課程資訊

Calculus (general Mathematics) (a)(1)

104-1

MATH1201

201 101A1

09

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1041MATH1201_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

James Stewart: Calculus, Early Transcendentals, Seventh Edition, International
Metric Version, c2012. 滄海書局代理;

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 35% 11/5（六） 9:00-11:30 考試範圍 1.5-4.9（英文命題） 2. 期末考 35% 1/7（六）9:00-11:30 考試範圍 5.1-10.6 + 17.1 - 17.2（英文命題） 3. 作業、小考與平時表現 30% 作業：自 9/19 起每周一交習題，共 16 次。 小考：暫定 10/3, 10/24, 12/5, 12/26 實習課測驗，約 25 分鐘，共 4 次。 平時成績計算方式：16 次作業取 15 次高分，一次佔學期成績 1.4 分，共 21 分。 4 次小考取 3 次高分，一次佔學期成績 3 分，共 9 分。

 課程進度
 週次 日期 單元主題 第0週 before 9/14 開學前我會放幾篇預備知識的文章，請同學自主學習，將對課程學習很有幫助。 [0.1] 直線 [0.2] 三角函數 [0.3] 反函數 [0.4] 不等式 第1週 9/16,9/18 [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 第2週 9/23,9/25 [2.4] The Precise Definition of a Limit [2.5] Continuity [2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change 第3週 9/30,10/02 [2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions [3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions 第4週 10/07,10/09 [3.4] The Chain Rule [3.5] Implicit Differentiation 10/9(五)國慶紀念日放假一天 第5週 10/14,10/16 [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 10/21,10/23 緩衝時間 [4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem 第7週 10/28,10/30 [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 11/04,11/06 [4.8] Newton’s Method（※） [4.9] Antiderivatives [5.1] Areas and Distances 緩衝時間 11/7(六) 09:00∼11:30 考試範圍1.5∼4.9 (英文命題) 第9週 11/11,11/13 [5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus [5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule 第10週 11/18,11/20 [6.1] Areas Between Curves [6.2] Volumes [6.3] Volumes by Cylindrical Shells [6.4] Work（※） [6.5] Average Value of a Function 第11週 11/25,11/27 [7.1] Integration by Parts [7.2] Trigonometric Integrals [7.3] Trigonometric Substitution [7.4] Integration of Rational Functions by Partial Fractions 第12週 12/02,12/04 [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems（※） [7.7] Approximate Integration（※） [7.8] Improper Integrals [8.1] Arc Length 第13週 12/09,12/11 緩衝時間 [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（※） 第14週 12/16,12/18 [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15週 12/23,12/25 [9.5] Linear Equations [9.6] Predator-Prey Systems （※） 緩衝時間 第16週 12/30,1/01 [10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves 1/1（五）開國紀念日放假一天 第17週 1/06,1/08 [10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates [10.6] Conic Sections in Polar Coordinates 緩衝時間 第18週 After 1/8 寒假教材 1: 圖形的平移、旋轉、縮放 寒假教材 2: 無窮數列 寒假教材 3: 無窮級數 寒假教材 4: 從二次曲面到二次曲面 寒假教材 5: 線性代數淺淡