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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 |
土木工程學系 |
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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 |
12 |
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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 |
星期二7,8,9(14:20~17:20)星期四5,6(12:20~14:10) |
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上課地點 |
新203新203 |
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備註 |
統一教學.二9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/1001CalAChu |
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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 |
課程大鋼
1. Functions and Models
2. Limit and Deriatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integral
6. Applications of Integration
7. Techniques of Integraion
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates
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課程目標 |
讓學生了解微積分的理論, 計算與應用
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課程要求 |
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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, Author: Robert A. Adams & Christopher Essex. Pearson Canada,Toronto
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指定閱讀 |
微積分統一教學網站:
www.math.ntu.edu.tw/~mathcal
課程教材網頁:
www.math.ntu.edu.tw/~hchu/Calculus |
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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. |
習題課與小考 |
20% |
各班助教給分 |
2. |
期中考 |
40% |
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3. |
期末考 |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
09/13,09/15 |
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 |
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第2週 |
09/20,09/21 |
1.5 The Formal Definition of Limit; <br>
2.1 Tangent Lines and Their Slopes; <br>
2.2 The Derivative; <br>
2.3 Differentiation Rules |
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第3週 |
9/27,9/29 |
2.4 The Chain Rule; <br>
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 |
10/04,10/06 |
2.9 Implicit Differentiation; <br>
2.10 Antiderivatives and Initial-Value Problems; <br>
2.11 Velocity and Acceleration; <br>
緩衝時間 |
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第5週 |
10/11,10/13 |
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 |
10/18,10/20 |
3.5 The Inverse Trigonometric Functions; <br>
3.6 Hyperbolic Functions; <br>
4.1 Related Rates |
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第7週 |
10/25,10/27 |
4.2 Finding Roots of Equations; <br>
4.3 Indeterminate Forms; <br>
4.4 Extreme Values; <br>
4.5 Concavity and Inflections |
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第8週 |
11/01,11/03 |
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 |
11/08,11/10 |
4.10 Taylor Polynomials; <br>
4.11 Roundoff Error, Truncation Error, and Computers（※）; <br>
緩衝時間; <br>
11/12(六) 09:00∼11:30 期中考考試範圍 1.1∼4.10 (英文命題) |
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第10週 |
11/15,11/17 |
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 |
11/22,11/24 |
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 |
11/29,12/01 |
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 |
12/06,12/08 |
6.6 The Trapezoid and Midpoint Rules; <br>
6.7 Simpson's Rule; <br>
6.8 Other Aspects of Approximate Integration; <br>
緩衝時間 |
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第14週 |
12/13,12/15 |
7.1 Volumes by Slicing ─ Solids of Revolution; <br>
7.2 More Volumes by Slicing; <br>
7.3 Arc Length and Surface Area |
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第15週 |
12/20,12/22 |
7.4 Mass, Moments, and Centre of Mass; <br>
7.5 Centroids（※）; <br>
7.6 Other Physical Applications（※）; <br>
7.7 Applications in Business, Finance, and Ecology（※）; <br>
7.8 Probability（※）; <br>
7.9 First-Order Differential Equations |
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第16週 |
12/27,12/29 |
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 |
1/03,1/05 |
8.5 Polar Coordinates and Polar Curves; <br>
8.6 Slopes, Areas, and Arc Lengths for Polar Curves; <br>
緩衝時間; <br>
1/7(六) 09:00∼11:30 期末考考試範圍 5.1∼8.6 (英文命題) |
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