微分方程
Differential Equation
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 微分方程 ED303（光復） | |
3 10:10–11:00 | 微分方程 ED303（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
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.
Linear algebra, Calculus
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期中考(30%),期末考(40%),作業(15%),平時考(15%)
First-order differential equations
1. Introduction 2. Integrals as General and Particular Solutions 3. Separable Equations and Applications 4. Linear First-Order Equations 5. Substitution Methods and Exact Equations
- 講授：
- 6
Linear equations of higher order
1. General solutions of Linear Equations 2. Homogeneous Equations with Constant Coefficients 3. Nonhomogenous Equations and Undetermined Coefficient
- 講授：
- 9
Power series methods
1. Introduction and Review of Power Series 2. Series Solutions Near Ordinary Points 3. Regular Singular Points 4. Method of Frobenius 5. Bessel’s Equations
- 講授：
- 9
Laplace transform methods
1. Laplace Transforms and Inverse Transforms 2. Transformation of Initial Value Problems 3. Translation and Partial Fractions 4. Derivatives, Integrals, and Products of Transforms 5. Periodic and Piecewise Continuous Input Functions 6. Impulse and Delta Functions
- 講授：
- 12
Linear System of Differential Equations
1. First-Order Systems and Applications 2. The Method of Elimination 3. Matrices and Linear Systems 4. The Eigenvalue Method for Homogeneous Systems 5. Second-Order Systems 6. Multiple Eigenvalue Solutions 7. Matrix Exponentials and Linear Systems 8. Nonhomogeneous Linear Systems
- 講授：
- 9
Fourier series methods
1. Periodic Functions and Trigonometric Series 2. General Fourier Series and Convergence 3. Fourier Sine and Cosine Series 4. Heat Conduction and Separation of Variables 5. Vibrating Strings and the One-Dimensional Wave Equation
- 講授：
- 9
| 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 3. Heat Conduction and Separation of Variables 4. Vibrating Strings and the One-Dimensional Wave Equation |
| 第 18 週 | Final exam. |
"Elementary Differential Equations with Boundary Value Problems", C. H. Edwards and D. E. Penney, 6th ed., Pearson (PNIE), 2014 ISBN:9781292025339
- 地點
- ED726
- 時間
- By appointment
- 聯絡方式
- e-mail: francis@nycu.edu.tw