| 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。 |
| 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 |
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| Written Presentation |
| Quiz |
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| 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
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| 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 |
Numerical methods for differentiations:
(1) Basic difference methods,
(2) Fourier pseudospectral methods |
| Week 7 |
(1)校慶及運動會補假:4/1-4/3
(2) 4/4兒童節、4/5民族掃墓節:4/4-4/5 |
| Week 8 |
Mid term (take home exam, one week) |
| Week 9 |
Numerical Ordinary Differential Equations
(1) Euler’s methods
(2) Explicit Runge-Kutta methods |
| Week 10 |
Numerical Ordinary Differential Equations
(3) Low-storage Runge-Kutta methods
(4) Implicit-Explicit Runge-Kutta methods |
| Week 11 |
Numerical Partial Differential Equations:
Model wave problems (periodic case) |
| Week 12 |
Numerical Partial Differential Equations:
Model wave problems (non-periodic case) |
| Week 13 |
專題討論 1:
Description of the term project:
Wave equations on a ring domain |
| Week 14 |
專題討論 2:
Progress report
Q & A |
| Week 15 |
專題討論 3
Progress report
Q & A |
| Week 16 |
學期專題報告繳與口頭報告 |
| Week 17 |
自主學習：全球大氣計算格式綜述之論文閱讀
論文將於學期處放置在ilearning |
| Week 18 |
自主學習:熵穩定計算格式回顧論文閱讀
論文將於學期處放置在ilearning |
|
| Evaluation |
Homework: 20%
Mid term (take home exam): 40%
Final project report 40% (including oral presentation and written report) |
| Textbook & other References |
參考書目：
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.
|
| Teaching Aids & Teacher's Website |
| 上課講義和筆記將放置於ilearning |
| Office Hours |
Mon, 15:00-16:00
其他時間電郵約定 |
| Sustainable Development Goals, SDGs(Link URL) |
| include experience courses：N |
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