課程資訊

Calculus (general Mathematics) (a)(1)

100-1

MATH1201

201 101A1

15

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001cal_15

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

To understand the fundamental skills and theory of finding the derivatives of functions and finding the integrations of functions

Office Hours

Stewart 5th Edition

(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