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

這是一門讓學生學習那些具有實際應用的分析入門課程。課程的內容包括:度量與賦範空間、連續函數、收縮映射定理、拓樸空間、巴拿赫空間、希耳伯特空間、傅立葉級數、(如果時間允許)希耳伯特空間上的有界算子。
The aim of this course is to supply an introduction for students to those parts of analysis that are most useful in applications. The following material will be covered in this one semester course: Metric and Normed Spaces, Continuous Functions, The Contraction Mapping Theorem, Topological Spaces, Banach Spaces, Hilbert Spaces, Fourier Series and (if time permitted) Bounded Linear Operators on Hilbert Spaces.

課程學習目標 Course Objectives

  • Students can learn the fundamentals of analysis.
  • Students learn to use the analysis in applied problems.
  • Students can solve a variety of problems from different fields.
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Ch3
    2Ch3
    3Ch3
    4Ch4
    5Ch4
    6Ch5
    7Ch5
    8Ch5
    9Ch6
    10Ch6
    11Ch8
    12Ch8
    13Ch8
    14Ch9
    15Ch9
    16Ch11
    17Ch11
    18Review
     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?