課程資訊

Calculus (general Mathematics) (a)(1)

103-1

MATH1201

201 101A1

09

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH1201_09

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.

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. 平常成績(含小考) 20%

 課程進度
 週次 日期 單元主題 第1週 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
[2.3] Calculating Limits Using the Limit Laws

[2.5] Continuity
[2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and Rates of Change

[3.1] Derivatives of Polynomials and Exponential Functions
[3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions

[3.5] Implicit Differentiation
10/10(五)國慶紀念日放假一天

[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
[3.11] Hyperbolic Functions（※）

[4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem

[4.4] Indeterminate Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators（※）
[4.7] Optimization Problems

[4.9] Antiderivatives
[5.1] Areas and Distances

11/8 (六) 09:00~11:30 期中考 (1.5~4.9)

[5.3] The Fundamental Theorem of Calculus
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule

[6.2] Volumes
[6.3] Volumes by Cylindrical Shells
[6.4] Work（※）
[6.5] Average Value of a Function

[7.2] Trigonometric Integrals
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions

[7.6] Integration Using Tables and Computer Algebra Systems（※）
[7.7] Approximate Integration（※）
[7.8] Improper Integrals
[8.1] Arc Length

[8.2] Area of a Surface of Revolution
[8.3] Applications to Physics and Engineering
[8.4] Applications to Economics and Biology（※）
[8.5] Probability（※）

[9.2] Direction Fields and Euler's Method
[9.3] Separable Equations
[9.4] Models for Population Growth

[9.6] Predator-Prey Systems（※）

[10.2] Calculus with Parametric Curves
[10.3] Polar Coordinates
[10.4] Areas and Lengths in Polar Coordinates
[10.6] Conic Sections in Polar Coordinates

1/10 (六) 09:00~11:30 期末考(5.1~10.6)