| Relevance of Course Objectives and Core Learning Outcomes(%) |
Teaching and Assessment Methods for Course Objectives |
| Course Objectives |
Competency Indicators |
Ratio(%) |
Teaching Methods |
Assessment Methods |
本課程的目標是使同學能將基本的數學知識，如微積分，線性代數，計算機概論，微分方程進行整合，並透過計算機來實現科學問題的求解模式。
The goal of this course is to enable students to integrate fundamental mathematical knowledge, such as calculus, linear algebra, computer fundamentals, and differential equations, and to use computers to implement solution frameworks for scientific problems. |
| 1.Basic Knowledge in Mathematical Sciences |
| 2.Professional Knowledge in Mathematical Analysis |
| 3.Professional Knowledge in Statistical Analysis |
| 4.Professional Knowledge in Scientific Computation |
| 5.Professional Knowledge in Computer Science |
| 6.Theory of Mathematical Analysis, Statistics, and Mechanics |
| 7.Mathematical and Statistical software skills |
| 8.English Language Ability |
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| Networking/Distance Education |
| Exercises |
| Discussion |
| Lecturing |
| topic Discussion/Production |
|
| Written Presentation |
| Quiz |
|
| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
課程說明
Discrete representations and visulations of functions |
| Week 2 |
Root finding by the Newton’s method and its application in waveguide problems
|
| Week 3 |
Approximating functions by their Taylor Polynomials:
Programming in a vectorize way |
| Week 4 |
Numerical methods for integrals:
(1) Mid-point rule
(2) Trapezodal methods,
(3) Simpson’s methods,
(4) Gaussian quadrature methods |
| Week 5 |
Lagrange Interpolating polynomials for functions
(1) non-peridic functions
(2) periodic functions |
| Week 6 |
Mid term |
| Week 7 |
Numerical methods for differentiations:
(1) Basic difference methods,
(2) Fourier pseudospectral methods |
| Week 8 |
Numerical Ordinary Differential Equations
(1) Euler’s methods
(2) Explicit Runge-Kutta methods |
| Week 9 |
Numerical Ordinary Differential Equations
(3) Low-storage Runge-Kutta methods
(4) Implicit-Explicit Runge-Kutta methods |
| Week 10 |
Numerical Partial Differential Equations:
Model wave problems (periodic case) |
| Week 11 |
Numerical Partial Differential Equations:
Model wave problems (non-periodic case) |
| Week 12 |
專題討論 1:
Description of the term project:
Wave equations on a ring domain |
| Week 13 |
專題討論 2:
Progress report
Q & A |
| Week 14 |
專題討論 3
Progress report
Q & A |
| Week 15 |
Final presentations and written reports |
| Week 16 |
Final presentations and written reports |
self-directed
learning |
Paper reading: Journal papers will be upladed to the Ilearning system. |
|
| Evaluation |
Homework: 20%
Mid term: 40%
Final project report 40% (including oral presentation and written report) |
| Textbook & other References |
Title: Time-Dependent Problems and Difference methods
Author(s):Bertil Gustafsson, Heinz-Otto Kreiss, Joseph Oliger
Print ISBN:9780470900567, Online ISBN:9781118548448
DOI:10.1002/9781118548448
Copyright © 2013 John Wiley & Sons, Inc.
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| Teaching Aids & Teacher's Website |
| Lecture notes will be provided in the I-learning system |
| Office Hours |
Mon, 15:00-16:00
Other time: Discusssion by emails and online meeting |
| Sustainable Development Goals, SDGs(Link URL) |
| include experience courses：N |
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