課程資訊
課程名稱
數學物理方程一
Equations of Mathematical Physics (Ⅰ) 
開課學期
106-1 
授課對象
理學院  數學研究所  
授課教師
夏俊雄 
課號
MATH7419 
課程識別碼
221 U5780 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期三6,7,8(13:20~16:20) 
上課地點
天數302 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH7419_2017 
課程簡介影片
 
核心能力關聯
本課程尚未建立核心能力關連
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

In this course, we shall explore a few interesting physics phenomena as well as some useful mathematical techniques in differential equations. 1>First, one of the main characteristics we are concerned is the time periodicity. On the one hand, we study different scenarios that give the periodic dynamics. On the other hand, we consider the synchronization problem for the system consisting of many oscillators which have strong coupling relation. This is a universal phenomenon including circadian rhythms, electrical generators, Josephson junction arrays, heart, intestinal muscles, menstrual cycles, and fireflies. We will give a concise account of the recent development of this research direction including the most updated results obtained by my research group. 2> Secondly, we shall introduce some recent results on the regularity issue of the stationary solutions for the linearized Boltzmann equations. Overall, we shall introduce at least three type physics equations : fluid equations, gas dynamics and the Kuramoto oscillator systems.  

課程目標
1> Time periodicity of fluid equations
2>Synchronization problems
3>Regularity of stationary solutions for the linearized Boltzmann equations on convex bounded domain. 
課程要求
We will set up a sequence of homework and assign journal paper readings. Students who take this course should turn in homework and make presentation of their reading assignments. Team work is allowed. 
預期每週課後學習時數
 
Office Hours
另約時間 
參考書目
1> Arkady Pikovsky, Michael Rosenblum, J\"urgen Kurths: Synchronization, a universal concept in nonlinear sciences.
2> Florin Diacu, Philip Holmes: Celestial Encounters
More to be added 
指定閱讀
1. Hemmen & Wreszinski, Lyapunov function for the Kuramoto model of nonlinerly coupled oscillators. Journal of statistical physics, vol 72, Nos. 1/2, 1993.
2. Young-Pil Choi, Seung-Yeal Ha, Sungeun Jung, Yongduck Kim: Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model, Physica D 241, pp 735-754, 2012.
More to be added 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
30% 
 
2. 
Presentation 
40% 
 
3. 
Exam 1 
15% 
 
4. 
Final exam 
15% 
 
 
課程進度
週次
日期
單元主題