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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 |
100-1 |
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授課對象 |
數學系 |
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授課教師 |
陳榮凱 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
07 |
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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/1001CA1 |
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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 |
上學期: 涵蓋微分(差分), 積分(求和), 級數(Taylor與Fourier)等基礎題材. 理論(要求證明)與計算並重. 包含一定程度歷史發展的介紹.
下學期: Vector Calculus, multivariable differentiation (as linear transformation), multiple-integral, Green, Divergence and Stokes Theorems. |
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課程要求 |
1. 按時上課(含習題課), 繳交作業以及參加考試.
2. 培養課前課後閱讀能力. |
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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 |
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參考書目 |
Courant and Robbins: What is Mathematics?
http://www.oup.com/us/catalog/general/subject/Mathematics/?view=usa&ci=9780195105193
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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 |
9/13,9/15 |
9/13 Introduction;
9/15 Continuity. |
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Week 2 |
9/20,9/22 |
9/20 Uniformly continuous, limits;9/22 Limits, real numbers. |
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Week 3 |
9/27,9/29 |
9/27 Real Numbers;9/29 Integrals. |
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Week 4 |
10/04,10/06 |
Integrals, mean value theorem, logarithm and exponential functions |
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Week 5 |
10/11,10/13 |
Derivative, Mean Value Theorem, Fundamental Theorem of Calculus |
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Week 6 |
10/18,10/20 |
Rules of differentiations; Inverse Function Theorem; Chain Rule. |
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Week 7 |
10/25,10/27 |
Extrema; Order of Magnitude; Some special functions; Integration by Substitution. |
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Week 8 |
11/01,11/03 |
Integration by parts; Partial fractions. |
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Week 9 |
11/08,11/10 |
11/8 Midterm; 11/10 Improper integral |
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Week 11 |
11/22,11/24 |
Taylor's Expansion |
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Week 12 |
11/29,12/01 |
Taylor's expansion; l'Hopital's rule. |
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Week 13 |
12/06,12/08 |
Interpolation; Numerical Methods |
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Week 15 |
12/20,12/22 |
Infinite series; Limits of functions |
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