課程資訊

Calculus (general Mathematics) (a)(1)

105-1

MATH1201

201 101A1

09

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1051MATH1201_09

Office Hours

 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/

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)

(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)