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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 |
98-2 |
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授課對象 |
數學系 |
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授課教師 |
李白飛 |
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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.兼通識A6。
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/982phlee |
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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 |
1. Infinite Series. 2. Vector Functions. 3. Partial Differentiation. 4. Multiple Integration. 5. Line and Surface Integrals. |
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課程目標 |
A relatively rigorous introduction of infinite series and calculus of functions of several variables and their applications to geometry and physics. |
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課程要求 |
Calculus (A) 1. |
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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 |
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參考書目 |
Robert A. Adams, Calculus, A Complete Course. 6th ed. |
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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. |
Mid-term Examination |
40% |
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2. |
Final Examination |
40% |
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3. |
Biweekly Quiz |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/23,2/25 |
Sequences and Convergence. |
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第2週 |
3/02,3/04 |
Infinite Series. Convergence Tests for positive Series. Absolute and Conditional Convergence. |
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第3週 |
3/09,3/11 |
Power Series. Taylor and MacLaurin Series. Binomial Series.
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第4週 |
3/16,3/18 |
Application of Taylor and MacLaurin Series. Improper Integrals.
註：小考一 |
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第5週 |
3/23,3/25 |
Cross Product. Vector Functions. Curves and Parametrizations. |
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第6週 |
3/30,4/01 |
Curvature. Functions of Several Variables. Limit and Continuity. Partial Derivatives. Directional Derivatives.
註：小考二 |
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第7週 |
4/06,4/08 |
Spring Break. Differentiability. Linear Approximations. Chain Rule. Tangent Planes. |
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第8週 |
4/13,4/15 |
Gradients. Implicit Differentiation. Higher-Order Derivatives. Taylor Polynomials and Approximations.
註：小考三 |
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第9週 |
4/20,4/22 |
Extrema Values. Lagrange Multipliers. |
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第10週 |
4/27,4/29 |
Critical Points. Second Derivative Test. Mid-term Examination. |
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第11週 |
5/04,5/06 |
Double Integrals. |
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第12週 |
5/11,5/13 |
Integralability of Contimuous Functions. Change of Variables.
註：小考四 |
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第13週 |
5/18,5/20 |
Triple Integrals. Cylindrical and Spherical Coordinates. |
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第14週 |
5/25,5/27 |
Applications of Multiple Integrals. Line Integrals. Green's Theorem.
註：小考五 |
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第15週 |
6/01,6/03 |
Surface Integrals. Divergence Theorem. |
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第16週 |
6/08,6/10 |
Stokes' Theorem, Differential Equations of First Order.
註：小考六 |
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第17週 |
6/15,6/17 |
Linear Differential Equations of Second Order. Series Solutions of Differential Equations. |
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