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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
103-1 |
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授課對象 |
物理學系 |
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授課教師 |
李白飛 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
05 |
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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 |
星期一9(16:30~17:20)星期二5,6(12:20~14:10)星期四7,8(14:20~16:20) |
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上課地點 |
新505新303新303 |
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備註 |
一9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/1031MATH1201_05 |
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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. Limits and Continuity
2. Differentiation
3. Applications of Derivatives
4. Integration
5. Applications of Definite Integrals.
6. Integrals and Transcendental Functions
7. Techniques of Integration
8. Infinite Series.
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課程目標 |
After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus. |
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課程要求 |
High School Mathematics
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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 |
Thomas, Weir and Hass, Thomas' Calculus, Early Transcendentals. 12th ed. |
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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. |
Midterm Examination |
40% |
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2. |
Final Examination |
40% |
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3. |
Quiz |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/15,9/16,9/18 |
Sequences. Limit and Limit Laws. Limit of a Function. |
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第2週 |
9/22,9/23,9/25 |
One-Sided Limits. Continuity. Limits Involving Infinity. |
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第3週 |
9/29,9/30,10/02 |
Derivatives. Differential Rules. Derivatives of Trigonometric Functions.
Chain Rule. Implicit Differentiation.
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第4週 |
10/06,10/07,10/09 |
Derivatives of Inverse Functions. Inverse Trigonometric Functions. Related Rates. Linearization. Extreme Values of Functions. |
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第5週 |
10/13,10/14,10/16 |
Quiz 1. Mean Value Theorem. Monotonic Functions and the First Derivative Test. Concavity. Asymptotes of Graphs. Curve Sketching. |
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第6週 |
10/20,10/21,10/23 |
Inderterminate Forms and L'Hopital's Rule. Taylor Expansion with Remainder. Applied Optimation. |
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第7週 |
10/27,10/28,10/30 |
Definite Integral. |
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第8週 |
11/03,11/04,11/06 |
Quiz 2. Riemann Sums. Fundamental Theorem of Calculus. Indefinite Integrals. Natural Logarithm. |
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第9週 |
11/10,11/11,11/13 |
Logarithm and Exponential. Midterm Examination. |
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第10週 |
11/17,11/18,11/20 |
More on Indeterminate Forms. Integration by Substitution. Integration by Parts. Integration of Rational Functions. |
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第11週 |
11/24,11/25,11/27 |
Integration by Rationalization. |
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第12週 |
12/01,12/02,12/04 |
Quiz 3. Numerical Integration. More on Polynomial Approximation. |
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第13週 |
12/08,12/09,12/11 |
Volumes. Arc Length. Areas of Surfaces of Revolution. Moments and Center of Mass. Centroid. |
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第14週 |
12/15,12/16,12/18 |
Parametrization of Plane Curves. Calculus with Parametric Curves. Polar Coordinates. |
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第15週 |
12/22,12/23,12/25 |
Quiz 4. Graphing in polar Coordinates. Areas and Arc Length in Polar Coordinates. Conic Sections. Conics in Polar Coordinates. |
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第16週 |
12/29,12/30 |
Classification of Curves Defined by Quadratic Forms. |
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第17週 |
1/05,1/06,1/08 |
Quiz 5. More on Conic Sections and Polar Curves. |
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