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
 電機工程學系  
授課教師
 蔡雅如 
課號
 MATH1202 
課程識別碼
 201 101A2 
班次
 01 
學分
 4 
全/半年
 全年 
必/選修
 必修 
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) 
上課地點
 新102新102新102 
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 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1012cal_a1 
課程簡介影片
 
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課程概述

11. Infinite Sequences and Series
13. Vector Functions
14. Partial Derivatives
15. Multiple Integrals
16. Vector Calculus (which includes Green's Theorem, Stokes' Theorem and the Divergence Theorem) 

課程目標
 After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus.  
課程要求
 High School Mathematics 
預期每週課後學習時數
  
Office Hours
  
指定閱讀
  
參考書目
 James Stewart, Calculus Early Transcendentals, 6th edition.  
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/18,2/20,2/22  [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.
 
第2週
 2/25,2/27,3/01  [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. 
第3週
 3/04,3/06,3/08  [12.9] Differentiation and Integration of Power Series.
[13.3] The Dot Product.
[13.4] The Cross Product. 
第4週
 3/11,3/13,3/15  Quiz 1, [13.5] Lines.
[13.6] Planes.
[13.7] Higher Dimensions.
[14.1] Limit, Continuity, Vector Derivative.
[14.2] The Rules of Differentiation. 
第5週
 3/18,3/20,3/22  [14.3] Curves.
[14.4] Arc Length.
[14.5] Curvilinear Motion; Curvature.
＊[14.6] Vector Calculus in Mechanics.(Optional) 
第6週
 3/25,3/27,3/29  [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. 
第7週
 4/01,4/03,4/05  Holiday (Spring break) 
第8週
 4/08,4/10,4/12  [16.1] Differentiability and Gradient.
[16.2] Gradients and Directional Derivatives.
[16.3] The Mean-Value Theorem; the Chain Rule. 
第9週
 4/15,4/17,4/19  Quiz 2, [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. 
第10週
 4/22,4/24,4/26  [16.8] Differentials.
[16.9] Reconstructing a Function from Its Gradient.

4/27(六) 13:30~16:00期中考 考試範圍 12.1~16.9 not including 14.6 (英文命題). 
第11週
 4/29,5/01,5/03  [17.1] Multiple-Sigma Notation.
[17.2] Double Integrals.
[17.3] The Evaluation of Double Integrals by Repeated Integrals. 
第12週
 5/06,5/08,5/10  [17.4] The Double Integral as the Limit of Riemann Sums; Polar Coordinates.
[17.5] Further Applications of Double Integration.
[17.6] Triple Integrals.
[17.7] Reduction to Repeated Integrals. 
第13週
 5/13,5/15,5/17  [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. 
第14週
 5/20,5/22,5/24  Quiz 3,[18.1] Line Integrals.
[18.2] The Fundamental Theorem for Line Integrals.
＊[18.3] Work-Energy Formula; Conservation of Mechanical Energy. (Optional) 
第15週
 5/27,5/29,5/31  [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. 
第16週
 6/03,6/05,6/07  [18.7] Surface Integrals.
[18.8] The Vector Differential Operator .
[18.9] The Divergence Theorem.
[18.10] Stokes’s Theorem. 
第17週
 6/10,6/12,6/14  Quiz 4,
6/15(六) 13:30~16:00期末考 考試範圍 17.1~18.10 not including 18.3 (英文命題).