| 週次 |
授課內容 |
| 第1週 |
課程說明
Discrete representations and visulations of functions |
| 第2週 |
Root finding by the Newton’s method and its application in waveguide problems
|
| 第3週 |
Approximating functions by their Taylor Polynomials:
Programming in a vectorize way |
| 第4週 |
Numerical methods for integrals:
(1) Mid-point rule
(2) Trapezodal methods,
(3) Simpson’s methods,
(4) Gaussian quadrature methods |
| 第5週 |
Lagrange Interpolating polynomials for functions
(1) non-peridic functions
(2) periodic functions |
| 第6週 |
Mid term |
| 第7週 |
Numerical methods for differentiations:
(1) Basic difference methods,
(2) Fourier pseudospectral methods |
| 第8週 |
Numerical Ordinary Differential Equations
(1) Euler’s methods
(2) Explicit Runge-Kutta methods |
| 第9週 |
Numerical Ordinary Differential Equations
(3) Low-storage Runge-Kutta methods
(4) Implicit-Explicit Runge-Kutta methods |
| 第10週 |
Numerical Partial Differential Equations:
Model wave problems (periodic case) |
| 第11週 |
Numerical Partial Differential Equations:
Model wave problems (non-periodic case) |
| 第12週 |
專題討論 1:
Description of the term project:
Wave equations on a ring domain |
| 第13週 |
專題討論 2:
Progress report
Q & A |
| 第14週 |
專題討論 3
Progress report
Q & A |
| 第15週 |
Final presentations and written reports |
| 第16週 |
Final presentations and written reports |
自主學習
內容 |
Paper reading: Journal papers will be upladed to the Ilearning system. |