本課程是常微分方程的延伸課程，介紹基本的線性偏微分方程與解法。課程目標是
1. 學習線性運輸方程 （linear transportation equation） ,熱方程 （heat equation）, 波方程 （wave equation）, Laplace 方程等線性方程的緣由，與推導過程。
2. 學習 Fourier 級數的理論，將其應用於解熱方程、Laplace 方程、波方程。
3. 學習 Fourier 轉換的理論，將其應用於導出 熱方程、Laplace 方程、波方程的通解形式。
4. 學習在平面或空間之熱方程、波方程的 Dirichlet 問題的解法。This course is an extension course of ordinary differential equations, introducing basic linear partial differential equations and solutions. The course goal is
1. Learn the origin and deduction process of linear transport equations, heat equations, wave equations, and Laplace equations.
2. Learn the theory of Fourier-level numbers and apply them to solve heat equations, Laplace equations, and wave equations.
3. Learn the theory of Fourier conversion and apply it to the general solution forms of hot equations, Laplace equations, and wave equations.
4. Learn the solution to the Dirichlet problem of heat equations and wave equations in planes or spaces.
1.Artem Novozhilov, Undergraduate Course in Partial Differential Equations,
2. Walter A. Strauss, Partial Differential Equation: An Introduction, 2nd Ed. John Wiley & Son.
1.Artem Novozhilov, Undergraduate Course in Partial Differential Equations,
2. Walter A. Strauss, Partial Differential Equation: An Introduction, 2nd Ed. John Wiley & Son.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 作業成績作業成績 Business achievements |
40 | 每週依教學進度指派習題，繳交後由教師給成績 |
| 考試考試 exam |
40 | 期中考30%、期末考30% |
