課程資訊

Calculus (general Mathematics) (a)(1)

103-1

MATH1201

201 101A1

01

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH1201_01

1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates

Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing
regular mappings with applications, and deepen the understanding of elementary functions.

High School Mathematics

Office Hours

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 2. 期末考 40% 3. 平時成績(含小考) 20%

 課程進度
 週次 日期 單元主題 第1週 9/15,9/17,9/19 [1.5] Exponential Functions
[1.6] Inverse Functions and Logarithms
[2.1] The Tangent and Velocity Problems
[2.2] The Limit of a Function

[2.4] The Precise Definition of a Limit
[2.5] Continuity
[2.6] Limits at Infinity; Horizontal Asymptotes

[2.8] The Derivative as a Function
[3.1] Derivatives of Polynomials and Exponential Functions
[3.2] The Product and Quotient Rules

[3.4] The Chain Rule
10/10(五)國慶紀念日放假一天

[3.6] Derivatives of Logarithmic Functions
[3.7] Rates of Change in the Natural and Social Sciences（※）
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and Differentials

[4.1] Maximum and Minimum Values

[4.3] How Derivatives Affect the Shape of a Graph
[4.4] Indeterminate Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching

[4.7] Optimization Problems
[4.8] Newton’s Method（※）
[4.9] Antiderivatives

11/8 (六) 13:30~16:00 期中考(1.5~4.9) 第9週 11/10,11/12,11/14 [5.1] Areas and Distances
[5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus
[5.4] Indefinite Integrals and the Net Change Theorem

[6.1] Areas Between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells

[6.5] Average Value of a Function
[7.1] Integration by Parts
[7.2] Trigonometric Integrals

[7.4] Integration of Rational Functions by Partial Fractions
[7.5] Strategy for Integration
[7.7] Approximate Integration

[8.1] Arc Length

[8.3] Applications to Physics and Engineering
[8.4] Applications to Economics and Biology（※）
[8.5] Probability（※）
[9.1] Modeling with Differential Equations

[9.4] Models for Population Growth
[9.5] Linear Equations
[10.1] Curves Defined by Parametric Equations

[10.2] Calculus with Parametric Curves
[10.3] Polar Coordinates

[10.6] Conic Sections in Polar Coordinates

1/10 (六) 13:30~16:00 期末考(5.1~10.6) 第18週 餘三班投影片