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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

資訊工程學系

授課教師

張鎮華

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303新103新103

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：100人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1012_Calculus_A03

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課程概述

Several variables calculus

統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/
臨時網站 https://sites.google.com/a/math.ntu.edu.tw/calculus/

課程目標

Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions.

課程要求

High School Mathematics & Calculus I.

預期每週課後學習時數

Office Hours

每週三 15:20~17:20

參考書目

Salas, Hille and Etgen, Calculus: One and Several variables, Tenth Edition,
Wiley.

指定閱讀

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	期末考	40%	6/15(六) 13:30~16:00 期末考考試範圍 16.4~18.10 (英文命題).
2.	期中考	40%	4/27(六) 09:00~11:30 期中考考試範圍 12.1~16.3 (英文命題).
3.	小考, 作業及出席率	20%	約兩至三週一次小考 ***** 作業不必繳但在週一演習課上台做

課程進度

週次	日期	單元主題
第0週	週一第9節實習週三56節上課週五56節上課	實習教室: 新生303 (學號後三碼除以3餘0), 401 (餘1), 402 (餘2) ********************* 上課教室: 新生103 ********* Office hours: 張鎮華週三78節天數館521室 ****** 許祐鴻週一56節天數館544室 ******** 蘇哲聖週五78節天數館456室 ********** 吳宜欣週四56節教研館326室
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	********3/01 Q1: [12.1]~[12.6]******** [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	[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	******** 3/16 Q2: [12.7]~[13.7] ****** [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	Holidays
第8週	4/08,4/10,4/12	******** 4/06 Q3: [14.1]~[15.6] ********** [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	[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. ******** Buffer time ****** 4/26 Q4: [16.1]~[16.9] ******** 4/27(六) 09:00~11:30 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 or 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	******** 5/11 Q5: [17.1]~[17.5] ******** [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	[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	******** 5/25 Q6: [17.6]~[17.10] ********[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	6/10 (Monday) Q7: [18.1]~[18.5] ******** 6/14 (Friday) Q8: [18.6]~[18.10] ******** 6/16 (Sunday) 13:30~16:00 期末考考試範圍 17.1~18.10 (not including 18.3 (英文命題).