複變函數

Abstract

課程首頁

本課程是由交通大學電機工程學系提供。

熟悉複數變數之理論及應用。

課程目標/概述

熟悉複數變數之理論及應用。

課程章節

課程章節

單元主題

Complex numbers

CV1 Complex Numbers: Basic Operations and Properties

CV2 Complex Numbers: Exponential Form and de Moivre’s Formula

CV3 Complex Numbers: Regions in the Complex Plane

Analytic Functions

CV4 Analytic Functions : Functions of Complex Variables

CV5 Analytic Functions : Limits and Continuity

CV6 Analytic Functions : Derivatives and Cauchy-Riemann Equations

CV7 Analytic Functions : Analytic Functions

Elementary Functions

CV8 Elementary Functions : LogarithmicFunctions

CV9 Elementary Functions : Trigonometric and Hyperbolic Functions

Integrals

CV10 Integrals : Contour Integrals

CV11 Integrals : Cauchy Integral Formula

Series

CV12 Series

Residues and Poles

CV13 Residues: Cauchy’s Residue Theorem

CV14 Residues: Poles and Zeros

CV15 Residues: Evaluation of Improper Integrals

CV16 Residues: Special Integral methods

CV17 Residues: Inverse Laplace Transform

Applications of Residues

CV18 Argument Principle

Mapping

CV19 Mapping: Elementary Transformations

CV20 Mapping: Conformal Transformation

課程書目

以課程講義為主。

參考書目

Complex Variable and Application by Brown and Churchill (Published by McGraw-Hill) 新月圖書/東華書局

評分標準

項目

百分比

第一次期中考

25%

第二次期中考

25%

期末考

25%

作業(含小考)

20%

專題報告

5%

授課對象：大學2年級學生

預備知識：微積分、微分方程