課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
111-1 
授課對象
地理環境資源學系  
授課教師
陳彥宇 
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 
 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
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,積分在機率的應用,和初步的微分方程等。最後,課程將簡介級數與泰勒展式,解釋如何以多項式逼近複雜的函數。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並完成學習單上的小型研究題目。

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, applications of integrals in probability, solving elementary differential equations and more. In addition to these, series and Taylor expansions are briefly introduced in the end of this course to explain how complicated functions are approximated by polynomials. 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 improve their skills in handling calculations in Calculus and complete small projects 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
每週二 10:10~11:30 
參考書目
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 」 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期考 
50% 
Time:12/24(Sat) 14:00~16:30  
2. 
小考 
20% 
11/17(Thu) 17:30-18:20 Quiz 1 (Range:5.1-5.5、6.1) 12/1(Thu) 17:30-18:20 Quiz 2 (Range:7.1-7.5、7.8) 12/15(Thu) 17:30-18:20 Quiz 3 (Range:8.5、9.1、9.3、9.5) 三次取最高兩次 
3. 
Webwork 
10% 
請依webwork的期限完成,成績的部分將直接由系統計算 
4. 
Worksheet 
10% 
worksheet的內容會在演習課由助教講解。 11/17前將worksheet 1上傳至作業區,準時交最高3%,遲交1% 12/1前將worksheet 2上傳至作業區,準時交最高3%,遲交1% 12/15前將worksheet 3上傳至作業區,準時交最高3%,遲交1% 分數計算部分,完成度80%以上拿3分,50%-79%拿2分,49%以下1分。 三次都準時交者,可額外得到1%,學習單請自己完成,如有抄襲,以零分計算 
5. 
紙本作業 
10% 
題號請見課程內容,請自己完成,如有抄襲,以零分計算。每次2分,取最高5次。 
6. 
額外練習 
0% 
請見額外作業區 
 
針對學生困難提供學生調整方式
 
上課形式
以錄影輔助
作業繳交方式
考試形式
其他
由師生雙方議定
課程進度
週次
日期
單元主題
第9週
11/1, 11/3  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
11/8, 11/10  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
11/15, 11/17  8.4 Applications to Economics (WS)
7.1 Integration by Parts
7.2 Trigonometric Integrals

11/17(Thu) 17:30-18:20 Quiz 1 (Range:5.1-5.5、6.1) 
第12週
11/22, 11/24  7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration

Worksheet (Integrals in Economics) 
第13週
11/29, 12/1  7.8 Improper Integrals
8.5 Probability(WS)
9.1 Modeling with Differential Equations

12/1(Thu) 17:30-18:20 Quiz 2 (Range:7.1-7.5、7.8) 
第14週
12/6, 12/8  9.3 Separable Equations
9.5 Linear Equations

Worksheet (Applications in Probability) 
第15週
12/13, 12/15  11.9 Representation of Functions as Power Series
11.10 Taylor and Maclaurin Series

12/15(Thu) 17:30-18:20 Quiz 3 (Range:8.5、9.1、9.3、9.5) 
第16週
12/20, 12/22  Review for the exam

Exam:12/24(Sat) 14:00~16:30