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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 |
101-1 |
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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 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
06 |
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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/1011phlee |
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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.Transcendental Functions 6.Techniques of
Integration 7. Applications of Integration 8. Parametric Curves and Polar Curves. |
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課程目標 |
A relatively rigorous introduction of differentiation and integration of functions of a single variable and some applications to geometry and
physics. |
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課程要求 |
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Office Hours |
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參考書目 |
E. Landau：Foundation of Analysis.
T. Apostol : Calculus, Vol.1.
曹亮吉等 微積分 |
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指定閱讀 |
R.A.Adams: Calculus, a Complete Course, 7th 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 |
40% |
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2. |
Final Examination |
40% |
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3. |
Quizzes |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/11,9/13 |
Sequences and Convergence. Limits of Functions. One-Sided Limits. Limits at Infinity. Infinite Limits. |
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第2週 |
9/18,9/20 |
Continuity. Complete Axiom. The Max-Min Theorem. The
Intermiate-Value Theorem. The Derivative. Differential Rules. |
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第3週 |
9/25,9/27 |
The Chain Rule. Derivatives of Trigonometric Functions. Higher-Order derivatives. Implicit
Differentiation. |
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第4週 |
10/02,10/04 |
The Mean Value Theorem. Increasing and Decreasing Functions. Extreme Values. Concativity and Inflections. Quiz 1. |
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第5週 |
10/09,10/11 |
Asymptotes. Sketching the Graph of a Function. Related Rates. Extreme-Value Problems. Using Differentials and
Derivatives. Linear Approximations. Definite Integrals. |
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第6週 |
10/16,10/18 |
Properties of the Definite Integral. |
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第7週 |
10/23,10/25 |
Fundamental Theorem of Calculus. Integrability of Continuous Functions. Riemann Sums. Inverse Functions. Quiz 2. |
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第8週 |
10/30,11/01 |
The Natural Logarithm and Exponential. Exponential and Logarithmic Functions. The Inverse Trigonometric Functions. The Method of Substitution. |
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第9週 |
11/06,11/08 |
Integration by Parts. Reduction Formulas. Midterm Examination. |
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第10週 |
11/13 |
Integration of Rational Functions. |
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第11週 |
11/20,11/22 |
Rationalization. The Trapezoid and Midpoint Rules. Simpson Rule. Quiz 3. |
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第12週 |
11/27,11/29 |
Areas of Plane Regions. Volumes by Slicing. Solid of Revolution. Arc Length and Surface Area. Mass. |
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第13週 |
12/04,12/06 |
Moments and Center of Mass. Centroid. Cauchy's Mean Value Theorem. Taylor Polynomials. Quiz 4. |
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第14週 |
12/11,12/13 |
Indeterminate Forms. Conics. Smooth Parametric Curves and Their Slopes. Arc Lengths of Parametric Curves. |
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第15週 |
12/18,12/20 |
Areas Bounded by Parametric Curves. Curves Defined by Implicit Functions. |
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第16週 |
12/25,12/27 |
Curves Defined by Quadratic Forms. Polar Coordinates and Polar Curves. Quiz 5. |
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第17週 |
1/03 |
Slopes, Areas and Arc Length for Polar Curves. |
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