課程名稱 |
微積分二 Calculus(Ⅱ) |
開課學期 |
107-2 |
授課對象 |
理學院 數學系 |
授課教師 |
余正道 |
課號 |
MATH1210 |
課程識別碼 |
201 49580 |
班次 |
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學分 |
5.0 |
全/半年 |
半年 |
必/選修 |
必帶 |
上課時間 |
星期二6,7(13:20~15:10)星期四6,7,10(13:20~18:20) |
上課地點 |
新302新302 |
備註 |
周四第10節為實習課。 限本系所學生(含輔系、雙修生) 總人數上限:90人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1072MATH1210 |
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 |
課程大綱
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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-variable calculus. |
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 |
課程要求 |
Calculus I (including rigorous proofs) |
預期每週課後學習時數 |
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Office Hours |
每週五 09:10~10:00 每週四 09:30~10:30 每週三 16:30~17:20 每週二 16:30~17:20 備註: Places: Tuesday, 441; Wednesday, 449; Thursday, 461; Friday, 103
at
Astro-Math Building |
指定閱讀 |
Courant and John, Introduction to calculus and analysis. Vol. II |
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 |
Week 1 |
2/19, 2/21 |
1. Continuity (§§1.1 - 1.3)
2. Partial derivative and differentiability (§§1.4, 1.5) |
Week 2 |
2/26 |
Chain rule (§1.6) |
Week 3 |
3/05, 3/07 |
1. Mean value theorem and Taylor expansion (§1.7)
2. Partial integral (§1.8) |
Week 4 |
3/12, 3/14 |
1. Line integral (§1.9)
2. 不上課但有習題課; Quiz 1 |
Week 5 |
3/19, 3/21 |
1. Finding potential (§1.10)
2. Compact set, etc. (§1.A); Implicit function (§§3.1, 3.2) |
Week 6 |
3/26, 3/28 |
1. Extrema (§3.7)
2. More on implicit function (§§3.3f, 3.7e); Quiz 2 |
Week 7 |
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Spring break |
Week 8 |
4/09, 4/11 |
1. Change of coordinates (§3.3)
2. Inverse function, Jacobian, extrema revisited (§§3.3, 3.A.1) |
Week 9 |
4/16, 4/18 |
1. Jordan measure (§§4.1, 4.A.1)
2. Midterm, 1pm - 4pm (Chap. 1 & 3) |
Week 10 |
4/23,4/25 |
1. Multiple integral and repeated integral (§§4.2 - 4.5)
2. Change of coordinates (§4.6) |
Week 11 |
4/30,5/02 |
1. Improper integral (§4.7)
2. More on improper integral (§4.12) |
Week 12 |
5/07,5/09 |
1. Surface area (§4.8)
2. Volume of n-disk (§§4.10, 4.11); Quiz 3 |
Week 13 |
5/14,5/16 |
1. Gauss's theorem (§§5.1 - 5.3)
2. Applications (§§5.4 - 5.6) |
Week 14 |
5/21,5/23 |
1. Integral on surface (§§5.7, 5.8)
2. Gauss's theorem for surface (§5.9); Quiz 4 |
Week 15 |
5/28,5/30 |
1. Stokes's theorem (§5.10)
2. More on surfaces (§5.A) |
Week 16 |
6/04,6/06 |
Supplement: Calculus of variations |
Week 17 |
6/11, 13 |
1. No class
2. Final (1 - 4 pm) |
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