微分方程
Differential Equations
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 微分方程 EC122（光復） | |
3 10:10–11:00 | 微分方程 EC122（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
課程概述: 1. First-Order Differential Equations 2. Linear Equations of Second and Higher Order 3. Laplace Transform Method 4. Linear Systems of Differential Equations 5. Power Series Method 6. Fourier Series, Partial Differential Equations, and Boundary Value Problems 課程目標: 1. 使學生能解常微分方程上的題目。 2. 使學生能解偏微分方程上的題目。
1.Must understand Chinese. (I will speak Chinese when I teach this course. If you are an international student, then you should go to the English-version class of this course, unless your Chinese comprehension can catch up with that of a domestic people. I no longer offer Dual-Languages teaching, because it delayed the teaching schedule while there were so many items must be taught.) 2. Must pass both Calculus I and II. That is, differentiation and Integration knowledge will be needed.
無備註
The teacher will teach the methods and examples, then the students will practice from homework assignments.
作業部份: About 5 homework sets 考試部份: One midterm exam One final exam 評量部份: 40% midterm exam, 40% final exam, 20% homework.
Basic methods and Laplace Transform (1-3)
1.First-Order Differential Equations 2. Linear Equations of Second and Higher Order 3. Laplace Transform Method
- 講授：
- 7+9+10 hours for Basic methods;
- 實作：
- Homewrk Explanation 1 hour
- 其他：
- Midterm exam 2 hours
Systems, Power Series methods, and Partial Differential Equations(4-6)
4.Linear Systems of Differential Equations 5.Power Series Method 6. Fourier Series, Partial Differential Equations, and Boundary Value Problems
- 講授：
- 7+7+9 hours for Special methods
- 實作：
- Homework Explanation 1 hour
- 其他：
- Final exam 2 hours
| 週次 | 主題 |
|---|---|
| 第 1 週 | First-Order Differential Equations (Introduction; Separable Equations; Liner Differential Equations) |
| 第 2 週 | First-Order Differential Equations: Bernoulli Equation ; Exact equations |
| 第 3 週 | Integration Factors to reduce to Exact equations. Second-Order Homogeneous Equations (Superposition or Linearity, Initial Value Problem) |
| 第 4 週 | Second-Order Homogeneous Equations with Constant Coefficients. Euler–Cauchy Equation. |
| 第 5 週 | Solution for Higher Order Non-homogeneous ODE by Undetermined Coefficients or by Variations of Parameters. . |
| 第 6 週 | Laplace Transforms. Inverse Transform, Linearity, Shifting; Transforms of Derivatives and Integrals. Differential Equations. |
| 第 7 週 | Unit Step Function, Second Shifting Theorem, Diracs Delta Function. |
| 第 8 週 | Differentiation and Integration of Transforms, Convolution, Integral Equations |
| 第 9 週 | Reviewing Material taught so far. |
| 第 10 週 | Homogeneous Systems with Constant Coefficients (Case of simple eigenvalues). |
| 第 11 週 | Homogeneous Systems with Constant Coefficients. (complex eigenvalues, repeated eigenvalues). |
| 第 12 週 | Non-homogeneous Linear Systems (Method of Undetermined Coefficients; Method of Variation of Parameters.) |
| 第 13 週 | Series Solutions of Differential Equations. Power Series Method, Legendre Polynomials. |
| 第 14 週 | Extended power Series Method (Frobenius Method). Indicial Equation. Orthogonal Functions. |
| 第 15 週 | Fourier Series (I) |
| 第 16 週 | Fourier Series (II) |
| 第 17 週 | Partial Differential Equations (boundary value problems) |
| 第 18 週 | Exam + Conclusion |
C. H. Edwards, Jr. and D. E. Penney, “Elementary Differential Equations with Boundary Value Problems,” 6-th edition, 2008 or 2014, Pearson Prentice Hall.
- 地點
- EC 240
- 時間
- Monday 14:30-16:30
- 聯絡方式
- jclin@cs.nctu.edu.tw