課程資訊

CALCULUS (GENERAL MATHEMATICS) (A)(1)

99-1

MATH1201

201 101A1

04

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991calculusA04

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

James Stewart, Calculus Early Transcendentals, 6th
edition.

(僅供參考)

 No. 項目 百分比 說明 1. Midterm exam 40% 微甲一組統一命題、閱卷 2. Final exam 40% 微甲一組統一命題、閱卷 3. Quizzes and/or homework 20% 四次小考成績、作業成績，及習題課上台表現

 課程進度
 週次 日期 單元主題 第1週 9/13,9/15,9/17 [1.5] Exponential Functions [1.6] Inverse Functions and Logarithms [2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function 第2週 9/20,9/22,9/24 9/22(三)中秋節放假一天 [2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit 第3週 9/27,9/29,10/01 [2.5] Continuity [2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change [2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions 第4週 10/04,10/06,10/08 Quiz 1 [3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions [3.4] The Chain Rule [3.5] Implicit Differentiation 第5週 10/11,10/13,10/15 [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 [3.11] Hyperbolic Functions（※） 第6週 10/18,10/20,10/22 [4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem 緩衝時間 第7週 10/25,10/27,10/29 [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 [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems 第8週 11/01,11/03,11/05 Quiz 2 [4.8] Newton’s Method（※） [4.9] Antiderivatives [5.1] Areas and Distances [5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus 第9週 11/08,11/10,11/12 [5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule 緩衝時間 11/13(六)13:30∼16:00期中考 考試範圍 1.5∼5.5 (英文命題) 第10週 11/15,11/17,11/19 [6.1] Areas between Curves [6.2] Volumes [6.3] Volumes by Cylindrical Shells [6.4] Work（※） 第11週 11/22,11/24,11/26 [6.5] Average Value of a Function [7.1] Integration by Parts [7.2] Trigonometric Integrals 第12週 11/29,12/01,12/03 [7.3] Trigonometric Substitution [7.4] Integration of Rational Functions by Partial Fractions 第13週 12/06,12/08,12/10 Quiz 3 [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration [7.8] Improper Integrals 第14週 12/13,12/15,12/17 緩衝時間 [8.1] Arc Length [8.2] Area of a Surface of Revolution 第15週 12/20,12/22,12/24 [9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method [9.3] Separable Equations [9.4] Models for Population Growth 第16週 12/27,12/29,12/31 Quiz 4 [9.5] Linear Equations [9.6] Predator-Prey Systems （※） [10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves 第17週 1/03,1/05,1/07 [10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates 緩衝時間 1/8(六)13:30∼16:00期末考 考試範圍 6.1∼10.4 (英文命題)