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課程名稱 |
微積分二
Calculus(Ⅱ) |
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開課學期 |
106-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
崔茂培 |
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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 |
必帶 |
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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302新302 |
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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 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1062MATH1210_ |
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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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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 |
備註： 每週三 13:30~15:30 or make appointment |
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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 |
TBA |
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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 and quiz |
25% |
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2. |
Midterm I |
25% |
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3. |
Midterm II |
25% |
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4. |
Final |
25% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/27,3/01 |
1.1-1.3 Functions of several variables and continuity.
1.4 Partial derivatives.
2017NTU math 微積分Facebook 群組
https://www.facebook.com/groups/279521942548767/ |
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第2週 |
3/06,3/08 |
1.5 Differential of a function.
1.6 Chain rule
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第3週 |
3/13,3/15 |
1.7 Mean value and Taylor theorem in several variables.
1.8 Integral of functions with a parameter. |
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第4週 |
3/20,3/22 |
1.9 Line integrals
1.10 The fundamental theorem on line integrals |
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第5週 |
3/27,3/29 |
Appendix to Ch.1.
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第6週 |
4/03,4/05 |
Spring Break!!!
No Class!!! |
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第7週 |
4/10,4/12 |
3.1 - 3.2 Implicit functions.
3.3 Inverse function. |
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第8週 |
4/17,4/19 |
第一次期中考四月17號: 範圍第一章。
3.7 Maxima and minima, Appendix 1.
3.7 Lagrange multiplier |
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第9週 |
4/24,4/26 |
3.3 Solving inverse map by iterations, Dependent functions.
3.4 Applications. |
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第10週 |
5/01,5/03 |
4.1-4.4 Area, double integrals and Integrals in higher dimensions.
4.5 Repeated integrals. |
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第11週 |
5/08,5/10 |
4.6 Change of variable formula.
4.8 Applications. |
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第12週 |
5/15,5/17 |
4.7 Improper multiple integrals. |
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第13週 |
5/22,5/24 |
期中考 II: May 27 (Sunday 1 pm, location: TBA)
4.10 Integrals in curvilinear coordinates.
4.11 Higher dimensional integrals. |
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第14週 |
5/29,5/31 |
4.12 Improper integrals with a parameter.
5.1-5.3 Green's theorem. |
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第15週 |
6/05,6/07 |
5.4-5.6 Applications and interpretations by flows. |
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第16週 |
6/12,6/14 |
5.7-5.8 Orientation of surfaces and surface integrals.
5.9 Gauss's theorem in space. |
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第17週 |
6/19,6/21 |
5.10 Stokes's theorem in space.
5.11 Higher dimensions. |
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第18週 |
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Final Exam |
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