응용수학 I
- 고려대학교
- 김준석
페이스북
트위터
카카오톡
네이버밴드
링크복사
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- 주제분류
- 자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
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- 강의학기
- 2011년 2학기
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- 조회수
- 3,650
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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 | |
연관 자료
