課程資訊

CALCULUS (GENERAL MATHEMATICS) (A)(1)

99-1

MATH1201

201 101A1

15

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991cal_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

CALCULUS Early Transcendentals
Stewart 6th Edition

(僅供參考)

 No. 項目 百分比 說明 1. 測驗 100% 期中考50% 期末考50%

 課程進度
 週次 日期 單元主題 第1週 9/13,9/17 Functions and its properties(Exponential functions, inverse functions, and logarithms) 第2週 9/20,9/24 The tangent and velocity problems, the limit of a function, calculating limits using the limits laws, the precise definition of a limit 第3週 9/27,10/01 Continuity, limits at infinity; horizontal asymptotes 第4週 10/04,10/08 Derivatives and rates of change, the derivative as a function, derivatives of polynomials and exponential functions, the product and quotient rules 第5週 10/11,10/15 Derivatives of trigonometric functions, the chain rule, Implicit differentiation 第6週 10/18,10/22 Derivatives of logarithmic functions, rates of change in the natural and social science, related rates 第7週 10/25,10/29 Linear approximations and differentials, hyperbolic functions 第8週 11/01,11/05 Maximum and minimum values,the mean value theorem, how derivatives affect the shape of a graph 第9週 11/08,11/12 Indeterminate forms and L’Hospital’s rule, summary of curve sketching, Graphing with calculus 第10週 11/15,11/19 Optimization problems, Newton’s method, antiderivatives 第11週 11/22,11/26 Areas and distances, the definite integral, the fundamental theorem of calculus 第12週 11/29,12/03 Indefinite integrals and the net change theorem, the substitution rule 第13週 12/06,12/10 Areas between curves, Volumes, Volumes by cylindrical shells 第14週 12/13,12/17 Work, average value of a function, Integration by parts 第15週 12/20,12/24 Trigonometric integrals, trigonometric substitution 第16週 12/27,12/31 Integration of rational functions by partial fractions, strategy for integration, integration using tables 第17週 1/03,1/07 Approximate integration, improper integrals