課程資訊

Calculus (general Mathematics) (a)(1)

100-1

MATH1201

201 101A1

12

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001CalAChu

1. Functions and Models
2. Limit and Deriatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integral
6. Applications of Integration
7. Techniques of Integraion
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates

Office Hours

Calculus, a complete course, seventh edition, Author: Robert A. Adams & Christopher Essex. Pearson Canada,Toronto

www.math.ntu.edu.tw/~mathcal

www.math.ntu.edu.tw/~hchu/Calculus

(僅供參考)

 No. 項目 百分比 說明 1. 習題課與小考 20% 各班助教給分 2. 期中考 40% 3. 期末考 40%

 課程進度
 週次 日期 單元主題 第1週 09/13,09/15 1.1 Examples of Velocity, Growth Rate, and Area;
1.2 Limit of Functions;
1.3 Limits at Infinity and Infinite Limits;
1.4 Continuity 第2週 09/20,09/21 1.5 The Formal Definition of Limit;
2.1 Tangent Lines and Their Slopes;
2.2 The Derivative;
2.3 Differentiation Rules 第3週 9/27,9/29 2.4 The Chain Rule;
2.5 Derivatives of Trigonometric Functions;
2.6 Higher-Order Derivatives;
2.7 Using Differentials and Derivatives;
2.8 The Mean-Value Theorem 第4週 10/04,10/06 2.9 Implicit Differentiation;
2.10 Antiderivatives and Initial-Value Problems;
2.11 Velocity and Acceleration;

3.2 Exponential and Logarithmic Functions;
3.3 The Natural Logarithm and Exponential;
3.4 Growth and Decay 第6週 10/18,10/20 3.5 The Inverse Trigonometric Functions;
3.6 Hyperbolic Functions;
4.1 Related Rates 第7週 10/25,10/27 4.2 Finding Roots of Equations;
4.3 Indeterminate Forms;
4.4 Extreme Values;
4.5 Concavity and Inflections 第8週 11/01,11/03 4.6 Sketching the Graph of a Function;
4.7 Graphing with Computers（※）;
4.8 Extreme-Value Problems;
4.9 Linear Approximations 第9週 11/08,11/10 4.10 Taylor Polynomials;
4.11 Roundoff Error, Truncation Error, and Computers（※）;

11/12(六) 09:00∼11:30 期中考考試範圍 1.1∼4.10 (英文命題) 第10週 11/15,11/17 5.1 Sums and Sigma Notation;
5.2 Areas as Limits of Sums;
5.3 Definite Integral;
5.4 Properties of the Definite Integral 第11週 11/22,11/24 5.5 The Fundamental Theorem of Calculus;
5.6 The Method of Substitution;
5.7 Areas of Plane Regions;
6.1 Integration by Parts 第12週 11/29,12/01 6.2 Integrals of Rational Functions;
6.3 Inverse Substitutions;
6.4 Other Methods for Evaluating Integrals;
6.5 Improper Integrals 第13週 12/06,12/08 6.6 The Trapezoid and Midpoint Rules;
6.7 Simpson's Rule;
6.8 Other Aspects of Approximate Integration;

7.2 More Volumes by Slicing;
7.3 Arc Length and Surface Area 第15週 12/20,12/22 7.4 Mass, Moments, and Centre of Mass;
7.5 Centroids（※）;
7.6 Other Physical Applications（※）;
7.7 Applications in Business, Finance, and Ecology（※）;
7.8 Probability（※）;
7.9 First-Order Differential Equations 第16週 12/27,12/29 8.2 Parametric Curves;
8.3 Smooth Parametric Curves and Their Slopes;
8.4 Arc Lengths and Areas for Parametric Curves 第17週 1/03,1/05 8.5 Polar Coordinates and Polar Curves;
8.6 Slopes, Areas, and Arc Lengths for Polar Curves;

1/7(六) 09:00∼11:30 期末考考試範圍 5.1∼8.6 (英文命題)