課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
111-1 
授課對象
財務金融學系  
授課教師
黃秀戀 
課號
MATH4007 
課程識別碼
201 49820 
班次
16 
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
普101普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 
 
課程簡介影片
 
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課程大綱
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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。
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 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 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,並應用在經濟學領域。
Students would be familiar with Calculus as a tool and be able to apply it in Economics areas after finishing this course. 
課程要求
學生應熟練高中數學,並完成為台大新生預備的線上「微積分學前自我檢測」。
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 Precalculus 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
每週四 08:30~09:30 
參考書目
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 」 
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 
50% 
期考12/24(星期六)14:00~16:30(英文命題) 
2. 
小考 
20% 
三次小考取最高分的兩次計算成績 
3. 
學習單(Worksheet) 
10% 
1.三份學習單 2.每次總分100分,模組一結束後的計算方式是(三次總分)/300*9 3.三次都有準時交作業的話,得到總成績1分 4.學習單遲交的話,成績打六折 
4. 
Webwork(線上作業) 
10% 
以完成率計分,模組二結束後的計算方式是 (完成率)*10 
5. 
隨堂測驗 
10% 
兩次隨堂測驗 每次總分是100分,模組二結束後的計算方式是(兩次次總分)/200*10 
 
課程進度
週次
日期
單元主題
第9週
10/31-11/6  5.1 The Area and Distance Problems
5.2 The Definite Integrals
5.3 The Fundamental Theorem of Calculus
5.4 The indefinite Integrals and the Net Change Theorem
11/4(五)微積分二退選截止日 
第10週
11/7-11/13  5.5 The Substitution Rule
6.1 Areas Between Curves
6.5 Average Value of a Function
Worksheet(Lorenz Curves and Gini Index) 
第11週
11/14-11/20  8.4 Application to Economics(WS)
7.1 Integration by Parts
7.2 Trigonometric Integrals
11/17(四)17:30-18:20 (Quiz1 範圍5.1-5.5, 6.1) 
第12週
11/21-11/27  7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
Worksheet(Integrals in Economics)
Pop_Quiz1 
第13週
11/28-12/4  7.8 Improper integrals
8.5 Probability(WS)
9.1 Modeling with Differential Equations
12/1(四)17:30-18:20 (Quiz2 範圍7.1-7.5) 
第14週
12/5-12/11  9.3 Separable Equations
9.5 Linear Equations
Worksheet(Applications in Probability) 
第15週
12/12-12/18  11.9 Representation of Functions as Power Series
11.10 Taylor and Maclaurin Series
12/15(四)17:30-18:20 (Quiz3 範圍8.5 , 9.1, 9.3, 9.5) 
第16週
12/19-12/25  緩衝時間
期考12/24(星期六)14:00~16:30(英文命題)
Pop_Quiz2