教學大綱表 (114學年度 第1學期)
請遵守智慧財產權，勿使用非法影印教科書，避免觸法。
課程名稱
Course Title		 (中文) 工程數學：微分方程
(英文) Engineering Mathematics : Differential Equations 		開課單位
Departments		 電機工程學系
課程代碼
Course No.		 G2020A
授課教師
Instructor		 李清坤
學分數
Credit		 3.0 必/選修
core required/optional		 必修 開課年級
Level		 大二
先修科目或先備能力(Course Pre-requisites)：微積分
課程概述與目標(Course Overview and Goals)：本課程主要是教授學生求解微分方程的方法，並培養學生在物理及工程問題上應用微分方程求解的能力。
教科書(Textbook) Kreyszig, E., Advanced Engineering Mathematics, 10th ed. John Wiley & Sons, Inc., 2011. (代理商：滄海書局)
參考教材(Reference) Peter V. O’neil, Advanced Engineering Mathematics, 6th edition (ISE), Thomson Brooks/Cole, 2007. (代理商：華泰書局)
圖書館電子書(E-book of the Library) Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll, Exploring ODEs.
課程大綱 Syllabus 學生學習目標
Learning Objectives		 單元學習活動
Learning Activities		 學習成效評量
Evaluation		 備註
Notes
序
No.		 單元主題
Unit topic		 內容綱要
Content summary
1 First-order ordinary differential equations (ODEs) 1. Basic Concepts. Modeling
2. Direction Fields, Euler's Method 		Understand basic concepts of ODE
建立微分方程的基本觀念		 講授
 		 
2 First order ordinary differential equations(ODEs) 1 Separable equations
2 Exact differential equations 		1 Separable equations
2 Exact differential equations		 講授
 		作業
 		 
3 First order ordinary differential equations(ODEs) 1 Exact differential equations
2 Integration Factors
3 Linear first ODEs, Bernoulli Equation
4.Existence and Uniqueness of Solutions for Initial Value Problems 		1 Exact differential equations/
2 Integration Factors
3 Linear first ODEs, Bernoulli Equation		 講授
 		作業
 		 
4 Second-Order Linear ODEs 1. Homogeneous Linear ODEs of Second Order
2. Homogeneous Linear ODEs with Constant Coefficients 		1. Homogeneous Linear ODEs of Second Order
2. Homogeneous Linear ODEs with Constant Coefficients		 講授
 		作業
 		 
5 Second-Order Linear ODEs 1. Modeling of Free Oscillations of a Mass–Spring System
2. Euler–Cauchy Equations 		1. Modeling of Free Oscillations of a Mass–Spring System
2. Euler–Cauchy Equations		 講授
 		平時考
 		 
6 Second-Order Linear ODEs 1. Existence and Uniqueness of Solutions. Wronskian
2. Nonhomogeneous ODEs
3. Modeling: Forced Oscillations. Resonance 		1. Existence and Uniqueness of Solutions. Wronskian
2. Nonhomogeneous ODEs
3. Modeling: Forced Oscillations. Resonance		 講授
 		作業
 		 
7 Second-Order Linear ODEs 1. Modeling: Electric Circuits
2. Solution by Variation of Parameters 		1. Modeling: Electric Circuits
2. Solution by Variation of Parameters		 講授
 		作業
 		 
8 期中考 Midterm 筆試 Midterm 課程複習及筆試
Understand first two chapters		 期中考
 		 
9 Higher Order Linear ODEs 1. Homogeneous Linear ODEs
2. Homogeneous Linear ODEs with Constant Coefficients 		1. Homogeneous Linear ODEs
2. Homogeneous Linear ODEs with Constant Coefficients		 講授
 		作業
 		 
10 Higher Order Linear ODEs Nonhomogeneous Linear ODEs Nonhomogeneous Linear ODEs 講授
 		作業
 		 
11 Laplace Transforms 1. Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 講授
 		平時考
 		 
12 Laplace Transforms 1. Laplace Transforms of Derivatives and Integrals. ODEs Laplace Transforms of Derivatives and Integrals. ODEs 講授
 		作業
 		 
13 Laplace Transforms 1. Unit Step Function (Heaviside Function)
2. Second Shifting Theorem (t-Shifting)
3. Short Impulses. Dirac’s Delta Function. Partial Fractions 		1. Unit Step Function (Heaviside Function)
2. Second Shifting Theorem (t-Shifting)
3. Short Impulses. Dirac’s Delta Function. Partial Fractions		 講授
 		作業
 		 
14 Laplace Transforms 1. Convolution. Integral Equations
2. Differentiation and Integration of Transforms. ODEs with Variable Coefficients 		1. Convolution. Integral Equations
2. Differentiation and Integration of Transforms. ODEs with Variable Coefficients		 講授
 		平時考
 		 
15 Laplace Transforms 1. Systems of ODEs
2. Laplace Transform: General Formulas 		1. Systems of ODEs
2. Laplace Transform: General Formulas		  
16 期末考 Final Exam 筆試 Final Exam 課程複習及筆試 期末考
 		 
17 Matlab 1. Basic Matlab.
2. Plotting by using the Matlab. 		自主學習
1. Basic Matlab.
2. Plotting by using Matlab.		 上機實習
 		彈性教學
 		 
18 Better understanding of ODE solutions Better understanding of ODE solutions Better understanding of ODE solutions by using the Matlab. 上機實習
 		作業
彈性教學
 		請於 2026/1/7 前於 Tronclass 繳交自主學習之 final report. Please submit your final report on independent study to Tronclass website by January 7, 2026.  
彈性教學週活動規劃
序
No.		 實施期間
Period		 實施方式
Content		 教學說明
Teaching instructions		 彈性教學評量方式
Evaluation		 備註
Notes
1 起:2025-12-29 迄:2026-01-03 5.小專題 Project 自主學習 1. Basic Matlab 2. Plotting by using the Matlab.
2 起:2026-01-04 迄:2026-01-07 5.小專題 Project Use Matlab for better understanding of ODE solutions Finish the final project. 請於 2026/01/07 前於 Tronclass 繳交自主學習 final report.


教學要點概述：
1.自編教材 Handout by Instructor：
■ 1-1.簡報 Slides
□ 1-2.影音教材 Videos
□ 1-3.教具 Teaching Aids
■ 1-4.教科書 Textbook
□ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

成績考核 Performance Evaluation： 期末考：25%   期中考：25%   彈性教學：10%   平時考：20%   作業：20%  

教學資源(Teaching Resources)：
■ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php