基本素養 Basic Literacy

畢業生應具備科技人文素養及資訊工程倫理之精神
graduates should equip with both the attitude of technological/cultural literacy and the consciousness of information engineering ethics
畢業生應具備良好溝通技巧及國際觀
graduates should equip with appropriate communication skill and global view

核心能力 Competence

畢業生應具備基礎專業數學及資訊理論知識之基本能力
graduates should equip with the basic capability of the fundamental of professional mathematics and theoretical knowledge in informatics
畢業生應具備資訊理論推導及實驗設計、數據分析歸納之能力
graduates should equip with the capability of information theory derivation、experiment design and experimental data analysis/induction
畢業生應具備培養學習興趣及持續學習之能力
graduates should equip with the capability of learning interest development and continuous learning
畢業生應具備獨立、創新思維及發掘、分析、解決資訊相關問題之能力
graduates should equip with the capability to think creatively and independently and to explore, analyze, and solve information-related problems
畢業生應具備資訊系統設計、測試及驗證之能力
graduates should equip with the information system ability in designing and verification
畢業生應具備資訊系統整合之能力
graduates should equip with the capability of system integration
畢業生應具備負責之工作態度及有效團隊合作之能力
graduates should equip with a responsible attitude in working and the capability of effective team-work collaboration
具備有效溝通表達的專業語文能力

課程概述 Course Description

1. 延續大一微積分基礎,介紹工程問題上,較常使用微分方程式的數學解析方法。 2. 探討如何利用拉普拉斯轉換將微分方程式的數學模式,轉換為代數型式,進而利用四則運算快速求解。 3 探討如何利用於特定點的級數解,分析微分方程式,進而介紹二個特別的數學函數。 4 透過實例介紹讓同學了解描述各類變量關係的一些微分方程式或分析變量關係的一些數學方法。
1.First-Order Differential Equations2.Linear Differential Equations of Second and Higher Order3.Systems of Differential Equations, Phase Plane, Qualitative Methods4.Series Solutions of Differential Equations. Special Functions5.Laplace Transform6.Fourier Series, Integral, and Transforms7.Numerical Methods for Differential Equations8.Differential Equations with MATLAB.

課程學習目標 Course Objectives

  • 了解微分程式
  • 了解Laplace transform
  • 了解 series solution
  • 課程進度 Progress Description

    進度說明 Progress Description
    1First-Order Ordinary Differential Equations (ODEs)
    2Integrating Factors
    3Linear ODEs, Bernoulli Equation
    4Second-Order Linear ODEs, Homogeneous Linear ODEs
    5Homogeneous Linear ODEs with Constant Coefficients
    6Differential Operators, Euler-Cauchy Equations
    7Wronskian, Nonhomogeneous ODEs, Solution by Variation of Parameters
    8Midterm
    9Laplace Transform basic property
    10Laplace Transform of basic functions
    11The first shifting theoremThe second shifting theorem
    12Other special properties of Laplace Transform
    13Ordinary points, Regular singular points, Irregular singular points
    14Taylor series expansion, Frobenius series, Indicial equation,
    15Legendre’s function, Bessel function
    16Periodic and aperiodic function
    17Fourier series and Fourier transform
    18Final examination
     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)?
    Are there any internships involved in the course? How many hours?
    3.本課程是否可歸認為學術倫理課程? 否
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
    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?