課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
109-1 
授課對象
科技管理組  
授課教師
王振男 
課號
MATH4007 
課程識別碼
201 49820 
班次
17 
學分
2.0 
全/半年
半年 
必/選修
必修 
上課時間
第10,11,12,13,14,15,16,17,18 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
初選不開放。密集課程。初選不開放.密集課程.統一教學.四10為實習課.
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/1091MATH4007_17 
課程簡介影片
 
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課程概述

這是一門半學期的課程,主要介紹單變數函數的積分運算,和積分在各領域豐富的應用。內容涵蓋積分的定義,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。課堂上將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;同時會強調微積分在經濟學的應用,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。

Integration 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 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 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,並應用在各學科和其他專業科目。

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 sess.
 
預期每週課後學習時數
 
Office Hours
每週三 10:00~12:00 備註: 王振男 
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

 
指定閱讀
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition.

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 
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。 2. 學習單 
2. 
小考 
20% 
小考共 5 次(11/26, 12/3, 12/10, 12/17, 12/24),取 4 次最高分平均 (小考不補考)  
3. 
期考 
50% 
期考 1/9(六) 14:00~16:30 考試以英文命題 (暫定)。  
 
課程進度
週次
日期
單元主題
第9週
11/10,11/12  Antiderivatives, The Area and Distance Problems, The Definite Integral, The Fundamental Theorem of Calculus. 
第10週
11/17,11/19  Indefinite Integrals and the Net Change Theorem, The Substitution Rule, Areas Between Curves, Volume. 
第11週
11/24,11/26  Volumes by Cylindrical Shells, Average Value of a Function (✽), Integration by Parts. 
第12週
12/01,12/03  Trigonometric Integrals, Trigonometric Substitution, Integration of Rational Functions by Partial Fractions. 
第13週
12/08,12/10  Strategy for Integration, Improper Integrals. 
第14週
12/15,12/17  Applications: Consumer and Producer Surplus, Applications: Integrals in Probability, Modeling with Differential Equations. 
第15週
12/22,12/24  Separable Equations, Models for Population Growth, Linear Equations. 
第16週
12/29,12/31  Curves Defined by Parametric Equations, Calculus with Parametric Curves, Polar Coordinates. 
第17週
1/05,1/07  緩衝時間