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 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

 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:2024-06-10 迄:2024-06-14 1.同步遠距教學 Synchronous distance learning Applications of Residues-I Homework 2 起:2024-06-17 迄:2024-06-21 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