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課程簡介 Course Introduction
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開課年度學期 Year / Term
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113 學年度 第 1 學期
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開課班級 Department
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應用數學系 應數三
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授課方式 Instructional Method
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課堂教學 、 全英-不加成
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課程電腦代號 Course Reference Number
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150015
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課程名稱(中文) Course Title(Chinese)
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複變數函數論
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課程名稱(英文) Course Title(English)
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Complex Analysis
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學分數/時數 Credit Hours
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3 /
3
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必(選)修 Requirement / Elective Course
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必修
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授課老師 Instructor
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黃彥彰
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助教 Teaching Assistant
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上課時間 Meeting Time
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星期五，節次3、4、5
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上課教室 Classroom
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C305
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Office Hours
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黃彥彰：2244/4545
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| 獲獎及補助情形 Awards and Grants |
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| 聯合國永續發展目標 (SDGs跨域類別) Sustainable Development Goals, SDGs |
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SDGs 04.
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優質教育：確保有教無類、公平以及高品質的教育，及提倡終身學習
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課程目標 Learning Objectives
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複變函數論主要討論解析函數的性質，可視為高等微積分的延伸，並為後續研究高等數學建立基礎。本課程將包含下列單元：algebra and topology of the complex plane, power series, differentiation, integration, logarithms and the winding number, Cauchy's theorem, Taylor and Laurent series, Residues, conformal transformation, analytic continuation
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先修 ( 前置 ) 課程 Prerequisite
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線性代數，微積分，高等微積分。
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| 彈性教學規劃 Flexible Teaching/Planning Schedules |
| ＊本課程實施16+2週彈性教學方案，其中第17、18週之彈性規劃如下： |
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課程大綱 Course Syllabus
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| 週次 Week |
課程單元大綱 Unit |
教學方式 Instructional Method/Style/Teaching Style |
參考資料或相關作業 References or Related Materials |
評量方式 Grading |
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1
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algebra of the complex plane
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lecture
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1.1 - 1.8
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2
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topology of the complex plane
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lecture
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2.1 - 2.3
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3
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topology of the complex plane 2
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lecture
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2.4 - 2.8
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4
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power series 1
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lecture
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3.1 - 3.3
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5
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power series 2
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lecture
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3.4 -3.5
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6
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differentiation 1
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lecture
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4.1 - 4.3
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7
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differentiation 2
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lecture
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4.4 - 4.6
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8
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exponential functions 1
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lecture
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5.1 - 5.6
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9
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midterm
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midterm
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10
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iexponential functions 2
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lecture
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5.7-5.9
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11
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integration
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lecture
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6.1-6.3
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12
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angles, logarithms, the winding number
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lecture
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6.3-6.7
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13
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Cauchy's theorem 1
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lecture
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7.1-7.4
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14
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Cauchy's theorem 2
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lecture
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8.1-8.4
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15
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Cauchy's theorem 3
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lecture
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8.5-8.7
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17
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Cauchy's theorem 4
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lecture
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9.1-9.4
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18
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Final exam
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Exam
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單一課程對應校能力指標程度 The Degree to Which Single Course Corresponds to School Competence
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| 編號 No. |
校核心能力 School Core Competencies |
符合程度 Degree of conformity |
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1
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公民力 (Citizen)
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5
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2
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自學力 (Self-learning)
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5
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3
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資訊力 (Information)
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5
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4
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創造力 (Creativity)
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3
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5
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溝通力 (Communication)
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5
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6
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就業力(Employability)
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4
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單一課程對應系能力指標程度 The Degree to Which Single Course Corresponds to Department Competence
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| 編號 No. |
類別 Category |
系核心能力 Department Core Competencies |
符合程度 Degree of conformity |
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01
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系所
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學生具備數學思考與推理能力
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5
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02
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系所
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學生擁有數學應用與解決問題能力
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5
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03
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系所
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學生具備代數、離散、統計及科學計算能力
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5
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04
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系所
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學生具有小學數學之專業教學能力
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5
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05
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系所
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學生具有跨領域之科學知識
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5
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06
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系所
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學生擁有閱讀討論與發表之專業能力
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5
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單一課程對應院能力指標程度 The Degree to Which Single Course Corresponds to College Competence
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| 編號 No. |
院核心能力 College Core Competencies |
符合程度 Degree of conformity |
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1
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語文能力
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5
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2
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溝通與合作能力
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3
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3
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創新與實踐能力
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3
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4
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專業知能
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5
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教科書或參考用書 Textbooks or Reference Books
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館藏書名 Library Books
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備註 Remarks
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Textbook: Complex Analysis, Ian Stewart, David Tall, Cambridge University Press, 2018
References:
(1) Visual Complex Analysis, Tristan Needham, Clarendon Press; 1999
(2) Complex Analysis, an introduction to the theory of analytic functions of one complex variable, Lars V. Ahlfors, 3rd, 1979
(3) Complex Variables and Applications, 8th Edition James Brown and Ruel Churchill, McGraw-Hill Education
(4) Real and Complex Analysis, Walter Rudin, McGraw-Hill Education; 3 edition, 1986
(5) Complex Analysis, for mathematics and engineering, 6nd edition, John H. Mathews, Russell W. Howell, 2012
(6) Functions of one complex variable, John B. Conway, 2nd, Springer
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※請尊重智慧財產權，不得非法影印教科書※
※ Please respect intellectual property rights and do not illegally photocopy textbooks. ※
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教學方法 Teaching Method
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教學方法 Teaching Method
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百分比 Percentage
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講述
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70 %
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問題導向學習
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30 %
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| 總和 Total |
100 % |
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成績評量方式 Grading
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| 評量方式 Grading |
百分比 Percentage |
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期中考
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40 %
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期末考
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60 %
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| 總和 Total |
100 % |
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成績評量方式補充說明
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1. 期中考於第9週舉行。
2. 期末考於第18週舉行。
3. 其餘未盡事宜將於第一次上課時公布。
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課程大綱補充資料 Supplementary Material of Course Syllabus
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