## 基本素養 Basic Literacy

graduates should equip with both the attitude of technological/cultural literacy and the consciousness of information engineering ethics

graduates should equip with appropriate communication skill and global view

## 核心能力 Competence

graduates should equip with the basic capability of the fundamental of professional mathematics and theoretical knowledge in informatics

graduates should equip with the capability of information theory derivation、experiment design and experimental data analysis/induction

graduates should equip with the capability of learning interest development and continuous learning

graduates should equip with the capability to think creatively and independently and to explore, analyze, and solve information-related problems

graduates should equip with the information system ability in designing and verification

graduates should equip with the capability of system integration

graduates should equip with a responsible attitude in working and the capability of effective team-work collaboration

## 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?