응용수학 I

고려대학교
김준석

페이스북 트위터 카카오톡 네이버밴드 링크복사

주제분류

자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2011년 2학기

조회수

2,437

In this course, we learn how to apply calculus of variation to derive mathematical models of physical phenomena. We learn regular perturbation method, lubrication approximation, Allen-Cahn, Cahn-Hilliard, Willmore problem, Green’s function, Euler-Lagrange equation, Wulff construction, KdV equation, thin-film equation, and block-coplymer equation.

차시별 강의

1.	Euler-Lagrange equations	Euler-Lagrange equations, Constrained problems
2.	Green’s function	Green function for ODE, MATLAB Code
3.	Sinc function	Sinc function, MATLAB Code
4.	Allen-Cahn equation	Allen-Cahn equation, Applications of Allen-Cahn equation, Previous numerical schemes, New hybrid scheme, Stability and accuracy test, Mean curvature flow
5.	Block-copolymer equation	Variational differentiation (Def), Governing equation, Free enerrgy functional, Simulation of the steady state in 2D/3D
6.	Equations of motion	The equations of motion
7.	Wulff construction	Wulff construction
8.	KdV equation	The KdV equation
9.	Numerical solution for KdV equation	Korteweg-de Vries equation
10.	Thin film equation - I	Derivation of thin film equation
11.	Thin film equation - II	Derivation of thin film equation
12.	Cahn-Hilliard equation	Cahn-Hilliard(CH) equation, Derivation of CH equation
13.	Willmore problem	A Phase-field approach
14.	Regular perturbation method	Regular perturbation, Regular perturbation method, The projectile problem