課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
103-1 
授課對象
生物機電工程學系  
授課教師
曾琇瑱 
課號
MATH1201 
課程識別碼
201 101A1 
班次
14 
學分
全/半年
全年 
必/選修
必修 
上課時間
星期一5,6(12:20~14:10)星期五1,2(8:10~10:00) 
上課地點
新203新204 
備註
大二以上限20人.
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/1031MATH1201_14 
課程簡介影片
 
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課程概述

1.Functions and its properties(Exponential functions, inverse functions, and logarithms)

2.The tangent and velocity problems, the limit of a function, calculating limits using the limits laws, the precise definition of a limit

3.Continuity, limits at infinity; horizontal asymptotes

4.Derivatives and rates of change, the derivative as a function, derivatives of polynomials and exponential functions, the product and quotient rules

5.Derivatives of trigonometric functions, the chain rule, Implicit differentiation

6.Derivatives of logarithmic functions, rates of change in the natural and social science, related rates

7. Linear approximations and differentials, hyperbolic functions

8.Maximum and minimum values,the mean value theorem, how derivatives affect the shape of a graph

9.Indeterminate forms and L’Hospital’s rule, summary of curve sketching, Graphing with calculus

10.Optimization problems, Newton’s method, antiderivatives

11.Areas and distances, the definite integral, the fundamental theorem of calculus

12.Indefinite integrals and the net change theorem, the substitution rule

13.Areas between curves, Volumes, Volumes by cylindrical shells

14.Work, average value of a function, Integration by parts

15.Trigonometric integrals, trigonometric substitution

16.Integration of rational functions by partial fractions, strategy for integration, integration using tables

17.Approximate integration, improper integrals 

課程目標
To understand the fundamental skills and theory of finding the derivatives of functions and finding the integrations of functions 
課程要求
同學必須帶筆和雙面空白的A4紙。 
Office Hours
備註: 星期一上課前或上課後。 
參考書目
Stewart 6th Edition 
指定閱讀
Calculus 4e Adoptation Edition

by Robert T. Smith and Roland B. Minton 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
第一次測驗 
20% 
 
2. 
第二次測驗 
30% 
 
3. 
第三次測驗 
25% 
 
4. 
第四次測驗 
25% 
 
 
課程進度
週次
日期
單元主題
第1週
9/15,9/19  Graphing Calculators and Computer Algebra Systems. Trigonometric Functions 
第2週
9/22,9/26  Transformations of Functions The concept of Limit 
第3週
9/29,10/03  Continuity 
第4週
10/06,10/10  Asymptotes Formal Definition of the Limit 
第5週
10/13,10/17  The derivative 
第6週
10/20,10/24  Computation of Derivatives 
第7週
10/27,10/31  The Chain Rule 
第8週
11/03,11/07  Implicit Differentiation The Mean Value Theorem 
第9週
11/10,11/14  Applications of Differentiation (I) 
第10週
11/17,11/21  Applications of Differentiation (II) 
第11週
11/24,11/28  Integration (I) 
第12週
12/01,12/05  Integration (II) 
第13週
12/08,12/12  Computation of Integration 
第14週
12/15,12/19  Applications of the Definite Integral (I) 
第15週
12/22,12/26  Applications of the Definite Integral (II) 
第16週
12/29,1/02  Transcendental Functions (I) 
第17週
1/05,1/09  Transcendental Functions (II)