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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 |
100-1 |
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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 |
陳君明 |
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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203新203新203 |
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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：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1001CalculusA05 |
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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 |
☆上課時間：三56 五56 、 實習課時間：一9。
☆各班實習課分組教室：將公告於微積分甲統一教學網站公佈。
☆微積分甲統一教學網站：http://www.math.ntu.edu.tw/~mathcal/a/ 。
☆各班助教Office Hour時間：將公告於微積分甲統一教學網站公佈。
☆習題：習題繳交與否依各授課教師規定；習題解答將於公佈於微積分甲統一教學網站。
☆期中、期末考題目以英文命題。
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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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參考書目 |
Calculus: A Complete Course seventh edition. |
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指定閱讀 |
Calculus: A Complete Course seventh edition. |
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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. |
作業以及小考 |
20% |
作業取十次較高成績, 佔學期成績 6%.
小考取十次較高成績, 佔學期成績 12%.
習題課表現佔學期成績 2%. |
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週次 |
日期 |
單元主題 |
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第1週 |
9/14,9/16 |
1.1 Examples of Velocity, Growth Rate, and Area <br>
1.2 Limit of Functions <br>
1.3 Limits at Infinity and Infinite Limits <br>
1.4 Continuity <br>
1.5 The Formal Definition of Limit |
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第2週 |
9/19,9/21,9/23 |
2.1 Tangent Lines and Their Slopes <br>
2.2 The Derivative <br>
2.3 Differentiation Rules <br>
2.4 The Chain Rule |
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第3週 |
9/26,9/28,9/30 |
2.5 Derivatives of Trigonometric Functions <br>
2.6 Higher-Order Derivatives <br>
2.7 Using Differentials and Derivatives <br>
2.8 The Mean-Value Theorem |
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第4週 |
10/03,10/05,10/07 |
2.9 Implicit Differentiation <br>
2.10 Antiderivatives and Initial-Value Problems <br>
2.11 Velocity and Acceleration |
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第5週 |
10/10,10/12,10/14 |
3.1 Inverse Functions <br>
3.2 Exponential and Logarithmic Functions <br>
3.3 The Natural Logarithm and Exponential <br>
3.4 Growth and Decay |
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第6週 |
10/17,10/19,10/21 |
3.5 The Inverse Trigonometric Functions <br>
3.6 Hyperbolic Functions <br>
4.1 Related Rates <br>
4.2 Finding Roots of Equations |
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第7週 |
10/24,10/26,10/28 |
4.3 Indeterminate Forms <br>
4.4 Extreme Values <br>
4.5 Concavity and Inflections |
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第8週 |
10/31,11/02,11/04 |
4.6 Sketching the Graph of a Function <br>
4.7 Graphing with Computers（※） <br>
4.8 Extreme-Value Problems <br>
4.9 Linear Approximations |
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第9週 |
11/07,11/09,11/11 |
4.10 Taylor Polynomials <br>
4.11 Roundoff Error, Truncation Error, and Computers（※） <br>
11/12(六) 13:30∼16:00 期中考 考試範圍 1.1∼4.10 |
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第10週 |
11/14,11/16,11/18 |
5.1 Sums and Sigma Notation <br>
5.2 Areas as Limits of Sums <br>
5.3 Definite Integral <br>
5.4 Properties of the Definite Integral |
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第11週 |
11/21,11/23,11/25 |
5.5 The Fundamental Theorem of Calculus <br>
5.6 The Method of Substitution <br>
5.7 Areas of Plane Regions <br>
6.1 Integration by Parts |
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第12週 |
11/28,11/30,12/02 |
6.2 Integrals of Rational Functions <br>
6.3 Inverse Substitutions <br>
6.4 Other Methods for Evaluating Integrals <br>
6.5 Improper Integrals |
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第13週 |
12/05,12/07,12/09 |
6.6 The Trapezoid and Midpoint Rules <br>
6.7 Simpson's Rule <br>
6.8 Other Aspects of Approximate Integration <br>
7.1 Volumes by Slicing ─ Solids of Revolution |
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第14週 |
12/12,12/14,12/16 |
7.2 More Volumes by Slicing <br>
7.3 Arc Length and Surface Area <br>
7.4 Mass, Moments, and Centre of Mass <br>
7.5 Centroids |
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第15週 |
12/19,12/21,12/23 |
7.6 Other Physical Applications <br>
7.7 Applications in Business, Finance, and Ecology <br>
7.8 Probability |
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第16週 |
12/26,12/28,12/30 |
8.1 Conics（※） <br>
8.2 Parametric Curves <br>
8.3 Smooth Parametric Curves and Their Slopes <br>
8.4 Arc Lengths and Areas for Parametric Curves |
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第17週 |
1/02,1/04,1/06 |
8.5 Polar Coordinates and Polar Curves <br>
8.6 Slopes, Areas, and Arc Lengths for Polar Curves <br>
1/11(三) 13:20∼15:20 期末考 考試範圍 5.1∼8.6 |
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