課程名稱 
微積分乙下 Calculus (general Mathematics) (b)(2) 
開課學期 
1032 
授課對象 
生命科學系 
授課教師 
夏俊雄 
課號 
MATH1204 
課程識別碼 
201 101B2 
班次 
10 
學分 
3 
全/半年 
全年 
必/選修 
必帶 
上課時間 
星期二1(8:10~9:00)星期四7,8,9(14:20~17:20) 
上課地點 
共201共201 
備註 
四9為實習課.大二以上限20人. 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/1032MATH1204_10_2015 
課程簡介影片 

核心能力關聯 
本課程尚未建立核心能力關連 
課程大綱

為確保您我的權利,請尊重智慧財產權及不得非法影印

課程概述 
Differentiation studies rate of change; while integration reveals the effect of accumulation.
These two ingredients (rate of change and eect of accumulation) are used to characterize
tons of principles, phenomena and criterions surrounding the daily life of everybody.
The history of development of calculus somehow reflects part of the most exciting experience
that all human beings who had ever lived on earth shared. 
課程目標 
The mission of calculus has at least the following concerns. (1) The philosophy of the theory of calculus is logically rigorous. The first benefit that a student who receives this training is to cultivate his/her solid logic thinking. In other words, he/she would have a better idea to make logically reasonable judgement and avoid to make funny mistakes. (2) The history of calculus is both heuristic and creative. With this cultivation, students are able to broaden their insights and get inspirations.
This might give them motivations to devote themselves to scientic research. (3) The philosophy
and the skills that students learn from this course give direct applications to a lot of scientic
work (including natural science and social science). (4) Nowadays, the use of network and scienti
c computing is getting more and more important. We integrate a few numerical computation
programming sessions in this class to train students the basic/important ingredients of calculus
including (a) input/output (b) do loop (c) if selection (d) graphics and (e) error control. 
課程要求 
3 exams
many quizzes

預期每週課後學習時數 

Office Hours 
另約時間 備註： 3 exmas + many quizzes 
指定閱讀 
The lecture notes will be delivered from time to time. 
參考書目 
The lecture notes will be delivered from time to time. 
評量方式 (僅供參考) 

週次 
日期 
單元主題 
第1週 
2/24,2/26 
integration by parts, techniques of integration 
第2週 
3/03,3/05 
Convergence of sequence: ratio test, root test, Abel test, Dirichlet test 
第3週 
3/10,3/12 
Taylor expansion theorem and its applications: convergence of sequence of functions, radius
of convergence 
第4週 
3/17,3/19 
Applications of Taylor expansion 
第5週 
3/24,3/26 
Exam 1 
第7週 
4/07,4/09 
Functions of several variables and their derivatives 
第8週 
4/14,4/16 
Implicit functions 
第9週 
4/21,4/23 
Multiple integrals 
第10週 
4/28,4/30 
Technique of integration from the point of view of multiple variables calculus 
第11週 
5/05,5/07 
Exam 2 
