課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
110-1 
授課對象
企業管理組  
授課教師
崔茂培 
課號
MATH4007 
課程識別碼
201 49820 
班次
15 
學分
2.0 
全/半年
半年 
必/選修
必修 
上課時間
第9,10,11,12,13,14,15,16 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101博雅101 
備註
初選不開放。本課程中文授課,使用英文教科書。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/1101MATH4007_15 
課程簡介影片
 
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課程概述

「微積分2」上課時間為第九週至第十六週。
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其豐富的應用。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;同時會示範微積分在經濟學的應用,幫助學生將微積分與其專業科目結合。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 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 illustrated 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and Calc I。
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.
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
 
參考書目
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 」  
指定閱讀
Textbook: James Stewart, Daniel Clegg, and Saleem Watson,
Calculus Early Transcendentals, 9th edition. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期考  
40% 
期考1/9(日) 14:00~16:30 (英文命題) 
2. 
統一的小考 
35% 
每次小考 50 分鐘(17:30-18:20) 三次小考,各佔總成績 12%。 三次小考加總若超過 35%,以35%計算。 Quiz on 12/2, 12/16, 12/30. 
3. 
作業、平時成績 
25% 
學習單成績 6% (每份 2 %), WeBWorK 作業8%。 每週手寫作業11% 
 
課程進度
週次
日期
單元主題
第9週
11/16,11/18  5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem 
第10週
11/23,11/25  5.5 The Substitution Rule
6.1 Areas Between Curves
6.2 Volume
6.3 Volumes by Cylindrical Shells 
第11週
11/30,12/02  6.5 Average Value of a Function (✽)
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution 
第12週
12/07,12/09  7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals 
第13週
12/14,12/16  8.4 Applications to Economics (Consumer and Producer Surplus)
8.5 Probability
9.1 Modeling with Differential Equations 
第14週
12/21,12/23  9.3 Separable Equations
9.4 Models for Population Growth
9.5 Linear Equations 
第15週
12/28,12/30  10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates 
第16週
1/04,1/06  緩衝時間 期考1/9(日) 14:00~16:30 (英文命題)