課程名稱 |
應用數學專題二 Special Topics on Applied Mathematics (Ⅱ) |
開課學期 |
101-2 |
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 |
星期五2,3,4(9:10~12:10) |
上課地點 |
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備註 |
上課教室:天數430 總人數上限:10人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012BEC |
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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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.
This course (Special Topics on Applied Mathematics) will focus on Nonlinear
Schr\"odinger Equations and Related Topics, such as Bose-Einstein condensates and Super-conductivities. Mathematical analysis and computational methods will be emphasized.
I will first give some introductory talks including introduction to quantum mechanics, introduction to Bose-Einstein condensates and Superductivity.
Then students will give talks on specific topics including
\I Exact solution of linear Schr\"odinger equations in one dimension.
\I Hydrogen atoms
\I Spins
\I Identical bosons
\I Derivation of Gross-Pitaevskii equation
\I Ground states of the Gross-Pitaevskii equations
\I Dynamics of the Gross-Pitaevskii equations
\I Dimension reduction issues
\I Normalized Gradient Flow method for computing ground states
\I Continuation method for computing ground states
\I Time splitting methods for compuing dynamics of Gross-Pitaevskii equation
\I Error estimates
\I WKB method and Hamilton-Jacobi theory
\I Semi-classical scaling and limits
\I Dipolar BECs
\I Multi-component BECs
\I Spinor BECs
\I Ginzburg-Landau theory for Superconductivity |
課程目標 |
The goal is to lead students to do research on mathematical theory and scientific computing for Bose-Einstein condensates and superconductivity.
During this problem-oriented study, you will learn three basic
tools in applied mathematics, namely, mathematical modeling, applied analysis, and computations. |
課程要求 |
1. This Special Topics on Applied Math II is completely independent of the the course ``Special Course on Applied Math I.
2. The general pre-requisite of such topical course on applied mathematics include:
Linear Algebra, Introduction to ODE, Introduction to PDEs, Advanced Calculus, Introduction to
Computational Mathematics. Basic matlab or C Language. It will be better if you have taken one semester PDE at graduate level, or Real Analysis, or Numerical PDEs. But this is not required. |
預期每週課後學習時數 |
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Office Hours |
備註: Friday afternoon, 2-3 |
指定閱讀 |
Books:
David J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall. (Chapter 1-5)
Review articles:
Weizhu Bao and Yongyong Cai, Mathematical theory and numerical methods for Bose-Einstein condensation, Kinetic and Related Models, Vol. 6, No. 1, March 2013, pp. 1-135.
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參考書目 |
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
presentation |
80% |
The grading is based on participation and the presentation. Each student will give presentation on the topics listed in the course description. The presentation will be a formal one. Students need to present their talks in powerpoint or beamer format.
Details of proofs are required. |
2. |
participation |
20% |
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週次 |
日期 |
單元主題 |
第1週 |
2/22 |
Introduction of the course and basic concept of quantum mechanics. |
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