課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
105-1 
授課對象
大氣科學系  
授課教師
崔茂培 
課號
MATH1201 
課程識別碼
201 101A1 
班次
09 
學分
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303新303 
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/1051MATH1201_09 
課程簡介影片
 
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課程大綱
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課程概述

第一學期會從極限的定義出發, 引入求導與微分的意義, 以此刻劃函數的圖形並應用到各
類生活的實際問題; 之後介紹積分的意義及應用, 而微積分基本定理將緊密連結函數求導
與積分這兩個概念。第一學期末會探討簡單的微分方程以及平面曲線。第二學期的一個主
軸是多變數微積分, 搭配一些特殊的主題如數列與級數、向量微積分等。
微積分甲05–10 班為統一教學, 班級進度一致, 期中、期末考時間與考題相同, 老師共
同開會評分。 

課程目標
熟悉微分與積分的概念並學會數學的操作。微積分是理工科系的基礎科目, 日後有助於同
學銜接工程數學及其他理論科學等科目。 
課程要求
待補 
預期每週課後學習時數
 
Office Hours
 
參考書目
其他相關資訊
微積分甲統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/
台大微甲考古題 http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7
 微積分經典範例: http://scicomp.math.ntu.edu.tw/calculus/
 數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
 免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
 免費線上數學軟體Wolfram Alpha: http://www.wolframalpha.com/ 
指定閱讀
微積分課本為 Calculus: Early Transcendentals
8th edition, 作者: James Stewart

​(用學長姊的舊版也可以,不一定要買新版,只是習題的題號跟著新版而已)
機械系的同學可以和機械系的系學會 聯絡購買.

可以跟滄海書局的 陳式政先生聯繫~電話是 0938-723-438

他們給的優惠是980元/本,50本送1本,如果持有清寒證明者可半價,這些都要直接跟陳先生連繫喔~

如果要單獨買的話,可以去學校對面的五南書局買,就1000元/本。 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
35% 
時間: 105 年11 月5 日(六) 09:00–11:30 考試範圍: 1.5–4.9 (英文命題) 
2. 
期末考 
35% 
時間: 期末考1/7(六) 13:30~16:00 考試範圍 5.1~10.6(英文命題)  
3. 
習題、小考、平時表現等 
30% 
習題: 自105 年9 月14 日起每週3交習題, 共16 次 小考: 暫定10/5, 10/26, 12/7, 12/28 實習課測驗, 約30分鐘, 共4 次 
 
課程進度
週次
日期
單元主題
第1週
9/14,9/16  1.4 Exponential Functions
1.5 Inverse Functions and Logarithms

HW1 due September 21
Sec 1.4 Problem 3, 14, 17, 21, 24, 25
Sec 1.5 Problem 13, 17, 21, 37 
第2週
9/21,9/23  2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limi

2.1.pdf, 2.2.pdf, 2.3.pdf and 2.4.pdf are lecture notes

TA-9-21-2016.pdf are problems in TA session

HW2.pdf are homework 2  
第3週
9/28,9/30  2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

Webwork HW can be found at

http://webwork.math.ntu.edu.tw/webwork2/1051MATH1201_09/

 
第4週
10/05,10/07  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

Homework 4 Due Friday, October 14, 2016 in class
(Please look at the PDF file in the homework assignment.)

Webwork Homework
3.1 open, due 10/17/2016 at 02:00am CST
3.2 open, due 10/17/2016 at 02:00am CST
3.3 open, due 10/17/2016 at 02:00am CST
3.4 open, due 10/17/2016 at 02:00am CST 
第5週
10/12,10/14  3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.8 Exponential Growth and Decay
3.9 Related Rates

First quiz on October 12 (Topics, Ch1 and Ch2, 3.1 and 3.2) 
第6週
10/19,10/21  3.10 Linear Approximations and Differentials
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph

Webwork HW
3.10 open, due 10/31/2016 at 02:00am CST
4.2 open, due 10/31/2016 at 02:00am CST
4.3 open, due 10/31/2016 at 02:00am CST
4.1 open, due 10/31/2016 at 02:00am CST
 
第7週
10/26,10/28  4.4 Indeterminate Forms and l''Hospital''s Rule
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives

4.4 due 11/03/2016 at 11:59pm CST
4.5 due 11/03/2016 at 11:59pm CST
4.7 due 11/03/2016 at 11:59pm CST
 
第8週
11/02,11/04  5.1 Areas and Distances
Review

Second quiz on Nov 2 (Topics, Ch 3 and Ch4)

期中考 11/5(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題)
新生302 化學、機械
新生304 其他 
第9週
11/09,11/11  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
11/16,11/18  6.1 Areas Between Curves
6.2 Volume
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function  
第11週
11/23,11/25  7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions  
第12週
11/30,12/02  7.4 Integration of Rational Functions by Partial Fractions
7.8 Improper Integrals
9.1 Modeling with Differential Equations

 
第13週
12/07,12/09  9.2 Direction Fields and Euler''s Method
9.3 Separable Equations

9.4 Models for Population Growth
9.5 Linear Equations
9.6 Predator-Prey Systems  
第14週
12/14,12/16  8.1 Arc Length
8.2 Area of a Surface of Revolution
8.3 Applications to Physics and Engineering

Quiz on December 14 
第15週
12/21,12/23  10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates

Cycloid (Just watch the first 40 seconds)

https://www.youtube.com/watch?v=ohP0clzK5rc

Brachistochrone problem

https://www.youtube.com/watch?v=li-an5VUrIA

https://www.youtube.com/watch?v=FAYWccuLVvY

A interesting introduction of the Brachistochrone problem

https://www.youtube.com/watch?v=Cld0p3a43fU

The following link can be used to draw the graph of parametric equations.

https://www.desmos.com/calculator/rnyjcjpouf 
第16週
12/28,12/30  10.4 Areas and Lengths in Polar Coordinates
10.6 Conic Sections in Polar Coordinates  
第17週
1/04,1/06  Review

1/7(六)微積分甲 期末考博雅101 13:30-16:00
Please read 考試須知

期末考1/7(六) 13:30~16:00 考試範圍 5.1~10.6(英文命題)