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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 |
材料科學與工程學系 |
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授課教師 |
朱 樺 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
01 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期一9(16:30~17:20)星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) |
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上課地點 |
新102新102新102 |
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備註 |
統一教學.大二以上限20人.一9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：130人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031MATH1201_01 |
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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 |
上學期：單變數微積分
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates |
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課程目標 |
Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing
regular mappings with applications, and deepen the understanding of elementary functions. |
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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 |
待補 |
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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. |
期中考 |
40% |
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2. |
期末考 |
40% |
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3. |
平時成績(含小考) |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/15,9/17,9/19 |
<html>
<head>
<title>
</title>
</head>
<body>
[1.5] Exponential Functions <br>
[1.6] Inverse Functions and Logarithms <br>
[2.1] The Tangent and Velocity Problems <br>
[2.2] The Limit of a Function <br>
</body>
</html> |
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第2週 |
9/22,9/24,9/26 |
<html>
<head>
<title>
</title>
</head>
<body>
[2.3] Calculating Limits Using the Limit Laws <br>
[2.4] The Precise Definition of a Limit <br>
[2.5] Continuity <br>
[2.6] Limits at Infinity; Horizontal Asymptotes <br>
</body>
</html> |
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第3週 |
9/29,10/01,10/03 |
<html>
<head>
<title>
</title>
</head>
<body>
[2.7] Derivatives and Rates of Change <br>
[2.8] The Derivative as a Function <br>
[3.1] Derivatives of Polynomials and Exponential Functions <br>
[3.2] The Product and Quotient Rules <br>
</body>
</html> |
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第4週 |
10/06,10/08,10/10 |
<html>
<head>
<title>
</title>
</head>
<body>
[3.3] Derivatives of Trigonometric Functions <br>
[3.4] The Chain Rule <br>
10/10(五)國慶紀念日放假一天 <br>
</body>
</html> |
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第5週 |
10/13,10/15,10/17 |
<html>
<head>
<title>
</title>
</head>
<body>
[3.5] Implicit Differentiation <br>
[3.6] Derivatives of Logarithmic Functions <br>
[3.7] Rates of Change in the Natural and Social Sciences（※） <br>
[3.8] Exponential Growth and Decay <br>
[3.9] Related Rates <br>
[3.10] Linear Approximations and Differentials <br>
</body>
</html> |
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第6週 |
10/20,10/22,10/24 |
<html>
<head>
<title>
</title>
</head>
<body>
[3.11] Hyperbolic Functions <br>
[4.1] Maximum and Minimum Values <br>
緩衝時間 <br>
</body>
</html> |
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第7週 |
10/27,10/29,10/31 |
<html>
<head>
<title>
</title>
</head>
<body>
[4.2] The Mean Value Theorem <br>
[4.3] How Derivatives Affect the Shape of a Graph <br>
[4.4] Indeterminate Forms and L’Hospital’s Rule <br>
[4.5] Summary of Curve Sketching <br>
</body>
</html> |
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第8週 |
11/03,11/05,11/07 |
<html>
<head>
<title>
</title>
</head>
<body>
[4.6] Graphing with Calculus and Calculators（※） <br>
[4.7] Optimization Problems <br>
[4.8] Newton’s Method（※） <br>
[4.9] Antiderivatives <br>
緩衝時間 <br>
11/8 (六) 13:30~16:00 期中考(1.5~4.9)
</body>
</html> |
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第9週 |
11/10,11/12,11/14 |
<html>
<head>
<title>
</title>
</head>
<body>
[5.1] Areas and Distances <br>
[5.2] The Definite Integral <br>
[5.3] The Fundamental Theorem of Calculus <br>
[5.4] Indefinite Integrals and the Net Change Theorem <br>
</body>
</html> |
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第10週 |
11/17,11/19,11/21 |
<html>
<head>
<title>
</title>
</head>
<body>
[5.5] The Substitution Rule <br>
[6.1] Areas Between Curves <br>
[6.2] Volumes <br>
[6.3] Volumes by Cylindrical Shells <br>
</body>
</html> |
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第11週 |
11/24,11/26,11/28 |
<html>
<head>
<title>
</title>
</head>
<body>
[6.4] Work（※）<br>
[6.5] Average Value of a Function <br>
[7.1] Integration by Parts <br>
[7.2] Trigonometric Integrals <br>
</body>
</html> |
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第12週 |
12/01,12/03,12/05 |
<html>
<head>
<title>
</title>
</head>
<body>
[7.3] Trigonometric Substitution <br>
[7.4] Integration of Rational Functions by Partial Fractions <br>
[7.5] Strategy for Integration <br>
[7.7] Approximate Integration <br>
</body>
</html> |
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第13週 |
12/08,12/10,12/12 |
<html>
<head>
<title>
</title>
</head>
<body>
[7.8] Improper Integrals <br>
[8.1] Arc Length <br>
緩衝時間 <br>
</html> |
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第14週 |
12/15,12/17,12/19 |
<html>
<head>
<title>
</title>
</head>
<body>
[8.2] Area of a Surface of Revolution <br>
[8.3] Applications to Physics and Engineering <br>
[8.4] Applications to Economics and Biology（※）<br>
[8.5] Probability（※） <br>
[9.1] Modeling with Differential Equations <br>
</html> |
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第15週 |
12/22,12/24,12/26 |
<html>
<head>
<title>
</title>
</head>
<body>
[9.3] Separable Equations <br>
[9.4] Models for Population Growth <br>
[9.5] Linear Equations <br>
[10.1] Curves Defined by Parametric Equations <br>
</html> |
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第16週 |
12/29,12/31,1/02 |
<html>
<head>
<title>
</title>
</head>
<body>
緩衝時間 <br>
[10.2] Calculus with Parametric Curves <br>
[10.3] Polar Coordinates <br>
</html> |
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第17週 |
1/05,1/07,1/09 |
<html>
<head>
<title>
</title>
</head>
<body>
[10.4] Areas and Lengths in Polar Coordinates <br>
[10.6] Conic Sections in Polar Coordinates <br>
緩衝時間 <br>
1/10 (六) 13:30~16:00 期末考(5.1~10.6)
</html> |
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第18週 |
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餘三班投影片 |
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