微分方程
Differential Equation
學期
108-1
學分
3
學分
當期課號
1779
永久課號
UEE2101
開課單位
電機學院與資訊學院共同課程
授課教師
陸曉峰
校區
光復
類別
必修
上課時間表
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 微分方程 ED117 | |
3 10:10–11:00 | 微分方程 ED117 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
In this course we will cover basic properties of differential equations, existence and uniqueness of solutions, general and particular solutions, Laplace and Fourier transform methods, and power series method.
先修科目
Linear algebra, Calculus
評分方式
期中考(35%),期末考(40%),作業(10%),平時考(15%)
課程大綱
- First-order differential equations
- Linear equations of higher order
- Power series methods
- Laplace transform methods
- Linear System of Differential Equations
- Fourier series methods
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1. Introduction 2. Integrals as General and Particular Solutions |
| 第 2 週 | 1. Separable Equations and Applications 2. Linear First-Order Equations |
| 第 3 週 | 1. Substitution Methods and Exact Equations 2. General solutions of Linear Equations 3. Homogeneous Equations with Constant Coefficients |
| 第 4 週 | 1. General solutions of Linear Equations 2. Homogeneous Equations with Constant Coefficients 3. Nonhomogenous Equations and Undetermined Coefficient |
| 第 5 週 | 1. Nonhomogenous Equations and Undetermined Coefficient 2. Introduction and Review of Power Series |
| 第 6 週 | 1. Series Solutions Near Ordinary Points 2. Regular Singular Points |
| 第 7 週 | 1. Regular Singular Points 2. Method of Frobenius |
| 第 8 週 | 1. Method of Frobenius 2. Bessel's Equations |
| 第 9 週 | 1. Midterm exam. 2. Laplace Transforms and Inverse Transforms |
| 第 10 週 | 1. Laplace Transforms and Inverse Transforms 2. Transformation of Initial Value Problems |
| 第 11 週 | 1. Translation and Partial Fractions, 2. Derivatives, Integrals, and Products of Transforms |
| 第 12 週 | 1. Periodic and Piecewise Continuous Input Functions 2. Impulse and Delta Functions 3. First-Order Systems and Applications |
| 第 13 週 | 1. The Method of Elimination 2. Matrices and Linear Systems |
| 第 14 週 | 1. The Eigenvalue Method for Homogeneous Systems 2. Second-Order Systems 3. Multiple Eigenvalue Solutions |
| 第 15 週 | 1. Matrix Exponentials and Linear Systems 2. Nonhomogeneous Linear Systems |
| 第 16 週 | 1. Periodic Functions and Trigonometric Series 2. General Fourier Series and Convergence |
| 第 17 週 | 1. General Fourier Series and Convergence 2. Fourier Sine and Cosine Series |
| 第 18 週 | Final exam. |
教科書
Elementary differential equations with boundary value problem: computing and modeling, 5th edition, 2016, Edwards, Penney and Calvis, Pearson Education
Office Hours
- 地點
- ED726
- 時間
- By appointment
- 聯絡方式
- e-mail: francis@mail.nctu.edu.tw