課程資訊
課程名稱
微積分2
CALCULUS (2) 
開課學期
110-1 
授課對象
土木工程學系  
授課教師
佐藤信夫 
課號
MATH4007 
課程識別碼
201E49820 
班次
11 
學分
2.0 
全/半年
半年 
必/選修
必帶 
上課時間
第9,10,11,12,13,14,15,16 週
星期二8,9,10(15:30~18:20)星期四6,7(13:20~15:10) 
上課地點
新203新203 
備註
初選不開放。本課程以英語授課。密集課程。英文授課.初選不開放.密集課程.統一教學.二10為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:120人 
 
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
修這門課以前,學生應熟練高中數學。
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
 
指定閱讀
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition.  
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

NTU Calculus Unified Website: http://www.math.ntu.edu.tw/~calc/Default.html
NTU Calculus Past Exams: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html  
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Final 
50% 
01/09 (Sun) 09:00-11:30 
2. 
Quiz 
30% 
3 Quizzes 
3. 
Written HW 
10% 
 
4. 
WeBWorK 
10% 
 
 
課程進度
週次
日期
單元主題
第9週
  5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus 
第10週
  5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule 
第11週
  6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function 
第12週
  7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution 
第13週
  7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals 
第14週
  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
  9.5 Linear Equations
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves 
第16週
  10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
* 01/09 (Sun) 09:00-11:30 Final Examination