課程資訊

Calculus (general Mathematics) (a)(1)

103-1

MATH1201

201 101A1

14

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH1201_14

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 6th Edition

Calculus 4e Adoptation Edition

by Robert T. Smith and Roland B. Minton

(僅供參考)

 No. 項目 百分比 說明 1. 第一次測驗 20% 2. 第二次測驗 30% 3. 第三次測驗 25% 4. 第四次測驗 25%

 課程進度
 週次 日期 單元主題 第1週 9/15,9/19 Graphing Calculators and Computer Algebra Systems. Trigonometric Functions 第2週 9/22,9/26 Transformations of Functions The concept of Limit 第3週 9/29,10/03 Continuity 第4週 10/06,10/10 Asymptotes Formal Definition of the Limit 第5週 10/13,10/17 The derivative 第6週 10/20,10/24 Computation of Derivatives 第7週 10/27,10/31 The Chain Rule 第8週 11/03,11/07 Implicit Differentiation The Mean Value Theorem 第9週 11/10,11/14 Applications of Differentiation (I) 第10週 11/17,11/21 Applications of Differentiation (II) 第11週 11/24,11/28 Integration (I) 第12週 12/01,12/05 Integration (II) 第13週 12/08,12/12 Computation of Integration 第14週 12/15,12/19 Applications of the Definite Integral (I) 第15週 12/22,12/26 Applications of the Definite Integral (II) 第16週 12/29,1/02 Transcendental Functions (I) 第17週 1/05,1/09 Transcendental Functions (II)