課程資訊

Calculus (general Mathematics) (a)(1)

107-1

MATH1201

201 101A1

04

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1071MATH1201_04

Differentiation and Integration, or, collectively, Calculus, on functions of a single variable together with their profound applications in various subject areas are introduced in this course. On differentiation, it includes the definitions of limits and continuity, techniques of differentiation, strategies in solving extreme-value problem and so on; on integration, it includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, finding areas and volumes, solving elementary differential equations and more.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides tutorial classes in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

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

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus A (1) and (2)" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.

Students participating in the course should be already skilled in high school mathematics.
Office Hours

James Stewart: Calculus, Early Transcendentals, 8th Edition, International
Metric Version, c2012. 滄海書局代理;

Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.

Website of the unified course on Calculus A: http://www.math.ntu.edu.tw/~mathcal/a/
NTU past-papers on Calculus A: http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7
Episte Math: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
Free online Desmos Graphing Calculator: https://www.desmos.com/calculator
Online computational knowledge engine: https://www.wolframalpha.com

(僅供參考)

 No. 項目 百分比 說明 1. 期末考 35% 1/6(日) 14:00~16:30 考試範圍 5.1-10.4（英文命題） 2. 期中考 35% 11/3(六) 09:00~11:30 考試範圍 1.4-4.9（英文命題） 3. 網路作業 15% 網路作業。至 http://webwork.math.ntu.edu.tw/webwork2/1071MATH1201_04/ 用自己帳號密碼登入 4. 小考 9% 暫定實習課測驗，約 25 分鐘，共 4 次。取其中3次計分。 5. 紙本作業 6% 會有4~6次，按照規定的繳交期限以紙本交給助教。

 課程進度
 週次 日期 單元主題 第1週 9/10, 9/12, 9/14 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 9/17, 9/19/ 9/21 2.4 The Precise Definition of a Limit 2.6 Limits at Infinity; Horizontal Asymptotes 2.3 Calculating Limits Using the Limit Laws 2.5 Continuity 第3週 9/26, 9/28 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 3.1 Derivatives of Polynomials and Exponential Functions(Polynomial) 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 9/24(一)中秋節放假 第4週 10/1, 10/3, 10/5 3.4 The Chain Rule 3.1 Derivatives of Polynomials and Exponential Functions(Exponential) 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 第5週 10/8, 10/12 3.8 Exponential Growth and Decay (*) 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions(*) 10/10(三)國慶紀念日放假 第6週 10/15, 10/17, 10/19 4.1 Maximum and Minimum Values 4.7 Optimization Problems 第7週 10/22, 10/24, 10/26 4.2 The Mean Value Theorem 4.4 Indeterminate Forms and l'Hospital's Rule 4.3 How Derivatives Affect the Shape of a Graph 第8週 10/29, 10/31, 11/2, 11/3 4.5 Summary of Curve Sketching Review 期中考 11/3(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) 第9週 11/5, 11/7, 11/9 4.9 Antiderivatives 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 第10週 11/12, 11/14, 11/16 5.5 The Substitution Rule 7.1 Integration by Parts 第11週 11/19, 11/21, 11/23 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 第12週 11/26, 11/28, 11/30 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 第13週 12/3, 12/5, 12/7 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 8.1 Arc Length 8.2 Area of a Surface of Revolution 第14週 12/10, 12/12, 12/14 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Areas and Lengths in Polar Coordinates 第15週 12/17, 12/19, 12/21, 12/22 6.5 Average Value of a Function 8.3 Application to Physics and Engineering 9.1 Modeling with Differential Equations 9.3 Separable Equations 12/22(六)補12/31(一)的課 第16週 12/24, 12/26, 12/28 9.4 Models for Population Growth 9.5 Linear Equations 第17週 1/2, 1/4, 1/6 Review 期末考 1/6(日) 14:00~16:30 考試範圍 5.1~10.4(英文命題)