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학과안내

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[학사일정] 2020-2학기 필답시험(전공종합시험) 일정 안내
작성일
2021.01.12
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2020-2학기 필답시험(전공종합시험)이 다음과 같이 있을 예정이오니 응시학생께서는 참고하시기 바랍니다.


필답시험일: 2021.02.04(목) 오전10시~오후12시 (2시간)

가이드라인: 2021.01.18일 공지 예정

시험장소: 첨단관6층 (당일 공지 예정/방역수칙 준수/오프라인시험 실시)



[NPDE Guidelines]

For the Numerical PDE qualifying exam, the following materials will be included, but not limited to.
Also in-class exams can be helpful.

1. . Finite difference methods
- Stability of time stepping

- Stability region in the complex plane

- Runge-Kutta methods

- Crank-Nicolson method

- Stability/consistency and difference formula

- Upwind scheme

- Role of advection vs diffusion in terms of stability

- Concept of inflow/outflow

2. Finite volume methods

- Basic concept


- FVM for advection equations

3. Finite element methods

- Basic concept

- Basic formulation for 1D Poisson

4. FDM vs. FVM vs. FEM vs. DG

- Basic concept and Comparison



[NA Guidelines]

For the Numerical Analysis qualifying exam, the following materials will be included, but not limited to.
Also midterm and final exams can be helpful.

1.  Rootfinding
-  Bisection, Newton, Secant
-  Fixed point iteration

2. Interpolation
- Lagrange, Newton, Hermite
-  Splines

3. Approximation of functions
- Least squares for discrete data
- Orthogonal polynomials
- Least Squares Approximation Problem

4. Numerical integration
- Trapezoidal, Simpson
- Gauss quadrature

5. Numerical ODE
- unique solvability
- Euler, Crank-Nicolson, Runge-Kutta
- Stability, Root condition

6. Linear algebra
- LU, SVD
- Condition number
- Jacobi, Gauss-Seidel, SOR
- Minimization Algorithm: Gradient method, CG