課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
107-1 
授課對象
資訊管理學系  
授課教師
張瑞恩 
課號
MATH1201 
課程識別碼
201 101A1 
班次
04 
學分
4.0 
全/半年
全年 
必/選修
必修 
上課時間
星期一10(17:30~18:20)星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) 
上課地點
新203新203新203 
備註
統一教學.大二以上限20人.一10為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:130人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1071MATH1201_04 
課程簡介影片
 
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課程概述

本課程介紹單變數函數的微分與積分運算,和它們在各領域豐富的應用。微分部分涵蓋極限與連續的定義,微分技巧,和極值問題等.。積分部分包含積分的定義,微積分基本定理,積分技巧,求面積體積,和初步的微分方程等。課堂上我們會講解定義並推導重要定理,以培養學生邏輯推理與分析能力;課堂上也會示範微積分在各領域的應用,幫助學生將微積分與其他專業科目結合。本課程還設有習題課,學生將在助教的帶領下熟練微積分的計算。

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.

上學期:單變數微積分
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
期中考時間:待定 考試範圍 1.4~4.9

5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates
期末考時間:待定 考試範圍 5.1~10.6+17.1~17.2

微積分甲 01--04 班為統一教學,班級進度一致。 

課程目標
修完本課程學生能熟悉微積分工具,並應用在各學科。「微積分甲上,下」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。

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. 
課程要求
學生們需要俱備高中數學的能力。

Students participating in the course should be already skilled in high school mathematics. 
Office Hours
 
參考書目
課本:
James Stewart: Calculus, Early Transcendentals, 8th Edition, International
Metric Version, c2012. 滄海書局代理;
訂書專線: 04-2708-8787; 0934095750。

註:今年使用的是第 8 版, James Stewart 的 Calculus。如果使用學長姊留下的課本要 
指定閱讀
Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.

其他相關資訊
微積分甲統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/
台大微甲考古題 http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com

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 
評量方式
(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)