課程資訊
課程名稱
數學物理方程一
Equations of Mathematical Physics (Ⅰ) 
開課學期
108-1 
授課對象
理學院  數學研究所  
授課教師
陳宜良 
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
星期二8(15:30~16:20)星期五8,9(15:30~17:20) 
上課地點
天數304天數304 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081MATH7419_MPEQ 
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
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課程概述

This course is an entry-level course in the applied mathematics program. It provides physical backgrounds for classical equations in mathematical physics, including mechanics of fluids, elasticity, viscoelasticity, and complex fluids. These backgrounds are important for students to study analytical theory or numerical computation for partial differential equations. Derivation of these equations and a brief introduction to the corresponding mathematical theory will be given.
The contents include (1) Gas dynamics: thermodynamics, inviscid Euler equations, Riemann problems (2) Fluid mechanics: potential flows, viscosity, Stokes and Navier-Stokes equations, two-phase flows (3) Elasticity: strain, stress, variational formulation, small strain theory, finite elasticity theory (4) Rheology: visco-elasticity (4) Complex fluids: liquid crystals
 

課程目標
This course provides a physical background for both PDEs, numerical PDEs. 
課程要求
Linear Algebra, Advanced Calculus (Vector Calculus), ODEs and basic PDEs.
 
預期每週課後學習時數
 
Office Hours
每週二 16:40~17:30 
參考書目
– Courant and Hilbert, Supersonic Flows and Shock Waves
– Landau and Lifshitz, Fluid Mechanics
– P. Cialet, Mathematical Elasticity, vol. I.
– Bird, Amstrong and Hassager, Dynamics of Polymeric Liquids, Vol. I 
指定閱讀
I will provide a lecture note. 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
第1週
9/10,9/13  Thermodynamics  
第2週
9/17,9/20  Fluid Mechanics 
第3週
9/24,9/27  Fluid Mechanics 
第4週
10/01,10/04  Vector and Tensor Calculus