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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 |
99-2 |
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授課對象 |
數學系 |
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授課教師 |
王金龍 |
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課號 |
MATH1202 |
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課程識別碼 |
201 101A2 |
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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/992math_calculus |
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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 |
Multivariable calculus for math majored students. |
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課程目標 |
1. Multivariable differentiation as linear approximation. Partial and total derivatives. Composition, inverse and implicit functions. Taylor formula, extremal value problems and the Lagrange multiplier.
2. Multivariable integration. Fubini theorem. Change of variable formula. Various coordinate systems and their applications to integrations. Introduction to integral transformations.
3. Vector calculus. Line integrals and surface integrals. Gradient, divergence and curl. Green's theorem, Gauss theorem and Stokes' theorem. Applications to physics. |
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課程要求 |
Quiz, midterm and final exams. |
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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 |
Courant and John: Introduction to Calculus and Analysis 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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第1週 |
2/22,2/24 |
2/22: 1.1-1.3 Functions of several variables and continuity.
2/14: 1.4 Partial derivatives. |
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第2週 |
3/01,3/03 |
3/01: 1.5 Differential of a function.
3/03: 1.6 Chain rule. |
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第3週 |
3/08,3/10 |
3/08: 1.7 Mean value and Taylor theorem in several variables.
3/10: 1.8 Integral of functions with a parameter. |
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第4週 |
3/15,3/17 |
3/15: 1.9 Line integrals.
3/17: 1.10 The fundamental theorem on line integrals. |
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第5週 |
3/22,3/24 |
3/22: Appendix to Ch.1.
3/24: 3.1 - 3.2 Implicit functions. |
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第6週 |
3/29,3/31 |
3/29: 3.3 Inverse function.
3/31: 3.7 Maxima and minima, Appendix 1. |
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第7週 |
4/05,4/07 |
4/07: 3.7 Lagrange multiplier, 3.3 Product of mappings. |
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第8週 |
4/12,4/14 |
4/12: Review.
4/14: Midterm exam I (Ch.1, Ch.3: 3.1-3.3, 3.7, A1 in 2 variables). |
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第9週 |
4/19,4/21 |
4/19: Discussion on Exam. 3.3 Dependent functions.
4/21: 3.3 Solving inverse map by iterations. 3.4 Applications. |
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第10週 |
4/26,4/28 |
4/26: 4.1-4.4 Area, double integrals and Integrals in higher dimensions.
4/28: 4.5 Repeated integrals.
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第11週 |
5/03,5/05 |
5/03: 4.6 Change of variable formula.
5/05: 4.8-4.9 Applications. |
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第12週 |
5/10,5/12 |
5/10: 4.7 Improper multiple integrals.
5/12: 4.10 Integrals in curvilinear coordinates.
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第13週 |
5/17,5/19 |
5/17: 4.11 Higher dimensional integrals.
5/19: 4.12 Improper integrals with a parameter.
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第14週 |
5/24,5/26 |
5/24: 5.1-5.3 Green's theorem.
5/26: 5.4-5.6 Applications and interpretations by flows. |
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第15週 |
5/31,6/02 |
5/31: 5.7-5.8 Orientation of surfaces and surface integrals.
6/02: 5.9 Gauss's theorem in space. |
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第16週 |
6/07,6/09 |
6/07: 5.10 Stokes's theorem in space.
6/09: 5.11 Higher dimensions. |
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第17週 |
6/14,6/16 |
6/14: Review.
6/16: Final exam (Ch.5). |
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