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 應用數學科學研究所 |
授課教師 |
陳宜良 |
課號 |
MATH7419 |
課程識別碼 |
221 U5780 |
班次 |
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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 |
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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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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 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
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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.
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預期每週課後學習時數 |
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Office Hours |
每週二 16:40~17:30 |
指定閱讀 |
I will provide a lecture note. |
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 |
評量方式 (僅供參考) |
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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 |
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