中正大學課程大綱
課程名稱(中文)： 微分方程 開課單位： 通訊工程學系(Department of Communications Engineering)
課程名稱(英文) Differential Equations 課程代碼 4302004_01
授課教師： 翁健家 學分數 3
必/選修 必修 開課年級 二年級
先修科目或先備能力：
Calculus 1 and 2, and Linear Algebra
課程概述：
To familiarize students with theories of differential equations and problem-solving techniques.
有預計選修本門課程的同學請務必出席第一堂課，任何事後理由均無法再進行加簽。
課程網頁詳見 https://sites.google.com/view/jjwengatccu/teaching/2025f-de
學習目標：
1. First-Order Differential Equations
2. Mathematical Models
3. Linear Differential Equations of Higher Order
4. Systems of Linear Differential Equations
5. Laplace Transforms
教科書：
Differential Equations with Boundary-Vale Problems, D. G. Zill, 9th Ed., International metric edition, Cengage Learning ISBN : 9781337559881
請尊重智慧財產權，不得非法影印教師指定之教科書籍。

課程大綱 分配時數 核心能力 備註
單元主題 內容綱要 講授 示範 隨堂作業 其他
Introduction to Differential Equations
Definitions and Terminology, Initial-value Problems, Differential Equations as Mathematical Models
 6 1.11.21.32.12.23.13.24.14.24.34.4
First-Order Differential Equations
Solution Curves Without the Solution, Separable Variables, Linear Equations, Solutions by Substitutions, A Numerical Solution
 6 1.11.21.32.12.23.13.24.14.24.34.4
Modeling with First-Order Differential Equations
Linear Equations, Nonlinear Equations, Systems of Linear and Nonlinear Different Equations
 6 1.11.21.32.12.23.13.24.14.24.34.4
Higher-Order Differential Equations
Preliminary Theory of Linear Equations, Reduction of Order, Homogeneous Linear Equations with Constant Coefficients, Undetermined Coefficients, Variation of Parameters, Cauchy-Euler Equation, Solving Systems of Linear
Equations by Elimination, Nonlinear Equations
 6 1.11.21.32.12.23.13.24.14.24.34.4
Modeling with Higher-Order Differential Equations
Linear Equations: Initial –Value Problems, Linear Equations: Boundary-
Value Problems, Nonlinear Equations
 6 1.11.21.32.12.23.13.24.14.24.34.4
Series Solutions of Linear Equations
Solutions About Ordinary Points,
Solutions About Singular Points, Two Special Equations
 6 1.11.21.32.12.23.13.24.14.24.34.4
The Laplace Transform
Definition of the Laplace Transform, Inverse Transform and Transform of Derivatives, Translation Theorems, Additional Operational Properties, Dirac Delta Function, System of Linear Equations
 6 1.11.21.32.12.23.13.24.14.24.34.4
Systems of Linear First-Order Differential Equations
Preliminary Theory, Homogenous Linear System with Constant Coefficients, Variation of Parameters, Matrix Exponential
 6 1.11.21.32.12.23.13.24.14.24.34.4

教育目標
1.傳授學生通訊工程相關知識，配合各種實驗的進行，達到理論與實務相結合之目的。
2.訓練學生具有分析與解決問題的能力。
3.訓練學生良好的溝通技巧，並培養分工合作發揮團隊力量的能力。
4.培養學生瞭解國內外相關產業之現狀與需求，並理解專業倫理及社會責任。

核心能力
1.1.瞭解通訊工程基礎知識。
1.2.培養通訊工程實作能力。
1.3.訓練技術報告寫作與簡報的能力。
2.1.培養分析問題的能力。
2.2.培養善用資源以解決問題的能力。
3.1.培養溝通與表達的能力。
3.2.訓練運用個人專長，與他人合作完成專案計畫。
4.1.瞭解國內外相關產業現況。
4.2.理解工程倫理及社會責任。
4.3.培養良好的資訊能力。
4.4.培養科技英文能力

請尊重智慧財產權，不得非法影印教師指定之教科書籍

教學要點概述：
1. 教材編選(可複選)：自編簡報(ppt)教科書作者提供
2. 教學方法(可複選)：講述板書講述
3. 評量工具(可複選)：上課點名 0%, 隨堂測驗40.00%, 隨堂作業0%, 程式實作0%, 實習報告0%,
                       專案報告0%, 期中考25.00%, 期末考25.00%, 期末報告0%, 其他10.00%,
4. 教學資源：課程網站 教材電子檔供下載 實習網站
5. 教學相關配合事項：

課程目標與教育核心能力相關性        
請勾選：1.11.21.32.12.23.13.24.14.24.34.4
1.1 瞭解通訊工程基礎知識。()
為何有關：
Differential Equations is an important subject for engineering students to understand how to build the mathematical models for physical problems, especially those in electric circuits and control systems. The course offers a fundamental study for time-
domain approaches.
達成指標：
評量工具(可複選)：
1.3 訓練技術報告寫作與簡報的能力。()
為何有關：
The course familiarizes students to verify the mathematical models and practical designs of engineering physical systems by theories and simulations.
達成指標：
評量工具(可複選)：
2.1 培養分析問題的能力。()
為何有關：
Throughout the study students will have capabilities to modeling, analyzing, and resolving physical problems encountered in engineering aspects.
達成指標：
評量工具(可複選)：