課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
109-1 
授課對象
工程科學及海洋工程學系  
授課教師
陳彥宇 
課號
MATH4007 
課程識別碼
201 49820 
班次
10 
學分
2.0 
全/半年
半年 
必/選修
必帶 
上課時間
第10,11,12,13,14,15,16,17,18 週
星期一6,7(13:20~15:10)星期五1,2(8:10~10:00) 
上課地點
新203新203 
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:130人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091MATH4007_10 
課程簡介影片
 
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課程概述

微積分2
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
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。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.
 
課程要求
課程要求:
修這門課以前,學生要熟練高中數學。學生應積極參與課堂和習題課的活動與討論。
Students participating in the course should be already skilled in high school mathematics. They 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 09:00~11:00 
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
教科書:Calculus: Early Transcendentals 9th edition, 作者: James Stewart

可與滄海書局陳式政先生聯繫購買,聯絡方式為 0938-723-438 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期考 
50% 
期考1/9(六) 09:00~11:30 考試以英文命題 
2. 
小考 
20% 
小考兩次各10%,於第12(12/02-12/03)及第15週(12/23-12/24)演習課進行 
3. 
webwork 
10% 
http://webwork.math.ntu.edu.tw/webwork2/1091MATH4007_10/instructor/sets2/ 12/18前完成ch5-ch7,01/11前完成ch8-ch10 
4. 
紙本作業 
10% 
依前一週教學進度完成課本習題,在演習課交給助教,習題請上微積分統一教學網查看 
5. 
演習課 
10% 
助教於第一週演習課向同學說明評量方式 
6. 
考古題練習 
0% 
此項為額外加分,週五會公布題目,請於下一週課堂時間交給教師,教師會根據繳交情況於平時成績上加分 
 
課程進度
週次
日期
單元主題
第9週
11/09,11/13  5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
 
第10週
11/16,11/20  5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule 
第11週
11/23,11/27  6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function 
第12週
11/30,12/04  7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution 
第13週
12/07,12/11  7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals 
第14週
12/14,12/18  8.1 Arc Length
8.2 Area of a Surface of Revolution
9.1 Modeling with Differential Equations
9.3 Separable Equations 
第15週
12/21,12/25  9.4 Models for Population Growth (✽)
9.5 Linear Equations
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves 
第16週
12/28  10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates 
第17週
1/04,1/08  緩衝時間