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 of ordinary differential equations and introduces basic linear partial differential equations and their solutions. The course objectives are
1. Learn the causes and derivation processes of linear equations such as linear transportation equation, heat equation, wave equation, Laplace equation, etc.
2. Learn the theory of Fourier series and apply it to solve the heat equation, Laplace equation, and wave equation.
3. Learn the theory of Fourier transformation and apply it to derive the general solution forms of the heat equation, Laplace equation, and wave equation.
4. Learn the solutions to Dirichlet problems of heat equations and wave equations in plane or space.
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 Homework results |
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% |
