課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
106-1 
授課對象
地理環境資源學系  
授課教師
劉瓊如 
課號
MATH1201 
課程識別碼
201 101A1 
班次
08 
學分
4.0 
全/半年
全年 
必/選修
必修 
上課時間
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) 
上課地點
新302新302 
備註
統一教學.大二以上限20人.三10為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:110人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH1201_08 
課程簡介影片
 
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課程概述

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
James Stewart, Calculus Early Transcendentals, 8th edition. (Metric version) 
指定閱讀
待補 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
平常 
20% 
作業,webwork,小考 
2. 
期中考 
40% 
11/4(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) 
3. 
期末考 
40% 
1/6(六) 09:00~11:30 考試範圍 5.1~10.6(英文命題) 
 
課程進度
週次
日期
單元主題
第1週
9/13,9/15  1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 
第2週
9/20,9/22  2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 
第3週
9/27,9/29  2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 3. Differentiation rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 
第4週
10/04,10/06  10/4 中秋節放假 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 
第5週
10/11,10/13  3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.8 Exponential Growth and Decay (✽) 3.9 Related Rates 
第6週
10/18,10/20  3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions 4. Applications of differentiation 4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 
第7週
10/25,10/27  4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and l''Hospital''s Rule 4.5 Summary of Curve Sketching 
第8週
11/01,11/03  4.7 Optimization Problems 4.9 Antiderivatives 緩衝時間 
第9週
11/08,11/10  5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 
第10週
11/15,11/17  11/15 校慶停課 6. Applications of integration 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 
第11週
11/22,11/24  6.5 Average Value of a Function 7. Techniques of integration 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 
第12週
11/29,12/01  7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 
第13週
12/06,12/08  8.1 Arc Length 8.2 Area of a Surface of Revolution 
第14週
12/13,12/15  8.1 Arc Length 10. Parametric equations and polar coordinates 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 
第15週
12/20,12/22  9.1 Modeling with Differential Equations 9.3 Separable Equations 
第16週
12/27,12/29  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 
第17週
1/03,1/05  10.4 Areas and Lengths in Polar Coordinates