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課程名稱 |
微積分二
Calculus(Ⅱ) |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
蔡忠潤 |
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課號 |
MATH1210 |
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課程識別碼 |
201 49580 |
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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 |
必修 |
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上課時間 |
星期二6,7(13:20~15:10)星期四6,7(13:20~15:10) |
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上課地點 |
新505新103 |
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備註 |
微積分甲下用此課替代。周四第10節在天數
101。
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATHCAL |
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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-variable calculus. |
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課程目標 |
Multi-variable 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 multi-variable 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 |
每週四 15:30~16:00
每週三 15:30~16:30 |
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指定閱讀 |
Richard Courant and Fritz John, Introduction to Calculus and Analysis (II)
You can download the file with an NTU IP address:
http://dx.doi.org/10.1007/978-3-642-57149-7
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參考書目 |
待補 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
30% |
You have three jokers: the lowest three grades will be discarded. |
2. |
Midterm I |
20% |
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3. |
Midterm II |
20% |
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4. |
Final |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/21,2/23 |
2/21: 1.1-1.3 Functions of several variables and continuity.
2/23: 1.4 Partial derivatives. |
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第2週 |
3/02 |
3/02: 1.5 Differential of a function. |
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第3週 |
3/07,3/09 |
3/07: 1.6 Chain rule.
3/09: 1.7 Mean value and Taylor theorem in several variables. |
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第4週 |
3/14,3/16 |
3/14: 1.8 Integral of functions with a parameter.
3/16: 1.9 Line integrals. |
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第5週 |
3/21,3/23 |
3/21: 1.10 The fundamental theorem on line integrals.
3/23: Appendix to Ch.1. |
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第6週 |
3/28,3/30 |
3/28: MIDTERM I.
3/30: 3.1 - 3.2 Implicit functions. |
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第7週 |
4/06 |
4/06: 3.3 Inverse function. |
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第8週 |
4/11,4/13 |
4/11: 3.7 Maxima and minima, Appendix 1.
4/13: 3.7 Lagrange multiplier |
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第9週 |
4/18,4/20 |
4/18: 3.3 Solving inverse map by iterations, Dependent functions.
4/20: 3.4 Applications. |
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第10週 |
4/25,4/27 |
4/25: 4.1-4.4 Area, double integrals and Integrals in higher dimensions.
4:27: 4.5 Repeated integrals. |
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第11週 |
5/02,5/04 |
5/02: 4.6 Change of variable formula.
5/04: 4.8 Applications. |
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第12週 |
5/09,5/11 |
5/09: MIDTERM II.
5/11: 4.7 Improper multiple integrals. |
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第13週 |
5/16,5/18 |
5/16: 4.10 Integrals in curvilinear coordinates.
5/18: 4.11 Higher dimensional integrals. |
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第14週 |
5/23,5/25 |
5/23: 4.12 Improper integrals with a parameter.
5/25: 5.1-5.3 Green's theorem. |
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第15週 |
6/01 |
6/01: 5.4-5.6 Applications and interpretations by flows. |
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第16週 |
6/06,6/08 |
6/06: 5.7-5.8 Orientation of surfaces and surface integrals.
6/08: 5.9 Gauss's theorem in space. |
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第17週 |
6/13,6/15 |
6/13: 5.10 Stokes's theorem in space.
6/15: 5.11 Higher dimensions. |
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第18週 |
6/20 |
Final Exam |
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