課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
100-1 
授課對象
電機工程學系  
授課教師
陳君明 
課號
MATH1201 
課程識別碼
201 101A1 
班次
05 
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203新203新203 
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/1001CalculusA05 
課程簡介影片
 
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課程概述

☆上課時間:三56 五56 、 實習課時間:一9。
☆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
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 
Office Hours
 
參考書目
Calculus: A Complete Course seventh edition. 
指定閱讀
Calculus: A Complete Course seventh edition. 
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. 
作業以及小考 
20% 
作業取十次較高成績, 佔學期成績 6%. 小考取十次較高成績, 佔學期成績 12%. 習題課表現佔學期成績 2%. 
 
課程進度
週次
日期
單元主題
第1週
9/14,9/16  1.1 Examples of Velocity, Growth Rate, and Area <br> 1.2 Limit of Functions <br> 1.3 Limits at Infinity and Infinite Limits <br> 1.4 Continuity <br> 1.5 The Formal Definition of Limit 
第2週
9/19,9/21,9/23  2.1 Tangent Lines and Their Slopes <br> 2.2 The Derivative <br> 2.3 Differentiation Rules <br> 2.4 The Chain Rule 
第3週
9/26,9/28,9/30  2.5 Derivatives of Trigonometric Functions <br> 2.6 Higher-Order Derivatives <br> 2.7 Using Differentials and Derivatives <br> 2.8 The Mean-Value Theorem 
第4週
10/03,10/05,10/07  2.9 Implicit Differentiation <br> 2.10 Antiderivatives and Initial-Value Problems <br> 2.11 Velocity and Acceleration 
第5週
10/10,10/12,10/14  3.1 Inverse Functions <br> 3.2 Exponential and Logarithmic Functions <br> 3.3 The Natural Logarithm and Exponential <br> 3.4 Growth and Decay 
第6週
10/17,10/19,10/21  3.5 The Inverse Trigonometric Functions <br> 3.6 Hyperbolic Functions <br> 4.1 Related Rates <br> 4.2 Finding Roots of Equations 
第7週
10/24,10/26,10/28  4.3 Indeterminate Forms <br> 4.4 Extreme Values <br> 4.5 Concavity and Inflections 
第8週
10/31,11/02,11/04  4.6 Sketching the Graph of a Function <br> 4.7 Graphing with Computers(※) <br> 4.8 Extreme-Value Problems <br> 4.9 Linear Approximations 
第9週
11/07,11/09,11/11  4.10 Taylor Polynomials <br> 4.11 Roundoff Error, Truncation Error, and Computers(※) <br> 11/12(&#63953;) 13:30∼16:00 期中考 考試範圍 1.1∼4.10 
第10週
11/14,11/16,11/18  5.1 Sums and Sigma Notation <br> 5.2 Areas as Limits of Sums <br> 5.3 Definite Integral <br> 5.4 Properties of the Definite Integral 
第11週
11/21,11/23,11/25  5.5 The Fundamental Theorem of Calculus <br> 5.6 The Method of Substitution <br> 5.7 Areas of Plane Regions <br> 6.1 Integration by Parts 
第12週
11/28,11/30,12/02  6.2 Integrals of Rational Functions <br> 6.3 Inverse Substitutions <br> 6.4 Other Methods for Evaluating Integrals <br> 6.5 Improper Integrals 
第13週
12/05,12/07,12/09  6.6 The Trapezoid and Midpoint Rules <br> 6.7 Simpson's Rule <br> 6.8 Other Aspects of Approximate Integration <br> 7.1 Volumes by Slicing ─ Solids of Revolution 
第14週
12/12,12/14,12/16  7.2 More Volumes by Slicing <br> 7.3 Arc Length and Surface Area <br> 7.4 Mass, Moments, and Centre of Mass <br> 7.5 Centroids 
第15週
12/19,12/21,12/23  7.6 Other Physical Applications <br> 7.7 Applications in Business, Finance, and Ecology <br> 7.8 Probability 
第16週
12/26,12/28,12/30  8.1 Conics(※) <br> 8.2 Parametric Curves <br> 8.3 Smooth Parametric Curves and Their Slopes <br> 8.4 Arc Lengths and Areas for Parametric Curves 
第17週
1/02,1/04,1/06  8.5 Polar Coordinates and Polar Curves <br> 8.6 Slopes, Areas, and Arc Lengths for Polar Curves <br> 1/11(三) 13:20∼15:20 期末考 考試範圍 5.1∼8.6