微分方程
Differential Equation
學期
113-1
學分
3
學分
當期課號
515004
永久課號
EEEC10002
開課單位
電機系共同課程
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 ED201 | |
3 10:10–11:00 | 微分方程 ED201 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(30%),期末考(40%),平時考(15%),作業(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.Introduction2.Integrals as General and Particular Solutions |
| 第 2 週 | 1. Separable Equations and Applications2. Linear First-Order Equations |
| 第 3 週 | 1. Substitution Methods and Exact Equations2. General solutions of Linear Equations3. Homogeneous Equations with Constant Coefficients |
| 第 4 週 | 1. General solutions of Linear Equations2. Homogeneous Equations with Constant Coefficients3. Nonhomogenous Equations and Undetermined Coefficient |
| 第 5 週 | 1.Nonhomogenous Equations and Undetermined Coefficient |
| 第 6 週 | 1.. Laplace Transforms and Inverse Transforms |
| 第 7 週 | 1. Transformation of Initial Value Problems |
| 第 8 週 | 1.Translation and Partial Fractions,2. Derivatives, Integrals, and Products of Transforms |
| 第 9 週 | Midterm |
| 第 10 週 | 1. Periodic and Piecewise Continuous Input Functions2. Impulse and Delta Functions3. First-Order Systems and Applications |
| 第 11 週 | 1. The Method of Elimination2. Matrices and Linear Systems |
| 第 12 週 | 1. The Eigenvalue Method for Homogeneous Systems2. Second-Order Systems3. Multiple Eigenvalue Solutions |
| 第 13 週 | 1.Matrix Exponentials and Linear Systems2. Nonhomogeneous Linear Systems |
| 第 14 週 | 1.Periodic Functions and Trigonometric Series 2. General Fourier Series and Convergence |
| 第 15 週 | 1.General Fourier Series and Convergence2.Fourier Sine and Cosine Series3. Heat Conduction and Separation of Variables4. Vibrating Strings and the One-Dimensional Wave Equation |
| 第 16 週 | 1. Introduction and Review of Power Series2. Series Solutions Near Ordinary Points |
| 第 17 週 | 1.Regular Singular Points2. Method of Frobenius |
| 第 18 週 | Final exam. |
教科書
"Elementary Differential Equations with Boundary Value Problems", C. H. Edwards and D. E. Penney, 6th ed., Pearson (PNIE), 2014 ISBN:9781292025339
Office Hours
- 地點
- ED726
- 時間
- By appointment
- 聯絡方式
- e-mail: francis@nycu.edu.tw