課程資訊
課程名稱
微積分1
CALCULUS (1) 
開課學期
109-1 
授課對象
科技管理組  
授課教師
王振男 
課號
MATH4006 
課程識別碼
201 49810 
班次
17 
學分
2.0 
全/半年
半年 
必/選修
必修 
上課時間
第1,2,3,4,5,6,7,8,9 週
星期二1,2(8:10~10:00)星期四3,4,10(10:20~18:20) 
上課地點
博雅103 
備註
密集課程。統一教學.四10為實習課.初選將直接帶入此班次的微積分2.加退選階段請自行加選微積分2.
限本系所學生(含輔系、雙修生)
總人數上限:180人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091MATH4006_17 
課程簡介影片
 
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課程概述

「微積分1」上課時間為第一週至第八週。

我們將介紹單變數函數的微分運算,和它豐富的應用。內容涵蓋極限與連續的定義,微分技巧,畫函數圖形,和極值問題等。課堂上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;同時也會強調微積分在經濟學的應用,幫助學生將微積分與自己的專業課程結合。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 on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem 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 Economics are emphasized in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.  

課程目標
修完本課程學生能熟悉微積分工具,並應用在經濟學和其他專業科目。

Students would be familiar with Calculus as a tool and be able to apply it in Economics and various subjects after finishing this course.  
課程要求
修這門課以前,學生應熟練高中數學,並完成台大為新生預備的「微積分自我檢測」線上測驗。
學生應出席並積極參與課堂與習題課的討論。

Before taking this course, students should be already skilled in high school mathematics and finish the online "Pre-Calculus Self Diagnostic Test" which is designed for NTU freshmen.
Students are expected to attend and participate actively in lectures as well as discussion sessions.  
預期每週課後學習時數
 
Office Hours
每週三 10:00~12:00 
指定閱讀
Textbook: James Stewart, Daniel Clegg, and Saleem Watson,
Calculus Early Transcendentals, 9th edition.

其他相關資訊
微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
台大微積分考古題: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html
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 」  
參考書目
1. Hoffmann, Bradley, Sobecki, and Price: Applied Calculus for Business, Economics, and the Social and Life
Science (11th Edition)

2. 翁秉仁:微積分乙。
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
平時成績  
30% 
1. 每週 WeBWorK 作業與 2. 每週課本習題紙本作業。 3. 學習單  
2. 
小考 
20% 
小考共 5 次(9/24, 10/8, 10/15, 10/22, 10/29),取 4 次最高分平均 (小考不補考)  
3. 
期考  
50% 
期考 11/8(日) 14:00~16:30 考試以英文命題  
 
課程進度
週次
日期
單元主題
第1週
9/15,9/17  1.4 Exponential Functions 1.5 Inverse Functions 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function  
第2週
9/22,9/24  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 09/24 Quiz 1  
第3週
9/29,10/01  2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 
第4週
10/06,10/08  3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 10/08 Quiz 2  
第5週
10/13,10/15  3.8 Exponential Growth and Decay (Compounded Interest, and Present Value) 3.10 Linear Approximations and Differentials 4.1 Maximum and Minimum Values 10/15 Quiz 3  
第6週
10/20,10/22  4.2 The Mean Value Theorem 4.3 What Derivatives Tell Us about the Shape of a Graph 4.4 Indeterminate Forms and l’Hospital‘s Rule 10/22 Quiz 4  
第7週
10/27,10/29  4.5 Summary of Curve Sketching 4.7 Optimization Problems Applications: Profit Maximization and Cost Minimization Applications: Demand and Elasticity 10/29 Quiz 5 
第8週
11/03,11/05  緩衝時間 期考 11/8(日) 14:00~16:30 (英文命題)