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課程名稱 |
微積分甲下
Calculus (general Mathematics) (a)(2) |
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開課學期 |
103-2 |
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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 |
MATH1202 |
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課程識別碼 |
201 101A2 |
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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/1032mathcal |
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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 |
This course generalizes the concepts of limits, continuity, differentiability and integrations in the study of functions of several variables from single-varibale calculus. |
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課程目標 |
Multivariable calculus including continuity, partial derivatives, linear approximation, Taylor formula, implicit function theorem, Lagrange multiplier, area, volume and integrations, change of variables, improper integral, line integral, fundamental theorems of multivariable calculus: Green, divergence and Stokes theorems |
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課程要求 |
Calculus I (including rigorous proofs) |
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預期每週課後學習時數 |
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Office Hours |
每週五 16:30~17:20
每週四 15:30~17:00
每週二 15:30~16:20
每週一 14:20~15:10 備註： Room: Astro-Math 304 (Monday); Astro-Math 430 (otherwise) |
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指定閱讀 |
Courant and John, Introduction to calculus and analysis. Vol. II |
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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 |
2/24,2/26 |
1. Continuity (§§1.1 - 1.3)
2. Partial derivative (§1.4) |
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Week 2 |
3/03,3/05 |
1. Differentiable function (§1.5)
2. Chain rule (§1.6) |
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Week 3 |
3/10,3/12 |
1. Mean value theorem and Taylor expansion (§1.7)
2. Partial integral (§1.8); Quiz 1 |
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Week 4 |
3/17,3/19 |
1. Line integral (§1.9)
2. Finding potential (§1.10) |
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Week 5 |
3/24,3/26 |
1. Compact set, etc. (§1.A)
2. Implicit function (§§3.1, 3.2); Quiz 2 |
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Week 6 |
3/31 |
Extrema (§3.7) |
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Week 7 |
4/07,4/09 |
1. More on implicit function (§§3.3f, 3.7e)
2. Change of coordinates (§3.3); Quiz 3 |
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Week 8 |
4/14,4/16 |
1. Inverse function, Jacobian, extrema revisited (§§3.3, 3.A.1)
2. Jordan measure (§§4.1, 4.A.1) |
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Week 9 |
4/21,4/23 |
1. Midterm (Chap 1,3)
2. Multiple integral (§§4.2 - 4.4) |
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Week 10 |
4/28,4/30 |
1. Repeated integral (§4.5)
2. Change of coordinates (§4.6) |
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Week 11 |
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Restoration |
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Week 12 |
5/12,5/14 |
1. Surface area (§4.8)
2. Improper integral (§4.7);
Quiz 4 |
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Week 13 |
5/19,5/21 |
1. More on improper integral (§4.12)
2. Gauss's theorem (§§5.1 - 5.3) |
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Week 14 |
5/26,5/28 |
1. Applications (§§5.4 - 5.6)
2. Integral on surface (§§5.7, 5.8);
Quiz 5 |
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Week 15 |
6/02,6/04 |
1. Gauss's theorem for surface (§5.9)
2. Stokes's theorem (§5.10) |
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Week 16 |
6/09,6/11 |
1. Multiple integral (review), volume of n-disk (§§4.10, 4.11)
2. Surface area, improper integral (review); integral on manifold (§§5.11, 5.A);
Quiz 6 |
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Week 17 |
6/16,6/18 |
1. 3D fundamental theorems (review)
2. Problem session |
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Week 18 |
6/21 Sunday |
Final (Chap 4,5), 2pm - 5pm at Astro-Math 101, 102 |
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