課程名稱 |
微積分甲上 CALCULUS (GENERAL MATHEMATICS) (A)(1) |
開課學期 |
98-1 |
授課對象 |
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授課教師 |
李白飛 |
課號 |
MATH1201 |
課程識別碼 |
201 101A1 |
班次 |
07 |
學分 |
4 |
全/半年 |
全年 |
必/選修 |
必修 |
上課時間 |
星期二5,6(12:20~14:10)星期四5,6,9(12:20~17:20) |
上課地點 |
新103新103 |
備註 |
四9為實習課.地點新103。可兼充通識名額3人。A6*:量化分析與數學素養領域。可充抵通識 限本系所學生(含輔系、雙修生) 總人數上限:80人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/981phlee |
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 |
1. Limits and Continuity. 2. Differentiation. 3. Transcendental Functions. 4. Applications of Differentiation. 5. Integration. 6. Techniques of Integration. 7, Applications of Integration. 8. Parametric Curves and Polar Curves. |
課程目標 |
A relatively rigorous introduction of differentiation and integration of functions of a single variable and their applications to geometry and physics. |
課程要求 |
None. |
Office Hours |
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參考書目 |
Textbook:R. A. Adams, Calculus, A complete Course. |
指定閱讀 |
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Mid-Term Examination |
40% |
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2. |
Final Examination |
40% |
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3. |
Biweekly Tests |
20% |
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週次 |
日期 |
單元主題 |
Week 1 |
9/15,9/17 |
Limits of Sequences. |
Week 2 |
9/22,9/24 |
Limits of Functions. Completeness Axiom. |
Week 3 |
9/29,10/01 |
Continuous Functions. Differentiation Rules. |
Week 4 |
10/06,10/08 |
Chain Rule. Implicit Differentiation. Related Rates. |
Week 5 |
10/13,10/15 |
Mean Value Theorem. Extreme Values. Concavity. |
Week 6 |
10/20,10/22 |
Graph Sketching. Definite Integral. |
Week 7 |
10/27,10/29 |
Properties of Definite Integral. Second Fundamental Theorem of Calculus. |
Week 8 |
11/03,11/05 |
First Fundamental Theorem of Calculus. Inverse Functions. Natural Logarithm and Exponential. |
Week 9 |
11/10,11/12 |
General Exponentials and Logarithms. Mid-Term Examination. |
Week 10 |
11/17,11/19 |
Invese Trigonometric Functions. Method of Substitution. Integration by Parts. |
Week 11 |
11/24,11/26 |
Integration of Rational Functions and Functions Reducible to Rational Functions. |
Week 12 |
12/01,12/03 |
Integration of Polynomial Functions of Trigonometric Functions. Inverse Trigonometric Substitution. Trapezoid, Midpoint and Simpson's Rules. |
Week 13 |
12/08,12/10 |
Areas, Volumes, Arc Lenhth and Surface Areas. |
Week 14 |
12/15,12/17 |
Center of Mass. Centroid. Linear Approximations. Taylor Polynomials. Indeterminate Forms. |
Week 15 |
12/22,12/24 |
More Indeterminate Forms. Parametric Curves. |
Week 16 |
12/29,12/31 |
Arc Length and Areas for Parametric Curves. Polar Curves. |
Week 17 |
1/05,1/07 |
Slopes, Areas and Arc Length for Polar Curves. Polar Conics. |
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