課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
107-1 
授課對象
化學工程學系  
授課教師
陳子安 
課號
MATH1201 
課程識別碼
201 101A1 
班次
05 
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202新202 
備註
本課程以英語授課。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/1071Calculus_A05 
課程簡介影片
 
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課程概述

Differentiation and Integration, or, collectively, Calculus, on functions of a single variable together with their profound applications in various subject areas are introduced in this course. On differentiation, it includes the definitions of limits and continuity, techniques of differentiation, strategies in solving extreme-value problem and so on; on integration, it includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, finding areas and volumes, solving elementary differential equations and more.

Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. 

課程目標
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus A (1) and (2)" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations. 
課程要求
Students participating in the course should be already skilled in high school mathematics. They are expected to attend and participate actively in lectures as well as discussion sections. 
Office Hours
每週五 15:00~17:00 備註: The time slot shown here is the office hours of the instructor. For the office hours of our teaching assistants, see the section on contact information of teaching assistants. 
參考書目
Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.

Reference book: Maurice D. Weir and Joel Hass,
Thomas' Calculus: Early Transcendentals, 13th Edition in SI units

Website of the unified course on Calculus A:
http://www.math.ntu.edu.tw/~mathcal/a/

WeBWorK system for online exercises:
http://webwork.math.ntu.edu.tw/webwork2/1071MATH1201_05/

NTU past-papers on Calculus A:
http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7

Episte Math:
http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal

Free online Desmos Graphing Calculator:
https://www.desmos.com/calculator

Online computational knowledge engine:
https://www.wolframalpha.com 
指定閱讀
James Stewart, Calculus: Early Transcendentals, 8th Edition (course textbook) 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Mid-term exam 
35% 
Contents include materials from Sections 1.4 ~ 4.9. 
2. 
Final exam 
35% 
Contents include materials from Sections 5.1 ~ 10.4. 
3. 
Others 
30% 
Including homework assignments, WeBWork online exercises, in-class quizzes and other possible bonuses. 
 
課程進度
週次
日期
單元主題
第1週
9/12,9/14  1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 2.1 The Tangent and Velocity Problems 
第2週
9/19,9/21  2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 
第3週
9/26,9/28  2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 
第4週
10/03,10/05  3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 
第5週
10/12  ※10/10(Wed) Double Tenth Day 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.8 Exponential Growth and Decay (✽) 
第6週
10/17,10/19  3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions (✽) 4.1 Maximum and Minimum Values 
第7週
10/24,10/26  4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and l'Hospital's Rule 
第8週
10/31,11/02,11/3  4.5 Summary of Curve Sketching 4.7 Optimization Problems 4.9 Antiderivatives ※Mid-term exam 11/3(Sat) 09:00~11:30 contents: 1.4~4.9 
第9週
11/07,11/09  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
11/14,11/16  6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 
第11週
11/21,11/23  7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 
第12週
11/28,11/30  7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 
第13週
12/05,12/07  8.1 Arc Length 8.2 Area of a Surface of Revolution 
第14週
12/12,12/14  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 
第15週
12/19,12/21  10.4 Areas and Lengths in Polar Coordinates 9.1 Modeling with Differential Equations 
第16週
12/26,12/28  9.3 Separable Equations 9.4 Models for Population Growth 
第17週
1/02,1/04,1/5  9.5 Linear Equations ※Final exam 1/5(Sat) 09:00~11:30 contents: 5.1~10.4