課程資訊

Calculus (general Mathematics) (a)(1)

106-1

MATH1201

201 101A1

08

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH1201_08

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.

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, 8th edition. (Metric version)

(僅供參考)

 No. 項目 百分比 說明 1. 平常 20% 作業，webwork，小考 2. 期中考 40% 11/4(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) 3. 期末考 40% 1/6(六) 09:00~11:30 考試範圍 5.1~10.6(英文命題)

 課程進度
 週次 日期 單元主題 第1週 9/13,9/15 1.4 Exponential Functions 1.5 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 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 第3週 9/27,9/29 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 3. Differentiation rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 第4週 10/04,10/06 10/4 中秋節放假 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 第5週 10/11,10/13 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.8 Exponential Growth and Decay (✽) 3.9 Related Rates 第6週 10/18,10/20 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions 4. Applications of differentiation 4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 第7週 10/25,10/27 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 第8週 11/01,11/03 4.7 Optimization Problems 4.9 Antiderivatives 緩衝時間 第9週 11/08,11/10 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 5.5 The Substitution Rule 第10週 11/15,11/17 11/15 校慶停課 6. Applications of integration 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 第11週 11/22,11/24 6.5 Average Value of a Function 7. Techniques of integration 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 第12週 11/29,12/01 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 第13週 12/06,12/08 8.1 Arc Length 8.2 Area of a Surface of Revolution 第14週 12/13,12/15 8.1 Arc Length 10. Parametric equations and polar coordinates 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 第15週 12/20,12/22 9.1 Modeling with Differential Equations 9.3 Separable Equations 第16週 12/27,12/29 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 第17週 1/03,1/05 10.4 Areas and Lengths in Polar Coordinates