課程大綱

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

機械工程學系

授課教師

陳厚伊

課號

MATH1202

課程識別碼

201 101A2

班次

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304新304

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/1012MATH1202_07

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課程概述

☆上課時間：07-10 班三 78 五 12 、實習課時間：三 9。
11 班二 78 四 56 、實習課時間：二 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。

課程目標

Reference material ( textbook(s) )：
Calculus: One And Several Variables, tenth edition.

課程要求

Course prerequisite：
High School Mathematics

預期每週課後學習時數

Office Hours

指定閱讀

Reference material ( textbook(s) )：
Calculus: One And Several Variables, tenth edition.

參考書目

Reference material ( textbook(s) )：
Calculus: One And Several Variables, tenth edition.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	平時成績	20%
2.	期中考	40%
3.	期末考	40%

課程進度

週次	日期	單元主題
第1週	2/20,2/22	[12.1] Sigma Notation.<br> [12.2] Infinite Series.<br> [12.3] The Integral Test; Basic Comparison, Limit Comparison.<br> [12.4] The Root Test; The Ratio Test.<br> [12.5] Absolute and Conditional Convergence; Alternating Series.
第2週	2/27,3/01	[12.6] Taylor Polynomials in x; Taylor Series in x.<br> [12.7] Taylor Polynomials and Taylor Series in x–a.<br> [12.8] Power Series.<br> [12.9] Differentiation and Integration of Power Series.
第3週	3/06,3/08	[13.3] The Dot Product.<br> [13.4] The Cross Product.<br> [13.5] Lines.<br> [13.6] Planes.<br> [13.7] Higher Dimensions.
第4週	3/13,3/15	[14.1] Limit, Continuity, Vector Derivative.<br> [14.2] The Rules of Differentiation.<br> [14.3] Curves.<br> [14.4] Arc Length.
第5週	3/20,3/22	[14.5] Curvilinear Motion; Curvature.<br> [14.6] Vector Calculus in Mechanics.
第6週	3/27,3/29	[15.1] Elementary Examples.<br> [15.3] Graphs; Level Curves and Level Surfaces.<br> [15.4] Partial Derivatives.<br> [15.5] Open Sets and Closed Sets.<br> [15.6] Limits and Continuity; Equality of Mixed Partials.
第7週	4/03,4/05	Holiday
第8週	4/10,4/12	[16.1] Differentiability and Gradient.<br> [16.2] Gradients and Directional Derivatives.<br> [16.3] The Mean-Value Theorem; the Chain Rule.
第9週	4/17,4/19	[16.4] The Gradient as a Normal; Tangent Lines and Tangent Planes.<br> [16.5] Local Extreme Values.<br> [16.6] Absolute Extreme Values.<br> [16.7] Maxima and Minima with Side Conditions.
第10週	4/24,4/26	[16.8] Differentials.<br> [16.9] Reconstructing a Function from Its Gradient.<br> 4/27(六) 13:30 ~ 16:00期中考考試範圍 12.1~16.3 (英文命題).
第11週	5/01,5/03	[17.1] Multiple-Sigma Notation.<br> [17.2] Double Integrals.<br> [17.3] The Evaluation of Double Integrals by Repeated Integrals.
第12週	5/08,5/10	[17.4] The Double Integral as the Limit or Riemann Sums; Polar Coordinates.<br> [17.5] Further Applications of Double Integration.<br> [17.6] Triple Integrals.<br> [17.7] Reduction to Repeated Integrals.
第13週	5/15,5/17	[17.8] Cylindrical Coordinates.<br> [17.9] The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates.<br> [17.10] Jacobians; Changing Variables in Multiple Integration.<br> [18.1] Line Integrals.
第14週	5/22,5/24	[18.2] The Fundamental Theorem for Line Integrals.<br> [18.3] Work-Energy Formula; Conservation of Mechanical Energy.
第15週	5/29,5/31	[18.4] Another Notation for Line Integrals; Line Integrals with Respect to Arc Length.<br> [18.5] Green’s Theorem.<br> [18.6] Parametrized Surfaces; Surface Area.
第16週	6/05,6/07	[18.7] Surface Integrals.<br> [18.8] The Vector Differential Operator.<br> [18.9] The Divergence Theorem.<br> [18.10] Stokes’s Theorem.
第17週	6/12,6/14	Holiday<br> Buffer time <br> 暫定6/15(六) 09:00~11:30期末考考試範圍 16.4~18.10 (英文命題).