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課程名稱 (中文) 複變數論
(英文) Complex Variables
開課單位 電機工程學系
課程代碼 E2080
授課教師 江江盛
學分數 3.0 必/選修 選修 開課年級 大二
先修科目或先備能力:微積分,工程數學
課程概述與目標: 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 J. W. Brown & R. V. Churchill (2003), "Complex Variables and Applications," McGraw-Hill International Editions.
參考教材
課程大綱 學生學習目標 單元學習活動 學習成效評量 備註
單元主題 內容綱要
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
  • 作業
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    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
  • 作業
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    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
  • 平時考
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    5 ELEMENTARY FUNCTIONS 1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
    1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
  • 作業
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    6 ELEMENTARY FUNCTIONS 1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
    1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
  • 作業
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    7 ELEMENTARY FUNCTIONS 1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
    1. Some Identities Involving Logarithms
    2. Inverse Trigonometric Functions
  • 作業
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    8 INTEGRALS 1. Contour Integrals
    2. Cauchy-Goursat Theorem
    3. Cauchy Integral Formula
    1. Contour Integrals
    2. Cauchy-Goursat Theorem
    3. Cauchy Integral Formula
  • 平時考
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    9 期中考 期中考 期中考
  • 期中考
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    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 INTEGRALS 1. Contour Integrals
    2. Cauchy-Goursat Theorem
    3. Cauchy Integral Formula
    1. Contour Integrals
    2. Cauchy-Goursat Theorem
    3. Cauchy Integral Formula
  • 作業
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    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
  • 作業
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    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
  • 平時考
  •  
    14 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
  • 作業
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    15 RESIDUES AND POLES 1. Residue Theorems
    2. Residues at Poles
    3.
    1. Residue Theorems
    2. Residues at Poles
    3.
  • 作業
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    16 RESIDUES AND POLES 1. Residue Theorems
    2. Residues at Poles
    3.
    1. Residue Theorems
    2. Residues at Poles
    3.
  • 平時考
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    17 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
  • 作業
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    18 期末考 期末考 期末考
  • 期末考
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    教學要點概述:
    教材編選: ■ 自編教材 □ 教科書作者提供
    評量方法: 期末考:30%   期中考:30%   平時考:20%   作業:20%  
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