite product (§Appendix) |
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Week 14 |
12/16,12/18 |
1. Interpolation, estimating integral (§§5.A.II, 6.1) 2. Numerical solution, Stirling (§§6.2 - Appendix); Quiz (Chap 7) |
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Week 15 |
12/23,12/25 |
1. Periodic functions (§§8.1 - 8.3) 2. Fourier expansion (§§8.4, 8.5) |
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Week 16 |
12/30 |
Refinement (§8.6) |
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Week 17 |
1/06,1/08 |
Chap 8 / Review |
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Week 18 |
1/11 |
[Sunday] Final exam (1 - 4 pm at Astro-Math 101, 102) |
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