1.藉由師生互動，培養學生正確的學習態度與學習「學習」的方法，並引導學生適應大學生活。

   2.培養學生獨立思考的能力以及激發其主動探索的精神。

   3.學生對數學模式之體用與美的感受

   4.跨領域的感受

科學研究是探索未知知識的建構過程，而數學是科學的語言，隨著電腦的進步，資料大幅度的數位化，科學計算更成為打開非線性科學研究的敲門磚。數學建模、科 學計算、分析詮釋與驗證等過程，更是現今數學科學的典範，此典範被廣泛應用於各類的複雜科學，例如大氣科學、生命科學、防疫學以及人文社會科學等許多領 域。課程內容介紹科學歷史，討論科學與哲學的分野，並介紹數學建模、科學計算、分析詮釋與驗證等科學研究過程，並以一些有趣的例子介紹非線性動力模式，介 紹混沌和蝴蝶效應，並以前述觀點，討論一些有趣的動力系統例子（如愛情模式，歷史模式等），最後就個人學習經驗，分享對生涯規劃看法。
   1. 自然科學發展簡史（光與科學）
   2. 科學與哲學
   3. 科學方法、數學模式與科學研究
   4. 線性與非線性
   5. 數學模式動力系統誰主浮沈（平衡、穩定與相位圖）
   6. 混沌和蝴蝶效應
   7. 問風雨雷霆之故
   8. 氣候與文明
   9. 科學與人生(一些有趣的生物、人文動力系統例子)
 10. 個人學習經驗，與生涯規劃的分享。
       

1. Introduction
2. Linear Algebra
3. Ordinary Differential Equations
4. Vector Analysis
5. Partial Differential Equations

1. Introduction to discrete-time dynamical   systems
2. Limits and derivatives
3. Application of derivatives and dynamical systems
4. Differential equations, integrals, and their applications
5. Analysis of differential equations
6. Probability theory and descriptive statistics
7. Probability models
8. Introduction to statistical reasoning

1-5週 Atmospheric Waves (Chap 7):

1. Basics
2. Acoustic waves
3. Shallow water gravity waves
4. Buoyancy waves
5. Kelvin waves
6. Rossby waves
7. Numerical dispersion

6-9週 Atmospheric instabilities (Chapter 8 and 9):

1. Baroclinic instability
2. Barotropic instability
3. Inertial instability
4. Symmetric instability
5. Conditional instability
6. Kelvin-Helmholtz instability

10週後General Circulation (Chapter 10 and 13):

1. The setup
2. Zonal averaged circulations
3. The angular momentum budget
4. The Lorenz energy cycle
5. Nonacceleration theorem
6. Data assimilation and predictability

1. 高效率計算方法介紹 

2. 大氣數值模式建立

3. 科學觀念之介紹

大致每二週一課題

1. Fundamentals

2. Iteration for nonlinear equations (fixed point iteration, a  scheme of simple moisture physics, convective adjustment)

3. Fast Fourier Transforms

4. Differential methods (finite difference, spectral and finite element methods)

5. Integration method Matrix equation (Gaussian elimination)

6. Poisson equation

7. 1D Linear  and nonlinear advection equations

8. 1D and 2D Shallow water models

9. Interpolation

10. Miscellaneous topics upon request

1. Levi-Civita張量符號

2. 流力方程式組，Hamilton dynamics

3. 準平衡物理

4. 熱力學 (1st and 2nd laws, entropy, enthalpy, and free energy; Legendre transformation)

5. 邊界層動力

6. 渦旋動力

7. 兩維與三維亂流

8. 無因次分析、擾動分析

9. 特徵函數與正模

10. 波譜方法

11. 波動與不穩定

12. 主環流與次環流

13. 其他課題

大致兩週一課題

1. Fundamentals and the ultimate problems

2. Thermodynamics (1st and 2nd laws, entropy, enthalpy, and free energy)

3. Potential vorticity

4. 2D and 3D turbulent flows

5. Vertical normal modes of a continues stratified fluid

6. The f-plane, β-plane, barotropic equations

7. The geostrophic adjustment and large scale dynamics

8. Boundary layer dynamics

9. Large scale ocean circulation

10. Tropical cyclone dynamics

1. 颱風對稱動力
2. 颱風不稱稱動力(最近十年)
      ．螺旋雨帶
      ．颱風眼動
      ．渦旋渦度波動
      ．渦旋交互作用
      ．雙眼牆形成的正壓理論
3. 大尺度、MJO和颱風
4. 垂直風切與颱風
5. 數值模擬

詳細課程介紹與論文清單 (pdf)

颱風與渦旋動力學 (課程綱要、講義與投影片) (pdf)

Earth’s atmosphere and ocean exhibit complex patterns of fluid motion over a wide range of space and time scales. This is a course on the fluid dynamics of the atmosphere and ocean, with emphasis on the concepts and mathematics. Arthur Eddington, the British astrophysicist once remarked, “Never trust an observation without a supporting theory.” The purpose of the course is to provide interpretations (theories) and its supporting mathematics rather than the specific observed phenomena. The course may be useful for people who are interested in understanding the physics, chemistry, and/or biology of Earth’s fluid environment.

   1. Conservation laws and basic equations

   2.  Circulation, vorticity, and potential vorticity

   3.  Normal modes

   4.  Quasi-balanced states and quasi-geostrophic analysis

   5.  Barotropic equations and geostrophic turbulence

   6.  Boundary layer dynamics

   7.  Waves and instabilities---linear perturbation analysis

   8.  The vortex dynamics

   9.  The general circulation dynamics

 10. Numerical modeling and prediction