課程資訊

Calculus (general Mathematics) (a)(1)

108-1

MATH1201

201 101A1

02

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081MATH1201_02

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/~calc
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. 期中考 35% 期中考 11/2(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) 2. 期末考 35% 期末考 1/4(六) 09:00~11:30 考試範圍 5.1~10.4+17.1~17.2(英文命題) 3. 網路作業 15% 網路作業請在以下網址完成。 http://webwork.math.ntu.edu.tw/webwork2/1081MATH1201_02/ 每週會按照當週進度指派新的作業，下下週的星期一之前需完成。 4. 小考 10% 共六次小考，取較高的五次計分。小考都在星期一的演習課舉行。日期為9/23、10/14、10/28、11/25、12/16、12/30。 5. 紙本作業 5% 共四次紙本作業，寫完後於助教課繳交。

 課程進度
 週次 日期 單元主題 第1週 9/09,9/11 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 9/13(五)中秋節 第2週 9/16,9/18,9/20 2.2 The Limit of a Function 2.6 Limits at Infinity; Horizontal Asymptotes 2.4 The Precise Definition of a Limit 2.3 Calculating Limits Using the Limit Laws 2.5 Continuity 第3週 9/23,9/25,9/27 9/23 小考一 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 第4週 9/30,10/02,10/04,10/05 3.4 The Chain Rule 3.1 Derivatives of Polynomials and Exponential Functions (Exponential) 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.8 Exponential Growth and Decay (*) 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions(*) 10/5(六)補10/11(五)的課 第5週 10/07,10/09 4.1 Maximum and Minimum Values 10/10(四)國慶紀念日，10/11(五)調整放假 第6週 10/14,10/16,10/18 4.7 Optimization Problems 4.2 The Mean Value Theorem 4.4 Indeterminate Forms and l'Hospital's Rule 10/14 小考二 第7週 10/21,10/23,10/25 4.3 How Derivatives Affect the Shape of a Graph 4.5 Summary of Curve Sketching 第8週 10/28,10/30,11/01,11/02 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 10/28 小考三 期中考 11/2(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) 第9週 11/04,11/06,11/08 5.5 The Substitution Rule 7.1 Integration by Parts 第10週 11/11,11/13 7.2 Trigonometric Integrals 11/15(五)校慶停課一天 第11週 11/18,11/20,11/22 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 第12週 11/25,11/27,11/29 7.8 Improper Integrals Laplace transform I 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 第13週 12/02,12/04,12/06 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 8.1 Arc Length 8.2 Area of a Surface of Revolution(*) 6.5 Average Value of a Function 12/02 小考四 第14週 12/09,12/11,12/13 10.3 Polar Coordinates 10.4 Areas and Lengths in Polar Coordinates 9.1 Modeling with Differential Equations 9.3 Separable Equations 第15週 12/16,12/18,12/20 9.4 Models for Population Growth(*) 9.5 Linear Equations 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 12/16 小考五 第16週 12/23,12/25,12/27 Laplace Transform II 第17週 12/30,1/03,1/04 Review 12/30 小考六 1/1(三)開國紀念日 期末考1/4(六) 09:00~11:30 考試範圍 5.1~10.4+17.1~17.2+Laplace transform(英文命題)