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
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
15 
學分
全/半年
全年 
必/選修
必帶 
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203 
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/1001cal_15 
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
無 
Office Hours
 
參考書目
Stewart 5th Edition 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
測驗 
90% 
第一次佔35%,第一次佔20%,第一次佔35% 
2. 
出席 
10% 
 
 
課程進度
週次
日期
單元主題
第1週
9/16  functions 
第2週
9/19,9/23  limits 
第3週
9/26,9/30  continuity 
第4週
10/03,10/07  derivatives 
第5週
10/10,10/14  extrema 
第6週
10/17,10/21  graphs 
第7週
10/24,10/28  curve sketch 
第8週
10/31,11/04  exam and reviews 
第9週
11/07,11/11  indefinite integrals 
第10週
11/14,11/18  definite integrals 
第11週
11/21,11/25  area and volumes 
第12週
11/28,12/02  exam transcendental functions 
第13週
12/05,12/09  calculus of transcendental functions 
第14週
12/12,12/16  L'hospital's rule and techniques of integrations 
第15週
12/19,12/23  techniques of integrations 
第16週
12/26,12/30  improper integrals 
第17週
1/02,1/06  reviews