課程資訊
課程名稱
微積分甲下
Calculus (general Mathematics) (a)(2) 
開課學期
101-2 
授課對象
化學工程學系  
授課教師
莊正良 
課號
MATH1202 
課程識別碼
201 101A2 
班次
09 
學分
全/半年
全年 
必/選修
必修 
上課時間
星期三7,8,9(14:20~17:20)星期五1,2(8:10~10:00) 
上課地點
新303新303 
備註
統一教學.大二以上限20人.三9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:100人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1012chuang 
課程簡介影片
 
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課程概述

[12.1] Sigma Notation.
[12.2] Infinite Series.
[12.3] The Integral Test; Basic Comparison, Limit Comparison.
[12.4] The Root Test; The Ratio Test.
[12.5] Absolute and Conditional Convergence; Alternating Series.
[12.6] Taylor Polynomials in x; Taylor Series in x.
[12.7] Taylor Polynomials and Taylor Series in x–a.
[12.8] Power Series.
[12.9] Differentiation and Integration of Power Series.
[13.3] The Dot Product.
[13.4] The Cross Product.
[13.5] Lines.
[13.6] Planes.
[13.7] Higher Dimensions.
[14.1] Limit, Continuity, Vector Derivative.
[14.2] The Rules of Differentiation.
[14.3] Curves.
[14.4] Arc Length.
[14.5] Curvilinear Motion; Curvature.
[14.6] Vector Calculus in Mechanics.
[15.1] Elementary Examples.
[15.3] Graphs; Level Curves and Level Surfaces.
[15.4] Partial Derivatives.
[15.5] Open Sets and Closed Sets.
[15.6] Limits and Continuity; Equality of Mixed Partials.
[16.1] Differentiability and Gradient.
[16.2] Gradients and Directional Derivatives.
[16.3] The Mean-Value Theorem; the Chain Rule.
[16.4] The Gradient as a Normal; Tangent Lines and Tangent Planes.
[16.5] Local Extreme Values.
[16.6] Absolute Extreme Values.
[16.7] Maxima and Minima with Side Conditions.
[16.8] Differentials.
[16.9] Reconstructing a Function from Its Gradient.
[17.1] Multiple-Sigma Notation.
[17.2] Double Integrals.
[17.3] The Evaluation of Double Integrals by Repeated Integrals.
[17.4] The Double Integral as the Limit or Riemann Sums; Polar Coordinates.
[17.5] Further Applications of Double Integration.
[17.6] Triple Integrals.
[17.7] Reduction to Repeated Integrals.
[17.8] Cylindrical Coordinates.
[17.9] The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates.
[17.10] Jacobians; Changing Variables in Multiple Integration.
[18.1] Line Integrals.
[18.2] The Fundamental Theorem for Line Integrals.
[18.3] Work-Energy Formula; Conservation of Mechanical Energy.
[18.4] Another Notation for Line Integrals; Line Integrals with Respect to Arc Length.
[18.5] Green’s Theorem.
[18.6] Parametrized Surfaces; Surface Area.
[18.7] Surface Integrals.
[18.8] The Vector Differential Operator .
[18.9] The Divergence Theorem.
[18.10] Stokes’s Theorem.
 

課程目標
Please see 統一教學網站.  
課程要求
High School Mathematics  
預期每週課後學習時數
 
Office Hours
備註: Please see 統一教學網站.  
參考書目
James Stewart, Calculus Early Transcendentals, 6th edition.  
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
40% 
 
2. 
期末考 
40% 
 
3. 
平時成績 
20% 
小考、實習課表現 
 
課程進度
週次
日期
單元主題
第1週
2/20,2/22  12.1~12.5 
第2週
2/27,3/01  12.6~12.9 
第3週
3/06,3/08  13.3~13.7 
第4週
3/13,3/15  14.1~14.4 [Quiz 1] 3/13 12.1~12.9 
第5週
3/20,3/22  14.5~14.6 
第6週
3/27,3/29  15.1~15.6 [Quiz 2] 3/27 13.3~14.6 
第7週
4/03,4/05  (Holiday) 
第8週
4/10,4/12  16.1~16.3 
第9週
4/17,4/19  16.4 [Quiz 3] 4/17 15.1~16.3 
第10週
4/24,4/26  16.5~16.9 [Midterm] 4/27 12.1~16.3 
第11週
5/01,5/03  17.1~17.3 
第12週
5/08,5/10  17.4~17.7  
第13週
5/15,5/17  17.8~18.1 [Quiz 4] 5/15 16.4~16.9 
第14週
5/22,5/24  18.2~18.3 [Quiz 5] 5/22 17.1~17.10 
第15週
5/29,5/31  18.4~18.6 
第16週
6/05,6/07  18.7~18.10 [Quiz 6] 6/5 18.1~18.5 
第17週
6/12,6/14  Buffer time. [Final] 6/16 16.4~18.10