課程名稱 |
應用數學專題二 Special Topics on Applied Mathematics (Ⅱ) |
開課學期 |
100-2 |
授課對象 |
理學院 數學系 |
授課教師 |
陳宜良 |
課號 |
MATH7418 |
課程識別碼 |
221 U5770 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二7(14:20~15:10)星期三7,8(14:20~16:20) |
上課地點 |
天數201天數201 |
備註 |
總人數上限:30人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002appl_topic2 |
課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This course is a problem-oriented course. It is designed for those students who are interested
in the interaction of mathematics and science,and plan to do research in this direction. Applied
mathematics is a huge eld and is growing prosperously. In the International Congress of Industrial
and Applied Mathematics 2011 at Vancouver, there are more than 3000 talks covering mathematical
applications raging from material science, biological science, data science to social science.
In this course, I shall focus only on one current research topics, the interface problems. I will
start from basic background, following literature study and computation experiment, then provide
some small research projects.
During this problem-oriented study, you will learn three basic tools in applied mathematics,
namely, mathematical modeling, applied analysis, and computations.
1.1 Interface Problems
Interface problems are those physical problems whose solutions are composed of several components
separated by interfaces. These interfaces could be material interfaces, phase boundaries,
flame fronts,
physical boundaries, etc. Sometimes, they may dynamically move. The interface problems appear
in fluid mechanics, solid mechanics, electrodynamics, material science, biochemistry, etc. They are
of fundamental in science and engineering. In this topics, we shall focus on two subtopics: (i)
fluid-structure interaction, (ii) structure and function of proteins, and (iii) Bose-Einstein condensates.
(i) Fluid-structure interaction
1. Basic fluid mechanics: Stokes flows and Navier-Stokes flows
2. Computation of Stokes flows and Navier-Stokes flows
3. Basic elasticity
4. Allan-Cahn and Cahn-Hilliard models for interfaces
5. Structure of interfaces
6. Geometry and evolution of interfaces: level set method
7. Diffusion interface methods
8. Fluid-structure interaction
9. Surfacants
10. Complex fluids
(ii) Structure and function of proteins.
1. Basic electrostatics
2. Numerical method for Poisson equation
3. Poisson-Boltzmann model for protein in solution
4. Elliptic interface problems
5. Computation of Poisson-Boltzmann equation
6. Poisson-Nerst-Planck models
7. Layer structure
(iii) Bose-Einstein condensates
1. Spin and spin-spin interaction
2. Mean field theory and Gross-Pitaevisky equation
3. Ground states
4. Vortex states |
課程目標 |
During this problem-oriented study, you will learn two subtopics of interface problems and three basic
tools in applied mathematics, namely, mathematical modeling, applied analysis, and computations. |
課程要求 |
Linear Algebra, Introduction to ODE, Introduction to PDEs, Advanced Calculus, Introduction to
Computational Mathematics. Basic matlab or C Language. |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Lecture Note and papers will be provided on the course website. |
參考書目 |
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評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
第1週 |
2/21,2/22 |
An introduction to elasticity |
第2週 |
2/28,2/29 |
incompressible fluid flows and interface problems |
第3週 |
3/06,3/07 |
incompressible fluid flows and interface problems
I am writing a lecture note on fluid mechanics and elasticity. The file is called a.pdf. It is incomplete. I will keep writing and put updated file. |
第4週 |
3/13,3/14 |
guest lecture: music and mathematics, image compression.
The classroom will be in Room 202, astro-math |
第5週 |
3/20,3/21 |
Navier Stokers Equations
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第6週 |
3/27,3/28 |
Navier-Stokers |
第7週 |
4/03,4/04 |
Projection method for N-S. |
第8週 |
4/10,4/11 |
travel to NingBo for a conference |
第9週 |
4/17,4/18 |
Elasticity |
第10週 |
4/24,4/25 |
Membrane |
第11週 |
5/01,5/02 |
Phase Field models |
第12週 |
5/08,5/09 |
Phase field models |
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