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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 |
96-1 |
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授課對象 |
機械工程學系 |
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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 |
08 |
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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 |
星期一5(12:20~13:10)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，限機械、材料等系學生修習
限本系所學生(含輔系、雙修生)
總人數上限：230人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/961Calculus |
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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 |
單變數微積分 |
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課程目標 |
(1) Limits and Continuity。
(2) Derivatives with Applications。
(3) Integration with Applications。
(4) Transcendental Functions。
(5) Integration Techniques and Improper Integrals。
(6) First rder Linear Differential Equation。
(7) Area and Lengths in Polar Coordinates |
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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 |
另約時間 |
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參考書目 |
Thomas' Calculus Early Transcendentals, 11th edition by Weir, Hass and Giordano |
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指定閱讀 |
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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. |
隨堂測驗 |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/17,9/19,9/21 |
1.5 Exponential Functions ;
1.6 Inverse Functions and Logarithms ;
2.1 Rates of Change and Limits ;
2.2 Calculating Limits Using the Limit Laws |
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第2週 |
9/24,9/26,9/28 |
2.3 The Precise Definition of a Limit ;
2.4 One-Sided Limits and Limits at Infinity |
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第3週 |
10/01,10/03,10/05 |
2.5 Infinite Limits and Vertical Asymptotes ;
2.6 Continuity ;
2.7 Tangents and Derivatives ;
3.1 The Derivative as a Function |
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第4週 |
10/08,10/10,10/12 |
3.2 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients ;
3.3 The Derivative as a Rate of Change |
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第5週 |
10/15,10/17,10/19 |
3.4 Derivatives of Trigonometric Functions ;
3.5 The Chain Rule and Parametric Equations ;
3.6 Implicit Differentiation ;
3.7 Derivatives of Inverse Functions and Logarithms |
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第6週 |
10/22,10/24,10/26 |
3.8 Inverse Trigonometric Functions ;
3.9 Related Rates ;
3.10 Linearization and Differentials ;
4.1 Extreme Values of Functions ;
4.2 The Mean Value Theorem |
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第7週 |
10/29,10/31,11/02 |
4.3 Monotonic Functions and the First Derivative Test ;
4.4 Concavity and Curve Sketching ;
4.5 Applied Optimization Problems |
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第8週 |
11/05,11/07,11/09 |
4.6 Indeterminate Forms and L' Hopital's Rule ;
4.7 Newton's Method ;
4.8 Antiderivatives |
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第9週 |
11/12,11/14,11/16 |
5.1 Estimating with Finite Sums ;
5.2 Sigma Notation and Limits of Finite Sums |
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第10週 |
11/19,11/21,11/23 |
5.3 The Definite Integral ;
5.4 The Fundamental Theorem of Calculus ;
5.5 Indefinite Integrals and the Substitution Rule ;
5.6 Substitution and Area Between Curves ; |
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第11週 |
11/26,11/28,11/30 |
6.1 Volumes by Slicing and Rotation About an Axis ;
6.2 Volumes by Cylindrical Shells ;
6.3 Lengths of Plane Curves ;
6.4 Moments and Centers of Mass ;
6.5 Areas of Surfaces of Revolution and the Theorems of Pappus |
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第12週 |
12/03,12/05,12/07 |
7.1 The Logarithm Defined as an Integral ;
7.2 Exponential Growth and Decay ;
7.3 Relative Rates of Growth ;
7.4 Hyperbolic Functions |
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第13週 |
12/10,12/12,12/14 |
8.1 Basic Integration Formulas ;
8.2 Integration by Parts ;
8.3 Integration of Rational Functions by Partial Frations |
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第14週 |
12/17,12/19,12/21 |
8.4 Trigonometirc Integrals ;
8.5 Trigonometirc Substitutions ;
8.7 Numerical Integration |
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第15週 |
12/24,12/26,12/28 |
8.8 Improper Integrals ;
9.1 Slope Fields and Separable Differential Equations ;
9.2 First-Order Linear Differential Equations ;
9.5 Applications of First-Order Differential Equations |
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第16週 |
12/31,1/02,1/04 |
10.4 Conics and Parametric Equations；The Cycloid ;
10.5 Polar Coordinates |
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第17週 |
1/07,1/09,1/11 |
10.6 Graphing in Polar Coordinates ;
10.7 Areas and Lengths in Polar Coordinates |
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