E2080 教學大綱表

教學大綱表 (113學年度第2學期)

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課程名稱 Course Title	(中文) 複變數論 (英文) Complex Variables			開課單位 Departments	電機工程學系
				課程代碼 Course No.	E2080
授課教師 Instructor	江江盛
學分數 Credit	3.0	必/選修 core required/optional	選修	開課年級 Level	大二
先修科目或先備能力(Course Pre-requisites)：微積分，工程數學
課程概述與目標(Course Overview and Goals)：此課程提供給學習者，結合微積分及複數的特性，推導出一套運算的數學工具，可以有效的解決一些工程上的演算問題。
教科書(Textbook)	J. W. Brown & R. V. Churchill (2003), "Complex Variables and Applications," McGraw-Hill International Editions.
參考教材(Reference)

課程大綱 Syllabus			學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
序 No.	單元主題 Unit topic	內容綱要 Content summary	學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
1	COMPLEX NUMBERS	1. Sum and Product 2. Exponential Form	1. Sum and Product 2. Exponential Form
2	ANALYTIC FUNCTIONS	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations
3	ANALYTIC FUNCTIONS	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations
4	ANALYTIC FUNCTIONS	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations	1. Functions of a Complex Variable 2. Limits; Cauchy-Riemann Equations
5	ELEMENTARY FUNCTIONS	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions
6	ELEMENTARY FUNCTIONS	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions
7	ELEMENTARY FUNCTIONS	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions	1. Some Identities Involving Logarithms 2. Inverse Trigonometric Functions
8	期中考	期中考	期中考
9	INTEGRALS	1. Contour Integrals 2. Cauchy-Goursat Theorem 3. Cauchy Integral Formula	1. Contour Integrals 2. Cauchy-Goursat Theorem 3. Cauchy Integral Formula
10	INTEGRALS	1. Contour Integrals 2. Cauchy-Goursat Theorem 3. Cauchy Integral Formula	1. Contour Integrals 2. Cauchy-Goursat Theorem 3. Cauchy Integral Formula
11	SERIES	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series
12	SERIES	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series
13	SERIES	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series	1. Convergence of Sequences and Series 2. Laurent Series 3. Multiplication and Division of power series
14	RESIDUES AND POLES	1. Residue Theorems 2. Residues at Poles 3.	1. Residue Theorems 2. Residues at Poles 3.
15	APPLICATIONS OF RESIDUES	1. Evaluation of Improper Integrals 2. Indented Paths 3. Inverse Laplace Transforms	1. Evaluation of Improper Integrals 2. Indented Paths 3. Inverse Laplace Transforms
16	期末考	期末考	期末考

彈性教學週活動規劃

序 No.	實施期間 Period	實施方式 Content	教學說明 Teaching instructions	彈性教學評量方式 Evaluation	備註 Notes
1	起:2025-06-09 迄:2025-06-13	1.同步遠距教學 Synchronous distance learning	Applications of Residues-I	Homework
2	起:2025-06-17 迄:2025-06-20	1.同步遠距教學 Synchronous distance learning	Applications of Residues-II	Homework

教學要點概述：
1.自編教材 Handout by Instructor：
□ 1-1.簡報 Slids
□ 1-2.影音教材 Videos
□ 1-3.教具 Teaching Aids
■ 1-4.教科書 Textbook
□ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

成績考核 Performance Evaluation：期末考：25% 期中考：25% 彈性教學：10% 平時考：20% 作業：20%

教學資源(Teaching Resources)：
□ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php