基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of using computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究的能力
Ability to do independent studies of mathematics.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

這門課主要是介紹基本的複變數函數的理論。主要的內容包括複數系、解析函數、初等函數、複數積分、解析函數的數列表示、留數理論、保角映射以及 Fourier 和 Laplace 轉換。除了基礎理論,我們也將簡單介紹一些在物理或工程方面的應用。
This course provides the mathematical foundations needed for understanding and working with the modern analysis. The main topics are complex number system, analytic functions, integrations, conformal mappings and some integral transformations. Some applications in physics and engineering will also be included.

課程學習目標 Course Objectives

  • Complex Numbers and Complex Functions
  • Analytic Functions, Harmonic Functions, and Elementary Functions
  • Sequences, Julia and Mandelbrot Sets, and Power Series
  • Complex Integration, Laurent Series, Residue Theory, and Conformal Mapping
  • Applications of harmonic functions, Fourier series, and Laplace transform
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Complex Numbers
    2Complex Functions
    3Analytic and Harmonic Functions
    4Sequences, Julia and Mandelbrot Sets, and Power Series
    5Sequences, Julia and Mandelbrot Sets, and Power Series
    6Elementary Functions
    7Elementary Functions
    8Complex Integration
    9Complex Integration
    10Taylor and Laurent Series
    11Taylor and Laurent Series
    12Residue Theory
    13Residue Theory
    14Conformal Mapping
    15Conformal Mapping
    16Applications of harmonic functions
    17Applications of harmonic functions
    18Fourier series, and Laplace transform
     以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

    有關課程其他調查 Other Surveys of Courses

    1.本課程是否規劃業界教師參與教學或演講? 否
    Is there any industry specialist invited in this course? How many times? No
    2.本課程是否規劃含校外實習(並非參訪)? 否
    Are there any internships involved in the course? How many hours? No
    3.本課程是否可歸認為學術倫理課程?
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
    4.本課程是否屬進入社區實踐課程?
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?

    教師上傳大綱內容
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    Complex Analysis-課程大綱-2018-02.pdf