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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
105-1 |
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授課對象 |
化學工程學系 |
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授課教師 |
崔茂培 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
09 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
新303新303 |
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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 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051MATH1201_09 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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。 |
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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。 |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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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。 |
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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/ |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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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)
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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 |
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週次 |
日期 |
單元主題 |
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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 |
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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 |
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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/
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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 |
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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) |
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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
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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
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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 |
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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 |
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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 |
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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 |
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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
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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 |
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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 |
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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 |
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第16週 |
12/28,12/30 |
10.4 Areas and Lengths in Polar Coordinates
10.6 Conic Sections in Polar Coordinates |
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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) |
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